Numericana Hall of Fame
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Here is a chronological list of notable mathematicians and scientists whose towering
achievements have helped shape the Science of their times and ours.  [ Nominate ]
50-word Biographies   ( © 2003-2017  Gérard P. Michon, Ph.D.)


263  Giants  of  Science
The Entire History of Science at a Glance

 Histogram of top scientists alive throughout History

Ada Lovelace
Agnesi (Maria)
Aryabhata  ( I )
Atiyah (Michael)
Bacon (Roger)
Baire (René)
Bassi (Laura)
Becquerel (H.)
Bell (Jocelyn)
Bell (John)
Bernoulli (D.)
Bernoulli (Jk)
Bernoulli (Jn)
Bohr (Niels)
Broglie (L. de)
Cartan (Elie)
Cartan (Henri)
Cohen (Paul)
Conway (J.H.)
Cornaro (Helen)
Curie (Marie)
Emilie du Ch.
Germain (S.)
Guth (Alan)
Harriot (T.)
't Hooft (Gerard)
Kármán (von)
Leonardo da V.
Lie (Sophus)
Liu Hui
Llull (Ramon)
Lorentz (H.A.)
Mach (Ernst)
Mandelbrot (B.)
Meitner (Lise)
Nash (John)
Neumann (von)
Noether (Emmy)
Pascal (Blaise)
Penrose (Roger)
Planck (Max)
Pointcaré (H.)
Rolle (Michel)
Schwartz (L.)
Tycho Brahe
Van der Waals
Van t'Hoff
Weil (André)
Yang (C.N.)

 Thales of Miletus Thales of Miletus,  engineer   (c. 624-546 BC)

First sage of Greece, he founded  classical geometry  and  natural philosophy.  Alchemists have claimed him as one of their own.  The theorem of Thales  (one of two)  is about two triangles with parallel sides:  The pyramid's shadow is to the pyramid what a man's shadow is to the man  [wow].

Electricity   |   Earliest Mathematics   |   MacTutor   |   Wikipedia   |   Weisstein   |   Facebook Fans

 Anaximander of Miletus Anaximander of Miletus   (610-546 BC)

First Greek scholar to  write  about Nature.  A student and/or friend of  Thales,  he succeeded him as head of his Milesian schoolAnaximander  founded  astronomy  and  cosmology  (cf. apeiron).  He introduced into Greece the gnomon, the sundial and cartographyPythagoras  was one of his pupils.

Philosophers   |   Ancient history   |   IEP   |   Britannica   |   MacTutor   |   Wikipedia   |   NNDB

 The Tetractys

 Pythagoras of Samos Pythagoras of Samos   (c. 569-475 BC)

In Croton, he founded the  mystic  cult of the  Phythagoreans, whose initiated members called themselves  mathematikoi.  They are credited with the first proof of the  Pythagorean Theorem  (itself known to the Chaldeans 1000 years before).  Irrational numbers  distressed them...

Tetractys   |   Constant of Pythagoras   |   MacTutor   |   Weisstein   |   Facebook Fans   |   NNDB

 Heraclitus of EphesusHeraclitus of Ephesus   (c. 535-475 BC)

No man ever steps into the same river twice.
Founder of metaphysics.  Called the  weeping philosopher  (as opposed to Democritus, the laughing philosopher)  Heraclitus argued that all things move and nothing remains still, which led him to a Mach-like  principle of Relativity.

IEP  |  Stanford   |   Wikipedia   |   NNDB

 Parmenides of Elea Parmenides of Elea   (c. 515-450 BC)

Existence is timeless; change is impossible.
Parmenides  upheld the extreme view of static monism.  He spent some time as a member of the Pythagorean community at Croton.  Zeno was his eromenos.  At age 65, Parmenides went to Athens and met a youthful  Socrates  (469-399 BC).

Bibliography   |   IEP  |  Stanford   |   Wikipedia   |   NNDB

 Empedocles of Agrigentum Empedocles of Acragas  (c. 492-432 BC)

Inventor of  rhetoric and borderline charlatan.  His arbitrary explanation of reality with 4 elements (Earth, Air, Fire and Water) and 2 forces (Love and Strife)  dominated Western thought for over two millenia.  Several of his intuitions were correct, though, including the finiteness of the speed of light.

MacTutor  |  Wikipedia  |  IEP  |  Stanford  |  NNDB

 Swift-footed Achilles and the Tortoise

 Zeno of Elea Zeno of Elea  (c. 490-425 BC)

In the most famous of his provocative paradoxes, Zeno asks how  swift-footed Achilles  could overcome a tortoise, since Achilles must first reach the initial position of the tortoise...  By the time he gets there, the animal is elsewhere and Achilles is left with a similar challenge,  ad infinitum.

Tortoise coordinates (GR)  |  Zeno's arrow  |  Quantum Zeno effect  |  MacTutor  |  Wikipedia  |  Stanford  |  Weisstein

 Trisectrix of Hippias

Hippias of Elis   (c. 460 - fl. 399 BC)

sophist  whom  Plato  despised  (he portrays him as vain and arrogant, with a wide but shallow knowledge).  Hippias devised the first transcendental curve,  known as  quadratrix  or  trisectrix  because the  quadrature of the circle  and the  trisection of an angle  would be trivial if its use was allowed.

Quadratrix of Hippias  |  Natural Law  |  MacTutor  |  Wikipedia  |  Britannica

 Democritus of Abdera Democritus of Abdera   (c. 460-370 BC)

The  atomists'  school in Abdera was founded by his teacher  Leucippus,  himself a student of Zeno and a proponent of the law of causality.  Democritus argued that all was made of indivisible  atoms  moving in the void.  One of his followers, the alchemist  Bolus of Mendes,  also signed "Democritus".

Pseudo-Democritus alchemical corpus (still?)  |  MacTutor  |  Wikipedia  |  Stanford  |  Weisstein  |  NNDB  |  video

 Hippocrates of Cos Hippocrates of Cos,  physician   (c. 450-377 BC)

Revolutionary founder of Western medicine.  An  asclepiad,  said to be a direct descendant  (17 or 19 generations)  of the legendary AesclepiusHippocrates  studied philosophy under Democritus and learned rudiments of medicine from his father, Heraclides, and from  Herodicus of Selymbria.

The 4 Humors of Hippocrates   |   Wikipedia   |   IEP   |   NNDB

 Archytas of Tarentum Archytas of Tarentum  (428-347 BC)

A statesman taught by  Philolaus  (student of Pythagoras)  he taught EudoxusArchytas  considered surfaces generated by rotating curves and could double the cube by intersecting three of those  (defining  Archytas' curve  in the process).

Steam-powered flying pigeon   |   Math Men   |   Britannica   |   MacTutor   |   Wikipedia

 Plato Plato   (427-347 BC)

On a land once owned by someone called Akademos,  Plato created the first institution of higher learning, in 387 BC.  His  Academia  lasted 915 years  (Justinian closed it in 529).  Initiation to Geometry was an entrance requirement.  The aim was to teach or discover ideal laws behind appearances.

MacTutor   |   Wikipedia   |   Weisstein   |   NNDB

 Eudoxus of Cnidus Eudoxus of Cnidus  (408-355 BC)

His definition of the comparison between ratios of (possibly irrational) numbers appears in the fifth book of Euclid.  It inspired  Dedekind's  definition of  real numbers  (1872).  Eudoxus invented the  method of exhaustion  built upon by  Archimedes.  He was the first Greek scholar to map the stars.

Geometric series   |   Spheres of Eudoxus by J.L.E Dreyer   |   MacTutor   |   Wikipedia   |   Weisstein   |   NNDB

 Aristotle of Stagira Aristotle of Stagira,  logician   (384-322 BC)

He shunned mathematics entirely in his  natural philosophy  which was lightly based on crude observations.  The lack of discussion of his dogma for two millenia greatly hindered the development of natural Science, especially when some Aristotelian misconceptions became part of Church doctrine.

Classical elements  |  Plenism  |  Aristotelian mechanics  |  MacTutor  |  Wikipedia  |  Stanford  |  Weisstein  |  NNDB

 Euclid of Alexandria Euclid of Alexandria   (c. 325-265 BC)

Father of axiomatic geometry and author of the most enduring textbook in the history of mathematics:  The Elements.  His presentation of the mathematics of his times would become the centerpiece of mathematical teaching for more than 2000 years.

MacTutor   |   Wikipedia   |   Weisstein   |   Facebook Fans   |   NNDB

 Aristarchus of Samos Aristarchus of Samos   (c. 310-230 BC)

Copernicus credited him for the idea that Earth rotates on its own axis and revolves around the Sun.  From rough angular measurements, he estimated the distance to the Sun.  As he couldn't detect the parallax of stars, he declared them to be  extremely  distant  (which Archimedes wouldn't accept).

Head of Aristotle's Peripatic School (c. 287 BC)   |   Britannica   |   MacTutor   |   Wikipedia   |   Weisstein   |   NNDB

 Ctesibius Water-Clock Ctesibius of Alexandria   (c. 310-222 BC)

Starting out as a barber, he became an engineer and founded the school of mathematics at the Library of Alexandria  (he may have served as its first head librarian).  He invented a suction pump, a compressed-air catapult, a water organ and the  regulated  water-clock  (fed by an overflowing vessel).

Ktesibios  |  Antikythera Mechanism (c. 70 BC)  |  Ktesibios Award (MCA, 2000)  |  Britannica  |  Wikipedia

 Archimedes of Syracuse Archimedes of Syracuse   (c. 287-212 BC)

A native and resident of Syracuse, Archimedes studied in Alexandria and maintained relations with Alexandrian scholars.  Although he became famous for designing war machines, this early physicist was, above all, an  outstanding  mathematician.  The 14 Archimedean solids are  uniform.

Lever  |  Spiral  |  Parabola  |  Sand Reckoner  |  "The Method"  |  Historical Tidbits  |  McT  |  WP  |  W  |  FB  |  NNDB

 Eratosthenes Eratosthenes of Cyrene   (276-194 BC)

Eratosthenes  headed the Library of Alexandria after  Apollonius of Rhodes.  In  number theory, he is remembered for the Sieve of Eratosthenes.  He also came up with the first accurate measurement of the circumference of the Earth.

Armillary sphere   |   MacTutor   |   Weisstein   |   NNDB   |   Facebook   |   Carl Sagan (video)   |   NNDB

 Circle of Apollonius Apollonius of Perga   (262-190 BC)

Apollonius  named and studied the conic sections.  He found that a circle consists of all points  M  whose distances to two  foci  (I,J)  are in a fixed ratio  (e.g., 2/3).  He said that planets revolve around the Sun and that the Earth itself might as well be thought of as  moving,  like planets do.

NO PORTRAIT   |   Circles of Apollonius   |   Polarity   |   MacTutor   |   Wikipedia   |   Weisstein   |   FB

 Hipparchus Hipparchus of Nicaea  (c. 190-126 BC)

Hipparch  founded trigonometry  (table of chords, spherical coordinates)  and discovered the precession of the equinoxes (130 BC).  The nova of 134 BC  inspired him to compile a catalog of 1080 stars.  His lunar and solar models were accurate enough to predict eclipses.

Magnitude of Stars   |   Astrolabe   |   MacTutor   |   Wikipedia   |   Weisstein   |   NNDB

 Lucretius Titus Lucretius Carus,  didactic poet  (99-55 BC)

The only extant work of  Lucretius  is the didactic poem  De rerum natura  (On the Nature of Things)  where the basic  Epicurean  tenets are expressed in a surprisingly modern way.  It's especially so about atomism, randomness and free-willRutherford's motto  is a quote from Lucretius.

Epicureanism   |   Three-age system   |   Wikipedia   |   Weisstein   |   NNDB

 Heron of Alexandria Hero of Alexandria,  physicist   (c. AD 10-75)

Influenced by Ctesibius.  Some of his works were meant to be lecture notes:  Pneumatica  (fluids & steamMetrica  (methods and formulas for areas and volumes, lost until 1896)  Mechanica  (statics and simple machines)  Catoptrica  (mirrors).  Hero thought that light-rays came  from  the eyes.

Heron's formula (Metrica, c. AD 50)   |   Britannica   |   MacTutor   |   Wikipedia   |   Weisstein   |   NNDB

 Pliny the Elder Pliny the Elder,  encyclopedist  (AD 23-79)

Gaius Plinius Secundus  was a public official who wrote a lot.  The 37 books of  Historia Naturalis (AD 77)  present, in an anthropocentric way, everything the Romans knew about the natural world.  In this,  Pliny  cites nearly 4000 authors  (his  "Ostanes" need not be the one who cited  Miriam).

Historia Naturalis (Bill Thayer)  =  The Natural History (Bostock & Riley)   |   Wikipedia   |   Weisstein   |   NNDB

 Maria Prophetissa Mary the Jewess,  alchemist  (1st century AD)

Earliest female experimentalist on record  (signing  Miriam the prophetess, sister of Moses).  The  tribikos  still  and the eponymous  balneum Mariae  may be due to her.  F. Hoefer  credits her for  muriatic acid.  The oldest extant alchemical texts  (by Zosimos of Panopolis)  quote her as a past master.

Opus Mulierum  |  Axiom of Maria  |  Chrysopoeia (1964) by Leonora Carrington  |  Jewish encyclopedia  |  Wikipedia

 Pedanius Dioscorides Dioscorides,  pharmacologist   (c. AD 40-90)

Pedanius Dioscorides  was the Greek author of the first major  pharmacopeia  (which never went out of print and remained authoritative for over 1500 years).  The 5 volumes of  De Materia Medica (AD 70)  present about 600 plants.

De Materia Medica   |   Greek Medicine   |   Wikipedia   |   Weisstein

 Menelaus Menelaus of Alexandria  (c. AD 70-135)

A resident of Rome who spent his youth in Alexandria,  he recognized  geodesics  on a curved surface as analog to straight lines on a plane.  Shunning arcs of parallels,  he defined spherical triangles as consisting of arcs of great circles.  This was a turning point in spherical trigonometry.

Sphaerica (c. AD 100)   |   Menelaus' theorem   |   Britannica   |   MacTutor   |   Wikipedia

 Ptolemy Ptolemy of Alexandria  (c. AD 87-165)

Claudius Ptolemaeus  was a Roman  citizen  who wrote in Greek  (his first name may have been  Tiberius).  His  Almagest  dominated astronomy for centuries.  Ptolemy's theorem  says that a tetragon is cyclic  iff  the product of its diagonals is the sum of the pairwise products of facing sides.

Ptolemy's theorem   |   Ptolemy's inequality   |   Almagest  (c. AD 150)   |   McT   |   WP   |   W   |   NNDB

 Galen Galen of Pergamos,  physician   (AD 129-217)

A Roman  citizen  of Greek ethnicity, he started out as physician to the gladiators.  He was so prolific (10 million words) that his surviving works (30%) represent nearly half of the extant literature from ancient Greece.  His thinking dominated medicine for more than a thousand years.

Britannica   |   Wikipedia   |   NNDB   |   IEP

 Alexander's dark band Alexander of Aphrodisias   (c. AD 170-230)

Leading commentator of Aristotle, he revived Aristotelian ideas.  Appointed to an endowed chair in Athens during the co-reign of Septimius Severus and Caracalla (AD 198-209).  He first described the dark band, named after him, between the brignt primary rainbow and the dim secondary rainbow.

Distillation   |   Alexander's dark band (c. AD 200)   |   Stanford   |   Britannica   |   Wikipedia

 Diophantus Diophantus of Alexandria  (c. AD 200-284)

Diophantine problem  is to find an integer satisfying a polynomial equation with integer coefficients,  or several such equations simultaneously.  Diophantus himself never considered irrational numbers or nonpositive ones.  His age at death was reportedly  x = x/6 + x/12 + x/7 + 5 + x/2 + 4.

Problems from Arithmetica  by Tinka Davis (MS Thesis, 2010)   |   Wikipedia   |   MacTutor   |   NNDB

 Liu Hui Liu Hui,  Chinese mathematician  (AD 225-295)

Possibly the best mathematician of ancient China, he was a descendant of Liu Yi, Marquis of Zixiang, and lived in the state of Cao Wei  (one of the feuding Three Kingdoms).  He expanded the Jiuzhang Suanshu with his own commentaries and an appendix which became an official surveying manual.

Commentary (AD 263) added to the Jiuzhang Suanshu   |   Haidao Suanjing   |   Pi   |   WP   |   McT   |   Britannica

 Pappus's Hexagon Theorem Pappus of Alexandria  (c. AD 290-350)

The  theorem of Pappus  (generalized by Pascal in 1639) is a fundamental theorem of  projective geometry.  The name is also used for the two centroid theorems published by Paul Guldin (1577-1643) in  Centrobaryca  (1635)  pertaining to the surface area and the volume of a solid of revolution.

Wikipedia   |   MacTutor   |   Freebase   |   Encyclopedia Britannica

 Hypatia of Alexandria Hypatia,  neoplatonist martyr  (c. AD 360-415)

Daughter of the mathematician  Theon (c. 335-405)  last librarian  of Alexandria, who raised her like a boy.  Her teaching of science was seen as  pagan.  She was ambushed and skinned alive by a mob of Christian fanatics.  Hypathia's murder marks the beginning of the  Dark Ages  in the West.

Wikipedia   |   MacTutor   |   Freebase   |   NNDB

 Aryabhata I Aryabhata the Elder   (AD 476-550)

Aryabhata  ushered Indian science into a  golden age  centered on Kusumapura and Ujjain.  His  Aryabhatiya  (499)  summarized Indian astronomy in  118 verses, 33 of which cover arithmetic, quadratic equations, spherical and planar trigonometry, continued fractions and power series...

Aryabhata satellite (ISRO, 1975)  |  Universität Klagenfurt  |  Britannica  |  Wikipedia  |  MacTutor

 Brahmagupta Bhillamalacarya Brahmagupta Bhillamalacarya  (AD 598-668)

Brahmagupta  (the "teacher from Bhillamal")  was the first to treat  0  like any other number.  Like Diophantus before him, he pioneered the use of symbols in equations.  He failed to specify that his famous formula for the area of a quadrilateral is only valid for  cyclic  quadrilaterals.

Brahmagupta's formula (c. 620)  |  Identity  |  Brahmagupta's theorem  |  Rational quadrilaterals  |  WP  |  McT

 Geber Geber,  experimental chemist  (c. AD 721-815)

Abu Musa Jabir ibn Hayyan al Azdi  was born in Tus (Persia) but the Arabs claim him as one of their own.  Geber (or Jabir) made remarkable scientific advances in practical chemistry but also produced eponymous  gibberish  on occult alchemy.

khemeia   |   retort   |   Wikipedia   |   Jabir   |   Chemical Heritage Foundation   |   al Shindagah

 Al Khwarizmi Al-Khwarizmi,  Algorismus  (c. AD 783, fl.847)

Al-jabr  (transposition from one side of an equation to the other)  is the technique which gave  algebra  its name.  The term is from the title of the masterpiece published around 810 by  Abu Abdallah Muhammed bin Musa al Khwarizmi.

Decimal numeration   |   Quadratic formula   |   Wikipedia   |   MacTutor   |   Weisstein

 Thabit ibn Qurra Al-Sabi Thabit ibn Qurra al-Harrani   (836-901)

Key disciple of the three  Banu Musa  brothers,   he's best known as  Thabit  or  Thebit.  All later editions of Euclid's Elements  were based on his revision.  He was a founder of statics.  He was a  Sabian,  not a Muslim. 

Thabit numbers  3 2n-1   |   Amicable numbers   |   Wikipedia   |   MacTutor

 Abu'l Wafa Mohammad Abu'l-Wafa al-Buzjani  (940-998)

Abu'l-Wafa  was the first to build a wall quadrant to observe the stars.  Whenever possible, he determined quantities by giving a ruler and compass construction for them.  He was an expert in Al-Khwarizmi's "Indian reckoning",  but still wrote out all numbers in arabic letters, for the sake of his audience.

Tangent function   |   (Sphericallaw of sines   |   Trigonometric identities   |   Wikipedia   |   MacTutor

 Al-Karaji Al-Karaji  /  al-Karkhi,  engineer   (953-1029)

Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji  was probably born in Karaj although his alternative name would imply a connection with Karkh, the west part of Baghdad, where he worked most of his life.  He devised the notion of  mathematical induction  and used it on the  binomial triangle.

Inventor of polynomials   |   Sum of cubes   |   Muslim Heritage   |   Britannica   |   Wikipedia   |   MacTutor

 International Year of Light (2015)

 Alhazen Alhazen, "First Scientist"   (965-1039)

Abu Ali Muhammed ibn al-Hasn ibn al-Haytham al-Basri was hired by Al-Hakim and had to feign madness to avoid impossible duties, until the "Mad Caliph" died (1021).  Early proponent of the scientific method, Alhazen pioneered optics and anticipated the first law of  Newton  (who quoted him).

De Aspectibus (1015)   |   Pinhole camera   |   Britannica   |   Wikipedia   |   MacTutor   |   Weisstein

 al-Biruni Abu Rayhan al-Biruni,  Alberonius  (973-1048)

Celebrated polymath who was first exposed to mathematics by associating with Abu Nasr Mansur (970-1036) of sine law fame.  Al-Biruni  pioneered scientific methods in astronomy and geology.  First mathematician to point out the limited validity of Brahmagupta's simplified formula.

Al-Marja   |   Iranica   |   Britannica   |   Wikipedia   |   MacTutor

 Omar Khayyam Omar al-Khayyám   (1048-1131)

The word  Khayyam  means "tentmaker"  (possibly, his father's trade).  His  Rubáiyát  ("quatrains")  were translated in 1859  by FitzGeraldKhayyam  reformed the calendar  of the Seljuq empire  (1079).  He solved  cubic equations  with conic sections, stating that ruler and compass didn't suffice.

Binomial theorem  |  Khayyam-Saccheri quadrilateral  |  Al-Marja  |  Iranica  |  Britannica  |  WP  |  McT  |  W  |  NNDB

 Bháscara-Áchárya,  Bhaskara II   (1114-1185)

Last and greatest mathematician in the Golden Age of Indian mathematics.  He developed trigonometry for its own sake, including spherical trigonometry, and introduced the addition formula:   sin (x+y)   =   sin x  cos y  +  cos x  sin y
He conceived  derivatives  and stated Rolle's theorem.

Siddhanta Shiromani (1150)   |   MacTutor   |   Wikipedia

 Robert Grosseteste

 Robert Grosseteste Robert Grosseteste   (1168-1253)

Educated at Oxford University, of which he became Chancellor in 1215  (until 1221).  Grosseteste  introduced the earliest teaching of the scientific method  in Oxford  (comparing theories with observations).  After holding other ecclesiastical posts, he became Bishop of Lincoln in 1235.

De Luce (1235)   |   Dawn of the Scientific Method   |   MacTutor   |   Wikipedia   |   NNDB

 Leonardo Fibonacci Leonardo Pisano Fibonacci  (1170-1250)

He ended a mathematical lull of eight centuries in the West.  As a teenager in Algeria,  Fibonacci  learned the Hindu-Arabic decimal system that he would advocate in Europe.  In  Liber Abaci  (1202)  he discussed many computational puzzles, including  one  about the Fibonacci sequence...

Hemachandra numbers  (c. 1150)  |  Fibonacci series  |  MacTutor  |  Wikipedia  |  Weisstein  |  Facebook Fans  |  NNDB

 Roger Bacon

 Roger Bacon Roger Bacon,  Franciscan   (1214-1292)

Nicknamed  Doctor Mirabilis.  He went to the University of Paris to take a degree (1241) and he started lecturing on Aristotle there (1234-1247) before returning to Oxford.  Influenced by GrossetesteRoger Bacon  became the most active early proponent of the scientific method in Europe.

The First Scientist: A Life of Roger Bacon   |   Blackpowder (1249)   |   MacTutor   |   Wikipedia   |   NNDB

 Ramon Llull

 Ramon Llull Ramon Llull,  TOSF   (1232-1316)

He was born and raised on the Island of  Mallorca,  off the coast of  Catalonia.  He was brought up in the Royal Court and would become the dominant figure in Medieval  Catalan literature.  In 1272, he conceived of reducing all knowledge to first principles.  His work greatly influenced  Leibniz.

Lull's voting method (1299)  |  Ars Magna (1305-1308)  |  Martyr (1316)  |  Beatified (1857)  |  McT  |  WP  |  NNDB

 William of Ockham William of Ockham,  friar   (c.1288-1348)

Arguably, the foremost Medieval logician.  His enduring contribution to  natural philosophy  is the "principle of parsimony" known as  Occam's Razor  (the simplest explanation compatible with observations is preferred).

MacTutor   |   Wikipedia   |   Weisstein

 Levi ben Gershon Levi ben Gershon,  Gersonides   (1288-1344)

Noted talmudist and philosopher known to the French as  Léon de Bagnols  (Magister Leo Hebraeus). Forefather of Group theory, he studied permutations for their own sake  (1321).  He published the modern proof of the law of sines in 1342.

Jewish Encyclopedia   |   MacTutor   |   Wikipedia

 Jean Buridan Jean Buridan,  secular teacher  (c.1297-1358)

In 1327 and 1340, Joannes Buridanus  was rector of  Paris  where he had studied under Ockham  (whom he condemned in 1340).  Buridan seeded Copernican ideas.  He contributed to probabilities and optics.  His concept of  impetus  (c.1340) anticipated  momentum.  Excommunicated for  nominalism.

Buridanica   |   Britannica   |   New Advent   |   Stanford   |   Wikipedia   |   Weisstein   |   NNDB

 Nicole Oresme bore these arms as
 Bishop of Lisieux, from 1377 to his death.

 Nicole Oresme Nicole Oresme,  bishop   (1323-1382)

Star student of Jean BuridanNicolas Oresme  is credited with the introduction of fractional exponents and the graphing of functions.  He also established the divergence of the harmonic series.  Oresme anticipated analytic geometry, the law of free fall and chemical structures...

MacTutor   |   Wikipedia   |   Weisstein   |   Université de Caen

 Madhava of Sangamagrama Madhava of Sangamagrama   (1350-1425)

Madhava  gave the first examples of  power series  (besides geometric series)  as expansions of trigonometric functions  (sin, cos, arctg).  Madhava's knowledge was perpetuated and expanded by the school he founded in Kerala and  may  have influenced similar developments in the West, much later.

The Story of Mathematics   |   Kerala school   |   Madhava series (c.1400)   |   MacTutor   |   Wikipedia

 Regiomontanus Regiomontanus,  publisher   (1436-1476)

Mathematical prodigy, earliest publisher of printed scientific works.  Johannes Müller von Königsberg  signed  Joannes de Monte Regio.  ( "Regiomontanus"  was coined in 1534,  by  Melanchthon).  Cardano scorned him for publishing Jabir ibn Aflah's spherical trigonometry without proper credit.

De triangulis omnimodis  (1464)   |   Angle maximization problem   |   MacTutor   |   Wikipedia

 Luca Pacioli Luca Pacioli,  Franciscan friar   (1445-1517)

Artist and full professor of mathematics,  Pacioli  invented modern  Venitian  double-entry accounting in 1494.  He shared living quarters in Milan (1494-1499) with  Leonardo da Vinci, who illustrated Pacioli's second masterpiece  "De divina proportione" (with iconic polyhedral frames).

"Summa de Arithmetica" (1494)  |  Father of accounting  |  Unsung hero (video)  |  Wikipedia  |  MacTutor

 Leonardo da Vinci

 Leonardo da Vinci Leonardo da Vinci   (1452-1519)

stellar  Renaissance painter,  he left 13000 pages of illustrated notes on science and engineering  (in mirror-image cursive).  He was taught mathematics by  Luca Pacioli  with whom he lived in Milan, while painting The Last Supper. (c. 1495) and illustrating Pacioli's "De divina proportione".

Anchiano (birthplace)  |  Mona Lisa  |  Codex Leicester  |  Birth of linear perspective (1413)  |  Wikipedia  |  NNDB

 Nicolaus Copernicus 

 Nicolaus Copernicus Nicolaus Copernicus   (1473-1543)

Mikolaj Kopernik  attended Krakow, Bologna, Padua and Ferrara.  Thanks to his uncle, he became a canon at Frauenberg (1497) where he would have an observatory.  Around 1514, he gave an heliocentric explanation to planetary retrograde motion  (published only posthumously).

De revolutionibus (1543)  |  Copernican revolution  |  MacTutor  |  Wikipedia  |  Weisstein  |  Copernicium (2010)

 Coat-of-arms of Paracelsus 

 Paracelsus (1493-1541) 
 Portrait by Quentin Matsys (1466-1529)  Paracelsus,  physician  (1493-1541)

Philippus Aureolus Theophrastus Bombastus von Hohenheim  chose the pseudonym  Paracelsus  in honor of the encyclopedist Celsus.  He is the first systematic botanist.  He named zinc (1526)  and revolutonized medicine (without freeing it from superstition) by using mineral chemicals.

The dose makes the poison  |  Alphabet of the Magi  |  Wikipedia  |  Weisstein  |  NNDB

 Niccolo Tartaglia 
 1499-1557 Niccolò Fontana Tartaglia  (1499-1557)

Son of a mounted postman who was murdered when he was only six.  The nickname  Tartaglia  (stutterer)  came from an infirmity due to the larynx injury he suffered in the Sack of Brescia (Feb. 1512).  He became a military engineer and founded  ballistics  (1531).  Solved the  cubic on 1535-02-13.

Founder of ballistics (1531)  |  Tartaglia triangle  |  MacTutor  |  Wikipedia  |  Weisstein   |   NNDB

 Coat-of-arms of Girolamo Cardano 

 Girolamo Cardano  Girolamo Cardano  (1501-1576)

First scholar to use negative numbers routinely.  In 1545,  he revealed the solution of  cubic  equations obtained by  del Ferro (1465-1526)  in 1516 and rediscovered (1535-02-13) by Tartaglia (1499-1557).  It had been extended to  quartics, in 1540, by his own assistant Lodovico Ferrari (1522-1565).

Founder of probability theory  |  Cardan joint  |  Ars Magna (1545)  |  MacTutor  |  Wikipedia  |  Weisstein   |   NNDB

 Ambroise Pare  Ambroise Paré,  surgeon  (1510-1590)

Ambroise Paré  was a royal military surgeon.  On one occasion on the battlefield, he had to use a makeshift ointment.  He observed that the soldiers so treated recovered much better than those who underwent the formerly "recommended" treatment  (i.e., burning wounds with oil).

Dubious portraits  |  Biography (French)  |  Wikipedia  |  Britannica   |   NNDB

 Andries Wijtinck van Wesele (1514-1564)
 ennobled by Charles V

 Andreas Vesalius  Andries Wijtinck van Wesele  (1514-1564)

Breaking with the precepts of GalenAndreas Vesalius Bruxellensis  revolutionized medicine in 1543 with the first modern book on human anatomy,  based on the detailed observations he made during the dissections that he carried out in front of medical students at the University of Padua.

De humani corporis fabrica (1543)   |   Wikipedia   |   NNDB

 Francois Viette, Francois Viete,
 Franciscus Vieta (1540-1603)

 Franciscus Vieta François Viète  (1540-1603)

His name is also spelled  Viette  (latin:  Franciscus Vieta).  Viète  pioneered modern algebraic notations, where known constants and unknown quantities are represented by letters.  The trigonometric  law of tangents  (c. 1580)  is due to him.  In 1593, he gave an expression of  p  as an infinite product.
 Signature of 
 Franciscus Vieta

Catholic Encyclopedia   |   MacTutor   |   Wikipedia   |   Weisstein

 Tycho Brahe

 Tycho Brahe Tycho Brahe, astronomer   (1546-1601)

Tyge Ottesen Brahe   was from the high Danish nobility.  His Uraniborg observatory, on Hven island, cost 1% of the state budget but allowed precise (naked-eye) observations of planetary positions which made possible the work of Kepler.

MacTutor   |   Wikipedia   |   Weisstein   |   Galileo Project   |   NNDB

 Simon Stevin

 Simon Stevin Simon Stevin,   Stevinus   (1548-1620)

Flemish engineer who introduced  decimal fractions  (1583) shortly after Viète (1579).  Stevin wrote in Dutch and coined many Dutch scientific terms (without the Latin/Greek roots used in other languages).  He found that the pressure exerted by a liquid at rest in a vessel depends only on  depth  (1586).
 Signature of 
 Simon Stevin

De Thiende (1585)  |  Epitaph of Stevinus (1586)  |  McT  |  WP  |  Magic is no Magic


 John Napier John Napier of Merchiston   (1550-1617)

Known as  Neper  to the French,  he invented an  early version  of logarithms which he spent years tabulating.  This improved upon prosthaphaeresis  (multiplication using trigonometry).  Common  (decimal)  logarithms are due to his younger contemporary  Henry Briggs (1561-1630).

History of Logarithms   |   Discovery of Kepler's third law (1618)   |   MacTutor   |   Wikipedia   |   Weisstein

 Thomas Harriot Thomas Harriot   (1560-1621)

Harriot  discovered the law of refraction in July 1601  (years before Snell or Descartes).  He made the first telescopic drawing of the moon (1609-07-26).  and was first to record sunspots  (1610-12-08).  He worked out the Sun's rotation.  His research waned after 1613, as he battled skin cancer.

Virginia (1585-1586)  "Roanoke Colonies"   |   Galileo Project   |   Britannica   |   MacTutor   |   Wikipedia


 Galileo Galilei, 1636
 portrait painted by 
 Justus Sustermans (1597-1681)Galileo Galilei   (1564-1642)

Using his own pulse as a timer, Galileo discovered the pendulum isochronism in 1581.  He found that all bodies fall with the same acceleration and declared mechanical laws valid for all observers in uniform motion.  He made the first telescopic observations of celestial bodies.

The Galileo Project (Rice University)   |   MacTutor   |   Wikipedia   |   Weisstein   |   NNDB


 Johannes Kepler, 1610 Johannes Kepler   (1571-1630)

Kepler's  precise calculations helped establish  heliocentric  astronomy.  In 1609 and 1619, he published his famous  3  laws of planetary motion.  He studied optics, polyhedra, logarithms, etc.  Arguably, he paved the road to  Calculus.

MacTutor   |   Wikipedia   |   Weisstein   |   Facebook Fans   |   NNDB


 William Harvey William Harvey,  physician   (1578-1657)

William Harvey started modern experimental medicine with his discovery of the circulation of the blood.  He had been a student at Padua, where the Flemish anatomist Andreas Vesalius (1514-1564) had started encouraging students to  observe  rather than conform to the precepts of Galen.

Encyclopedia of Science by David Darling   |   Wikipedia   |   NNDB   |   BBC

 Marin Mersenne Marin Mersenne,  Minim friar   (1588-1648)

Of modest origins,  Mersenne attended the newly-created Jesuit college of  La Flèche (1604-1609)  then studied in Paris until July 1611, when he joined the  Order of Minims  (founded in 1436).  He was ordained one year later.  His informal  Academia Parisiensis (1635)  had 140 members.

Cycloid (1615)  |  Father of acoustics (1636)  |  Mersenne primes (1644)  |  MacTutor  |  Wikipedia  |  Weisstein  |  NNDB


 Girard Desargues Gérard Desargues   (1591-1661)

Building on the fundamental results of PappusDesargues  invented  projective geometry  in 1639.  That innovation was largely ignored, except by the likes of Pascal and La Hire, until a key manuscript rediscovered in 1845 was published in 1864, following a remarkable rebirth of the subject.

Desargues graph   |   MacTutor   |   Wikipedia   |   Weisstein

 Albert Girard, le Samielois Albert Girard,  engineer   (1595-1632)

French-born mathematician who took refuge in Holland  (he was a  Calvinist).  Generalizing Viète's formulasGirard  saw the coefficients of  any  monic polynomial as  symmetric functions  of its roots.  In 1629, he foresaw the fundamental theorem of algebra  (proved by Gauss in 1799).

Spherical excess  |  Fibonacci recursion  |  Triangle of extraction  |  Early reciprocity (1632)  |  Galileo  |  McT  |  WP


 Rene Descartes, 1649
 portrait painted by Dutch master
 Frans Hals (c. 1580-1666) René Descartes   (1596-1650)

Descartes attended the famous Jesuit college of  La Flèche from 1607 to 1615.  He met his scientific mentor Isaac Beeckman (1588-1637) in 1618.  He introduced  cartesian geometry  in one of the three appendices to  Discours sur la méthode  (1637).  Proponent of  substance dualism  (1641).
 Signature of 
 Rene Descartes

La Géométrie   |   MacTutor   |   Wikipedia   |   Weisstein   |   Facebook Fans

 Bonaventura Cavalieri Bonaventura Cavalieri,  Jesuit   (1598-1647)

In Pisa, Cavalieri was mentored by Benedetto Castelli (1578-1643) who put him in touch with GalileoCavalieri's principles  can be construed as the preliminary conceptual foundations for  integral calculus,  stating  (in modern terms)  that the integrals of equal functions are equal...

Cavalieri quadrature   |   Galileo   |   Britannica   |   MacTutor   |   Wikipedia   |   Weisstein

 Pierre de Fermat

 Pierre de Fermat Pierre de Fermat   (1601-1665)

Fermat attended Toulouse and Bordeaux,  got a law degree from Orléans and purchased an office at the parlement of Toulouse in 1631.  He pursued investigations in mathematics and physics in his spare time  (his judicial work suffered).

Fermat's Little Theorem  |  Fermat's Last Theorem (& proof thereof)  |  MacTutor  |  Wikipedia  |  Weisstein  |  FB

 Evangelista Torricelli Evangelista Torricelli   (1608-1647)

Orphan.  Assistant to  Castelli,  then Galileo.  Torricelli invented the barometer in 1644:  He figured out that what's above a column of 760 mm of mercury is a near-perfect vacuum  (just rarefied mercury vapor).  What pushes the liquid up the tube is the  (variable)  atmospheric pressure.

Torricelli points  |  Cycloidal arch  |  Trattato del Moto (1640)  |  Succeeded Galileo (1642)  |  McT  |  WP  |  W  |  NNDB

 Infinity Sign

 John Wallis in 1701 John Wallis   (1616-1703)

Appointed to the Savilian Chair of Geometry at Oxford by  Oliver Cromwell  in 1649,  John Wallis  held that position for more than 50 years.  In 1655, he published his great  Arithmetica Infinitorum,  which helped pave the way for the introduction of modern Calculus by Newton and Leibniz.

Infinity symbol  |  Wallis' integral  |  Wallis product, 1655   (Quantum proof, 2015)  |  McT  |  WP  |  W  |  NNDB

 Francesco Maria Grimaldi Francesco Maria Grimaldi   (1618-1663)

The  Jesuit (1632)  who discovered  light diffraction  and named it so.  His  posthumous  book sparked Newton's interest in optics.  Huygens  also owned a copy,  which may have inspired his formulation of  Huygens' principle  in 1678  (which Fresnel only applied to  diffraction patterns  in 1816).

"Physico-mathesis de lumine, coloribus, et iride" (1665)  |  Catholic encyclopedia  |  MacTutor  |  Wikipedia  |  W

 Blaise Pascal

 Blaise Pascal Blaise Pascal   (1623-1662)

At 16, he generalized the theorem of Pappus.  At 19, he built a celebrated mechanical calculator.  In 1647, Pascal thought of using a Torricelli barometer as an  altimeter,  which established experimentally (1648) the origin of atmospheric pressure.  The SI unit of  pressure  (Pa)  is named after him.
 Signature of 
 Blaise Pascal

Pascal's hexagram theorem (1639)  |  MacTutor  |  Wikipedia  |  W  |  FB  |  NNDB

 Christiaan Huygens

 Christiaan Huygens 1671 Christiaan Huygens   (1629-1695)

He improved lensmaking (1654) discovered Titan (1655) described Saturn's rings (1656) invented the pendulum clock (1656) and achromatic eyepieces (1662).  He formulated the centrifugal law (deducing the inverse-square law of gravity) & conservation of momentumWave theory of light (1678).

Spacecraft (2005)  |  Impacts  |  FRS 1663  |  Académie des sciences 1666  |  Tutor of Leibniz 1672  |  McT  |  WP  |  W


 Takakazu Seki Kowa (1642-1708) Takakazu Seki  [Kowa]   (1642-1708)

The Japanese Newton.  Second son of a  Samurai warrior Adopted by a technocrat  (Gorozaemon SEKI )  whose name he took.  Some of  Seki's  discoveries predate their Western counterparts:  Determinants (1683)  Bernoulli numbers, etc.  He taught Katahiro TAKEBE (1664-1739).

Origins   |   Wasan   |   Ellipse circumference (approximation)   |   MacTutor   |   Wikipedia   |   Britannica   |   Springer


 Sir Isaac Newton, 1689
 portrait painted by
 Godfrey Kneller (1646-1723) Sir Isaac Newton   (1643-1727)

Lucasian professor of mathematics in 1669.  FRS in 1672.  Publishes  Principia  in 1687.  Retires from research in 1693.  Warden (1696) then Master (1699) of the Royal Mint.  President of the Royal Society from 1703.  Knighted in 1705.  Proponent of the corpuscular theory of light.
 Signature of 
 Isaac Newton

Dynamics   |   Gravity   |   MacTutor   |   Wikipedia   |   Weisstein   |   FB   |   NNDB


 Elena Cornaro Helen Cornaro,  OblSB   (1646-1684)

Also known as  Lucrezia PiscopiaElena Lucrezia Cornaro-Piscopia  was from the Venetian nobility.  She was an Oblate of the Order of St. Benedict (1665) and a mathematician...  On 25 June 1678,  she became the first woman to be awarded a  doctorate  (from Padua).  54 years before  Laura Bassi.

Cornaro Family (Piscopia Branch)   |   Catholic Encyclopedia   |   Women pholosophers   |   Wikipedia


 Gottfried von Leibniz Gottfried Wilhelm Leibniz   (1646-1716)

A major philosopher and a polymath,  Leibniz  invented differential calculus independently of Newton.  He introduced a consistent notation for integrals and infinitesimals (1675).  Unlike  d'Alembert  or  Cauchy,  Leibniz didn't think of derivatives as limits  (cf. Robinson).
 Signature of 
 G. W. Leigniz

Against Atomism   |   MacTutor   |   Wikipedia   |   Weisstein   |   Facebook Fans

 Michel Rolle Michel Rolle,  autodidact  (1652-1719)

In 1691, he proved a statement of Bháscara:  If a polynomial has equal values at two points, then its  derivative  vanishes somewhere between those points.  The result was generalized beyond polynomials by Cauchy (1823) and it was first called  "Rolle's theorem"  by Drobisch (1834) and Bellavitis (1846).

Born in Ambert  |  Ozanam's puzzle (1682)  |  Cascades (1690)  |  "Gaussian" eliminnation  |  Galileo  |  McT  |  WP  |  W

 Pierre Varignon Pierre Varignon,  jesuit   (1654-1722)

He reformulated statics (1687) and introduced the notion of torque.  With Guillaume de l'Hôpital, he pioneered calculus in France.  First holder of the chair of mathematics at the  Collège des quatre-nations (1688).  Inventor of the manometer (1705).  Varignon rejected divergent series.

Torque   |   Varignon parallelogram   |   Hyperbolic spiral   |   MacTutor   |   Wikipedia   |   Weisstein

 Jacob Bernoulli

 Jacob Bernoulli Jacob [Jacques] Bernoulli   (1655-1705)

Earliest mathematician in a family that would produce many  (but none among his descendants).  With his younger brother JohannJacob  pioneered the  calculus of variations  (which Euler would tackle in 1744).  He found  Bernoulli numbers  (independently of Seki)  and formalized  probability theory.

Law of large numbers  |  Bernoulli numbers  |  Ars Conjectandi  |  McT  |  WP  |  Weisstein

 Jacob Bernoulli

 Johann Bernoulli Johann Bernoulli   (1667-1748)

Father of Daniel and main teacher of  Leonhard Euler.  Initiated by his older brother Jacob, he collaborated with him on early topics in the  calculus of variations. Hired to teach Guillaume de l'Hôpital,  Johann had to name after his student the famous rule he discovered during that work-for-hire.

L'Hôpital's rule  |  Catenary  |  Bracchistochrone (1696)  |  McT  |  WP  |  W  |  NNDB

 Brook Taylor

 Brook Taylor Brook Taylor   (1685-1731)

He invented the  calculus of finite differences  and  integration by parts.  In 1772Lagrange  would place Taylor's theorem  at the  root  of  differential calculus.  In discussing the  stretched string  (1712) Taylor himself stressed the need for functions  lacking  a Taylor expansion!

Taylor expansion (1712)  |  Linear perspective (1715,1719)  |  Britannica  |  MacTutor  |  Wikipedia

 James Stirling

 James Stirling, the Venetian James Stirling,  the Venetian  (1692-1770)

Scottish  mathematician  (FRS, 1726).  In his first publication  Lineae Tertii Ordinis Neutonianae (1717)  he extended to 76 the number of types of planar cubic curves  (Newton had identified 72).  The  Stirling series  is a classic example of a  divergent  asymptotic series.

Methodus differentialis (1730)   |   Britannica   |   MacTutor   |   Wikipedia   |   NNDB

 Pierre Louis Moreau de Maupertuis

 Pierre Louis Moreau de Maupertuis Maupertuis   (1698-1759)

Pierre-Louis Moreau de Maupertuis  used his  principle of least action  (1744)  to reformulate  Newtonian mechanics.  This paved the way for  Lagrangian  and  Hamiltonian  mechanics and provided an elegant key for an historical derivation of  Schrödinger's equation,  published in 1928.

Système de la Nature (1751, anticipating Mendel's genetics)   |   Britannica   |   MacTutor   |   Wikipedia   |   NNDB

 Daniel Bernoulli

 Daniel Bernoulli Daniel Bernoulli   (1700-1782)

The feuding Bernoulli family produced five leading Swiss mathematicians, born in 1655, 1667, 1695, 1700 and 1710.  Pioneer of fluid dynamicsDaniel  formulated  Bernoulli's Law  (the cornerstone of aircraft wing design).  His solution of the St Petersburg paradox helped define  utilities (1731).
 Signature of 
 Daniel Bernoulli

Bessel functions  |  Atomic origin of pressure (1738)  |  McT  |  WP  |  W  |  NNDB


 Benjamin Franklin Benjamin Franklin   (1706-1790)

 Signature of 
 Benjamin Franklin At the same time as Watson  (1746)  Franklin formulated the law of conservation of charge by positing opposite signs for  resinous (-)  and  vitreous (+)  electricity.

A famous quote   |   Bifocals   |   Electric Kite (1752)   |   Gulf Stream   |   MacTutor   |   Wikipedia   |   Weisstein

 Gabrielle-Emilie de Breteuil, 
 marquise du Châtelet

 Emilie du Chatelet Emilie du Châtelet   (1706-1749)

At 19, Gabrielle-Emilie de Breteuil  married the Marquis  Florent-Claude du Chastellet.  She was the lover of Voltaire whom she and her husband protected in their  château.  She was tutored by Maupertuis (1733) and Clairaut (1735).  She popularized the concept of  energy  introduced by  Leibniz.

Breteuil ring in the French West Indies   |   Britannica   |   MacTutor   |   Wikipedia   |   Weisstein


 Leonhard Euler 
 portrait painted by 
 Johann Georg Brucker Leonhard Euler   (1707-1783)

He solved the  Basel Problem  in 1735.  The most prolific mathematician of all times, Euler became totally blind in 1771.  He still produced nearly half of his 866 works after 1766 (in St. Petersburg) with the help of several assistants,  including Nicolaus Fuss (1755-1826) who joined in 1773.
 Signature of 
 Leonhard Euler

The Euler Archive  |  Tercentenary  |  MacTutor  |  WP  |  Weisstein  |  FB

 Laura Bassi 

 Laura Bassi Laura Bassi,  physicist   (1711-1778)

Gabriele Manfredi (1681-1761)  initiated her to higher mathematics and newtonian physics.  In 1732 (at age 21)  Laura Bassi  became the second woman to earn a doctorate and the first to teach at a European university  (Bologna).  She was finally named  professor of physics  there, in 1776.

Stanford (2012-01-04)   |   Tribute   |   MacTutor   |   Wikipedia   |   Mike Rendell

 Alexis Clairaut Alexis Clairaut   (1713-1765)

At age 16, he introduced the study of space curves.  He was the youngest member ever of the Académie des Sciences  (July 1731).  Clairaut's theorem (1740)  says that, provided it's continuous, a partial derivative with respect to several variables doesn't depend on the order of the differentiations.

Home  |  Clairaut's equation (1734)  |  Théorie de la figure de la Terre (1743)  |  Family  |  Statue  |  McT  |  WP  |  W

 Jean le Rond d'Alembert 

 Jean d'Alembert 
 portrait painted by 
 Maurice Quentin de La Tour Jean-le-Rond d'Alembert   (1717-1783)

Editor of the  momentous  Encyclopédie.  Born illegitimately to  Louis Camus des Touches "Canon"  (1668-1726)  and  Claudine de Tencin.  He founded analytical mechanics on a principle of virtual work and solved the wave equation.  He mentored Laplace.  The  d'Alembertian  is a 4D operator.

Remarkable Mathematicians   |   MacTutor   |   Wikipedia   |   Weisstein   |   Rouse Ball   |   FB   |   NNDB

 Maria-Gaetana Agnesi 

 Maria-Gaetana Agnesi Maria-Gaëtana Agnesi   (1718-1799)

Child prodigy and author of the first mathematical book by a woman  (1748).  In 1750, she was appointed to the chair of mathematics at Bologna by Caution sign Pope Benedict XIV  but she never went there  (the first woman to  hold  a chair in Europe was thus  Laura Bassi, in 1776).

Witch of Agnesi (curve)   |   MacTutor   |   Wikipedia   |   1911   |   NNDB

 Jean-Etienne Montucla Jean-Etienne Montucla   (1725-1799)

Etienne Montucla  was a mathematician and an historian.  He authored the first book on the history of mathematics:  Histoire des mathématiques (1758, 1798).  The third volume (1799) was completed and published by Lalande (1732-1807) who also wrote the fourth and final one  (1802).

Rectangle-to-Rectangle Dissection (1778)   |   MacTutor   |   Wikipedia   |   1911   |   Weisstein

 Jean-Henri Lambert Johann Heinrich Lambert   (1728-1777)

Johann Heinrich Lambert  (French:  Jean-Henri Lambert)  was born in Mulhouse, which was then in Switzerland  (it's now in France). 

Lambert's W function (1758)   |   Proof that p is irrational   |   MacTutor   |   Wikipedia   |   Weisstein   |   NNDB

 Etienne Bezout Etienne Bézout,  algebraist   (1730-1783)

His 6-volume mathematical textbook (1770-1782) was once standard for students wishing to enter  Polytechnique  (this was also used at Harvard for calculus).  His theory (1779) of algebraic equations led to  algebraic geometryBézout's little theorem  says  (x-a)  divides the polynomial  P(x)-P(a).

Ph.D. 1756  |  Bézout's lemma  |  Bézout's theorem  |  Bézout Domain  |  Bézoutian  |  MacTutor  |  Wikipedia

 Henry Cavendish 

 Lord Henry Cavendish Henry Cavendish,  FRS   (1731-1810)

Retro-diagnosed with Asperger's syndrome,  absent-minded and pathologically shy, he could not  talk  to women at all.  In 1766,  Cavendish  discovered what Lavoisier  would call  hydrogen.  In 1798, he measured Newton's  Universal constant of gravity  (G) to an accuracy of 1%.

Torsion balance of John Michell (1724-1793)   |   Wikipedia   |   Weisstein   |   Video (Roger Bowley)   |   NNDB

 Joseph Louis Lagrange 

 Joseph Louis Lagrange Joseph Louis Lagrange   (1736-1813)

In 1760, Lagrange tackled the calculus of variations (named by Euler in 1766).  He applied it to analytical mechanics and invented Lagrange multipliers (1788).  He gave accurate secular variations of solar orbits (1782).  Lagrange was the first  professor of analysis  at  Polytechnique  (1794-1799).

Lagrange-Bürmann   |   Remarkable Mathematicians (pdf)   |   MacTutor   |   Wikipedia   |   Weisstein   |   FB   |   NNDB

 Antoine-Laurent de Lavoisier 

 Antoine Lavoisier Antoine-Laurent de Lavoisier (1743-1794)

Antoine Lavoisier  founded quantitative chemistry by establishing that mass is conserved in any chemical transformation.  He was infamously executed during the French Revolution because of his rôle as a tax collector.
 Signature of 
 Antoine-Laurent de Lavoisier

Chemical Heritage Foundation  |  Wikipedia  |  Weisstein  |  Video Bio  |  NNDB

 Nicolas de Condorcet 

 Nicolas de Condorcet Nicolas de Condorcet  (1743-1794)

Marie, Jean, Antoine, Nicolas de Caritat, Marquis de Condorcet  founded  Social Choice Theory  in 1785 with his  Essay on the Application of Analysis to the Probability of Majority Decisions  (introducing  Condorcet's paradox).  He was a moderate leader during the French revolution.

Condorcet's paradox  |  (Conform) Condorcet method  |  Wikipedia  |  Weisstein  |  MacTutor  |  NNDB

 Alessandro Volta 

 Alessandro Volta Alessandro Volta   (1745-1827)

Correctly interpreting the 1791 observation by Luigi Galvani (1737-1798) of muscle contractions in a dead frog,  Volta  reasoned that electricty is generated upon contact of two different metals.  Replacing living tissue by paper soaked with saline electrolyte, he built the first  battery  in 1799.

(Misleading) Google Doodle  |  Electrochemistry  |  Britannica  |  Wikipedia  |  Weisstein  |  NNDB

 Gaspard Monge 

 Gaspard Monge Gaspard Monge   (1746-1818)

In 1768, he succeeded his mentor Charles Bossut to the chair of mathematics at the Ecole de Mézières.  Monge would use that school as a model for  Ecole Polytechnique,  founded in 1794 with himself as Director and instructor in  descriptive geometry  (the drafting technique he had devised in 1765).

Brouette de Monge (optimal transport)  |  Lines of curvature 1776  |  Disphenoids 1809  |  McT  |  WP  |  W

 Pierre-Simon Laplace 

 Pierre Simon Laplace Pierre Simon Laplace   (1749-1827)

Initiated to mathematics, in Caen, by  Christophe Gadbled  and  Pierre Le CanuLaplace  was mentored by d'Alembert  (in Paris)  and became one of the most influential scientists ever  (Laplacian, Laplace transform).  With Lavoisier,  he proved  respiration  to be a form of  combustion  (1783).  Signature of 
 Pierre-Simon Laplace

Taupe Laplace (Caen)  |  |  McT  |  WP  |  W  |  FB  |  NNDB

 Edward Jenner Edward Jenner,  immunologist   (1749-1823)

Before Jenner,  risky  variolation  and other inocculations were  believed  to induce immunity to dangerous diseases  (20% of human deaths were due to smallpox).  Putting some human lives at risk, Jenner proved that innoculation with harmless  cowpox  did protect against the dreaded  smallpox.  Signature of 
 Edward Jenner

Vaccination (1796)   |   BBC   |   Wikipedia   |   NNDB

 Adrien-Marie Legendre

 Adrien-Marie Legendre, 1752-1833 
 by Julien-Leopold Boilly (1820) Adrien-Marie Legendre   (1752-1833)

Legendre was one of the greatest contributors to the mathematics of his times.  Many concepts are named after him.  At left is what seems to be his only extant portrait  (it was found among 73 caricatures of members of the French academy of Sciences).
 Signature of 
 Adrien-Marie Legendre

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 Jean-Baptiste Meusnier Jean-Baptiste Meusnier  (1754-1793)

In 1776,  under  Monge,  Meusnier read to the  Académie  two papers about surface curvature and the  helicoid  (both published in 1785).  With  Lavoisier, he mass-produced hydrogen by oxydizing 600°C iron with water vapor  (1777).  Meusnier fought as a general and died in battle near Mainz.

bio  |  |  Meusnier's theorem  |  Mean curvature  |  Meusnier's dirigible (1784)  |  Wikipedia

 Niepce de Saint-Victor

 Nicéphore Niepce Nicéphore Niépce,  engineer  (1765-1833)

Joseph Nicéphore Niépce  invented photography  (1826).  He built the first internal combustion engine  (Pyréolophore, 1807)  with his brother Claude (1763-1828).  His cousin Abel Niépce de Saint-Victor (1805-1870)  photographed radioactivity in 1857  (39 years before Henri Becquerel did).

bio  |  Partnered with Louis Daguerre (1787-1851) in 1829  |  Niépce House  |  WP  |  Photo  |  Film  |  NNDB

 Joseph Fourier, 1768-1830

 Jean-Baptiste Joseph Fourier Joseph Fourier  (1768-1830)

In January 1795,  Jean-Baptiste Joseph Fourier  was the star trainee in the new  Ecole normale de l'an III  (the forerunner of ENS)  simultaneously  teaching  at  Polytechnique.  He is the founder of  Harmonic Analysis  (cf. Fourier transform).
 Signature of Joseph Fourier

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 Thomas Young Thomas Young,  polymath   (1773-1829)

Notorious for his two-slit experiment demonstrating the wavelike nature of light (1802)  and for Young's modulus of elasticity (1807).  Young's rule  gives the posology for an n-year old child as  n/(n+12)  of the adult dose.  Young paved the way for the decoding of hieroglyphics by  Champollion.

MD 1795? (Edinburgh)  |  Ph.D. 1796 (Göttingen)  |  Young's equation  |  Young-Dupré equation (1805)  |  WP  |  W

 Andre-Marie Ampere Andre-Marie Ampère   (1775-1836)

Appointed professor of mathematics at  Polytechnique in 1809.  In september 1820, he discovered that like currents attract each other whereas opposite currents repel.  The effect is now used to define the SI unit of current, which is named after him.
 Signature of 
 Andre Ampere

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 Sophie Germain

 Sophie Germain Sophie Germain   (1776-1831)

At 13, the story of the death of Archimedes inspired her to become a mathematician.  She was 18 when  Polytechnique  opened  (it was male-only until 1972)  and made available  Lagrange's lecture notes.  This gave her a start to correspond with him and others  (signing  Monsieur LeBlanc  at first).
 Signature of 
 Sophie Germain

Father  |  Chladni patterns  |  Safe primes  |  Mean curvature  |  McT  |  WP  |  W

 Carl F. 

 Carl Friedrich Gauss, 1840 
 portrait by the Danish painter
 Christian Albrecht Jensen (1792-1870) 
 for the Pulkovo observatoryCarl Friedrich Gauss   (1777-1855)

At the age of 7, the  Prince of Mathematics  found instantly the sum (5050) of all integers from 1 to 100  (as the sum of 50 pairs, each adding up to 101).  At age 19, his breakthrough about constructible polygons helped him choose a mathematical career.
 Signature of 
 C. F. Gauss

Quadratic reciprocity  |  MacTutor  |  Wikipedia  |  Weisstein  |  Facebook  |  NNDB

 Simeon Poisson

 Simeon Denis Poisson Siméon Poisson   (1781-1840; X1798)

Among his many mathematical contributions is a very abstract construct in  analytical mechanics  (Poisson Brackets, 1809)  which helped Dirac  Ecole Polytechnique (X) formulate a precise correspondence between classical and quantum mechanics  (Sunday, Sept. 20, 1925).

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 Francois Jean Dominique Arago François Arago   (1786-1853; X1803)

He taught analysis and geometry at Polytechnique from 1810 to 1830, at the peak of his creativity  (electromagnet, 1820).  A popular left-wing deputy elected in 1830, Arago became Minister of Marine and War in 1948 and was instrumental in abolishing slavery in the French Colonies (1848).  Ecole Polytechnique (X)
 Signature of 
 Francois Arago

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 Joseph von Fraunhofer Joseph von Fraunhofer  (1787-1826)

In 1814, his observation of the Sun's dark-line spectrum  (Fraunhofer lines)  marked the beginning of  astrophysics.  Fraunhofer is also remembered for related studies of diffraction in optical systems with small Fresnel numbers  (Fraunhofer diffraction).  Knighted in 1824  (Bavaria).

Spectroscope (1814)   |   Diffraction grating (1821)   |   Fraunhofer diffraction  (equation)   |   Weisstein   |   Wikipedia


 Augustin Fresnel Augustin Fresnel   (1788-1827; X1804)

Trained in Caen (1801-1804) then at  Polytechnique.  Poor physicist at first...  In 1821, Augustin Fresnel  established  (with Arago)  that light is a transverse wave  Ecole Polytechnique (X) whose two polarizations  don't  interfere with each other.  He invented Fresnel lenses for use in lighthouses.

Equations (1821)  |  2015 Celebrations  |  Born in Broglie, raised in Mathieu  |  Thomass  |  W  |  McT  |  WP  |  NNDB

 Jean-Victor Poncelet Jean-Victor Poncelet   (1788-1867; X1807)

POW in Russia for 15 months  (1812-1814)  he brought back from Saratov the 7 notebooks in which he had invented modern  projective geometry Ecole Polytechnique (X) Promoted to Colonel in 1845 and General in 1848,  Poncelet  headed  Polytechnique  from 1848 to 1850.

Cyclic points   |   Euler's circle   |   Porism   |   Unit  (980.665 W)   |   Britannica   |   Weisstein  |  MacTutor  |  Wikipedia


 Louis Augustin Cauchy Augustin Cauchy   (1789-1857; X1805)

A devout royalist,  Cauchy  wrote 789 papers in all areas of the mathematics and theoretical physics of his time.  In 1821, his  Cours d'analyse  at Polytechnique  Ecole Polytechnique (X) made analysis rigorous.  He originated the calculus of residues (1826) and complex analysis (1829).

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 Moebius strip

 August Moebius August Möbius   (1790-1868)

Like his mentor Karl Mollweide, he was both an astronomer and a mathematician.  He invented homogeneous coordinates (1827)  and gave his name to many concepts:  Möbius planeMöbius groupMöbius functioninversion formula, etc.  He established angles as  signed  quantities.

Ph.D. 1815  |  Möbius strip (1858; simultaneous discovery by Listing)  |  McT  |  WP  |  W  |  NNDB  |  Superb VIDEO

 Michael Faraday Michael Faraday   (1791-1867)

In 1831,  Faraday  discovered the  Law of Electromagnetic Induction, which made the electric era possible.  He is widely regarded as one of the greatest experimentalists who ever lived.  Yet, he had little or no grasp of higher mathematics.
 Signature of 
 Michael Faraday

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 Charles Babbage Charles Babbage   (1791-1871)

He was Lucasian Professor (1828-1839) at Cambridge but never taught.  He designed two computing machines:  The  Difference Engine  (funded in 1822)  was never completed.  The more advanced  Analytical Engine  would have been the first true computer  (Ada Lovelace wrote programs for it).
 Signature of 
 Charles Babbage

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 Gustave Gaspard 
 de Coriolis

 Gaspard Gustave de Coriolis Gaspard de Coriolis   (1792-1843; X1808)

He gave the terms   Ecole Polytechnique (X) work  (travail)  and  kinetic energy  their precise mechanical meanings.  At  Ponts-et-Chaussées  since 1832,  Coriolis inherited the chair of Mechanics there, in 1836, upon the death of Navier, and became director of studies at  Polytechnique.

Coriolis effect   |   Coriolis acceleration   |   Billiards (1835)   |   Britannica   |   McT   |   WP   |   W   |   NNDB

 Michel Chasles Michel Chasles   (1793-1880; X1812)

Professeur of geodesy at  Polytechnique from 1841 to 1851, he inaugurated the  Sorbonne  chair of projective geometry, then called  higher geometry  (1846-1867).  His reputation as a science historian was all but ruined when he bought forged manuscripts  (1861-1869)  from Denis Vrain-Lucas.  Ecole Polytechnique (X)

Ph.D. 1814   |   Chasles' theorem   |   Britannica   |   McT   |   WP   |   Weisstein  

 Jakob Steiner Jakob Steiner,  Swiss geometer   (1796-1863)

In his first published paper (1826) he devised geometrical inversion  (paving the way for homographic transforms)  which embodies  duality  for  polyhedra, convexes, etc.  He contributed to the rebirth of  projective geometry in the first half of the eighteenth century.  Roman surface (1844).

Ph.D. 1821  |  Power (1826)  |  Constructions (1833)  |  Systems (1853)  |  Points  |  Britannica  |  McT  |  WP  |  W  

 Julius Pluecker Julius Plücker,  scientist   (1801-1868)

In 1858, using the handiwork of Heinrich Geissler (1814-1879) he paved the way for the invention of the CRT  (by Crookes, c. 1875).  He was the doctoral advisor of Klein.  In 1866. Plücker received the Copley Medal for his work in analytical geometry, magnetism and spectral analysis.

Ph.D. 1823  |  Homogeneous coordinates (1828)  |  McT  |  WP  |  Britannica  |  W  |  NNDB


 Niels Henrik Abel Niels Henrik Abel   (1802-1829)

Niels Abel  produced many brilliant results during a short life spent in poverty:  Non-solvability of quintic equations by radicals, double periodicity of the elliptic functions, etc.  An offer for his first professorship  (at Berlin)  arrived  two days  after he had succombed to tuberculosis.
 Signature of 
 Niels H. Abel

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 Carl Jacobi Carl Gustav Jacob Jacobi   (1804-1851)

An inspiring teacher, he was an outstanding and prolific creator of mathematics who has been likened to Euler.  He introduced    and  Jacobians  in 1841.  Jacobi  admired  Poisson brackets  and proved that they satisfy what's now called Jacobi's identity.

Ph.D. 1825   |   MacTutor   |   Wikipedia   |   Weisstein   |   Facebook Fans   |   NNDB

 Johann Dirichlet Peter Gustav Lejeune Dirichlet   (1805-1859)

Johann Peter Gustav Lejeune-Dirichlet.  signed  Gustav Lejeune Dirichlet, (no hyphen)  published as  P.G.L. Dirichlet  and was quoted as  Lejeune-Dirichlet.  He contributed to number theory, mechanics and analysis.  He was the first to consider unrestricted functions.

h.c. 1827  |  Theorems  |  D-branes  |  DE  |  Life and Work (pdf)  |  MacTutor  |  Wikipedia  |  Weisstein  |  FB

 William Rowan Hamilton Sir William Rowan Hamilton   (1805-1865)

A calculating prodigy who lost to Zerah Colburn at age 8,  Hamilton started to teach himself higher mathematics at 13.  In 1833, he devised a version of  rational mechanics (based on   conjugate momenta)  which would help clarify quantum mechanics later.  He invented quaternions in 1843.
 Signature of 
 William R. Hamilton

DIT 2005   |   MacTutor   |   Weisstein   |   Facebook   |   NNDB


 Charles Darwin at age 31 
 Portrait by George Richmond (1840) Charles Robert Darwin   (1809-1882)

Against strong religious animosity  (which lasts to this day in the US)  Darwin established that the mechanism of  natural selection  was powerful enough to explain the evolution of the humblest ancient lifeforms into the most advanced modern ones, featuring very sophisticated organs.

The Origin of Species by Means of Natural Selection (1859)   |   Wikipedia   |   Facebook   |   NNDB

 Joseph Liouville Joseph Liouville   (1809-1882; X1825)

Many of Liouville's 400+ papers include key contributions, like his conservation of Hamiltonian phase-measure.  In 1836, he founded the   Ecole Polytechnique (X) Journal de mathématiques pures et appliquées  and promoted the work of others, including the late  Evariste Galois.

MacTutor   |   Wikipedia   |   Weisstein

 Hermann Grassmann Hermann Grassmann   (1809-1877)

Around 1832, he pioneered the modern approach to vectors and went on to invent  exterior algebra  (the correct basis for Cartan's differential forms and/or  Bourbaki's "Stokes' theorem").  Grassmann had little mathematical influence during his own lifetime  (he became successful as a linguist).

Older brother of Robert Grassmann   |   Ph.D. 1840   |   Grassmann's formula   |   MacTutor   |   Wikipedia   |   Weisstein

 Eduard Kummer Ernst Eduard Kummer   (1810-1893)

Eduard Kummer  was Kronecker's inspirational high-school teacher.  He had  55  doctoral students, including Frobenius and Hermann Schwarz  (his son-in-law).  He proved  FLT  for all  regular primes  and invented the  ideal numbers  which prompted Dedekind to build the theory of  ideals.

Ph.D. 1831   |   Kummer transformations   |   Gauss-Kummer series   |   MacTutor   |   Wikipedia   |   Weisstein

 Evariste Galois Evariste Galois  (1811-1832)

Galois theory is about symmetries  of polynomials on fields.  Galois "didn't have time" to extend that to transcendental functions  (nobody else has done so).  He died in a stupid duel at the age of 20 and his fundamental work might have been lost if Liouville hadn't revived it in 1843.
 Signature of 
 Evariste Galois

Numericana  |  Archives  |  Galois theory  |  MacTutor  |  Wikipedia  |  Weisstein  |  FB

 Ludwig Schlaefli Ludwig Schläfli,  Swiss geometer   (1814-1895)

He introduced the notion of higher-dimensional  vectors  (between 1850 and 1852, full treatise published in 1901).  He pioneered multi-dimensional Riemannian manifolds by considering the 3D-hypersurface of a  4D-hypersphereSchläfli  also classified  all  regular polytopes.

Ph.D. 1860   |   4th dimension (video)   |   Schläfli symbols   |   Schläfli integral (1871)   |   McT   |   WP

 Ecole Polytechnique (X)

 Eugene Catalan Eugène Catalan   (1814-1894; X1833)

In 1838, he founded the preparatory school at  Sainte-Barbe  with Sturm and Liouville.  His left-wing activism damaged his academic career.  He was elected to the  French National AssemblyCatalan's conjecture (1843)  saying that the only solution of  1+x= yn  is  1+2= 32,  was proved in 2002.

Helicoid  |  Catalan surfaces  |  Catalan numbers  |  Catalan solids  |  Catalan constant  |  Identity  |  McT  |  WP  |  W

 J.J. Sylvester James J. Sylvester  (1814-1897)

Sylvester  made fundamental contributions to matrix theory, invariants, number theory, partitions and combinatorics.  He inaugurated the chair of mathematics at Johns Hopkins (1877-1883) and founded the  American Journal of Mathematics (1878).  Then, he became Savilian Professor.

Ph.D. 1841 (Dublin)  |  Discriminant (1851)  |  "Law of Inertia" (1852)  |  MacTutor  |  Wikipedia  |  Weisstein  |  NNDB

 Karl Weierstrass Karl Weierstrass,  analyst   (1815-1897)

The  father of analysis  spent 15 years teaching secondary school before one paper earned him an honorary doctorate and a professorship.  He gave the rigorous metric definition of limits and invented the concept of analytic continuation.

Hon. Dr. 1854  |  MacTutor  |  Wikipedia  |  Weisstein  |  Facebook Fans

 George Boole George Boole,  logician  (1815-1864)

Boole shares credit with Augustus De Morgan (1806-1871)  (author of  Formal Logic,  1847)  for  Boolean logic,  now a fundamental ingredient in  digital electronics.  He also published about differential equations.  His wife Mary (niece of G. Everest) and daughter Alicia were mathematicians too.

Mathematical Analysis of Logic (1847)  |  Laws of Thought (1854)  |  MacTutor  |  Wikipedia  |  Weisstein  |  NNDB

 Byron arms

 Lady Lovelace Ada Byron, Lady Lovelace  (1815-1852)

Daughter and heiress of  Lord Byron  (the poet)  whom she never knew.  Ada  was introduced by  Mary Somerville  to  Charles Babbage  on June 5, 1833.  She then developped an intense interest in the  mathematics of computation  and is now regarded as the first  computer programmer.  [ Video ]
 Signature of Ada Lovelace

Women in Computer Science   |   Yale CS  |  MacTutor  |  Wikipedia  |  NNDB

 Stokes coat-of-arms

 George Gabriel Stokes George Gabriel Stokes  (1819-1903)

A former Senior Wrangler, Sir George Stokes was Lucasian Professor of Mathematics at Cambridge for 53 years.  He was made a baronet in 1889.  He pioneered advances in  fluid dynamics, wave propagation, diffraction, fluorescence, differential forms and divergent series.  [Stokes line]
 Signature of George Stokes

B.A. 1841  |  Stokes' theorem  |  Navier-Stokes  |  MacTutor  |  WP  |  Weisstein  |  NNDB

 Pafnuty Chebyshev Pafnuty Lvovich Chebyshev   (1821-1894)

Home-schooled Russian aristocrat.  His mathematics tutor was the textbook author  Platon Nikolaevich Pogorelski  (1800-1852).  Chebyshev contributed to number theory, algebra, analysis, mechanics, etc.  In 1850, he derived Bertrand's postulate from the totient function's asymptotics.

Ph.D. 1849  |  MacTutor  |  Wikipedia  |  Weisstein  |  Orthogonal polynomials.  |  Economization

 Arthur Cayley 
(by Barraud and Jerrard) Arthur Cayley,  mathematician   (1821-1895)

He wrote 996 papers on many mathematical subjects (200 of these while praticing law, for 14 years).  In 1858, Cayley established  (without a formal proof)  the  Cayley-Hamilton theorem:  A matrix is a zero of its characteristic polynomial.

Dr Sc. 1875  |  MacTutor  |  Wikipedia  |  Weisstein  |  Group Th.  |  Cayley-Dickson  |  Length of a flat ellipse

 Helmholtz coat-of-arms

 Hermann von Helmholtz Hermann von Helmholtz   (1821-1894)

We use his initial (H) for enthalpy,  not for the  Helmholtz free energy (F).  Helmholtz is primarily known for his work in physics  (thermodynamics, acoustics, elasticity, etc.)  but the  fundamental theorem of vector calculus  (3D only)  is also named in his honor  (Helmholtz decomposition).

Ph.D. 1842  |  Energy conservation (1847)  |  Resonance (1850)  |  Coil  |  Equation  |  McT  |  WP  |  W  |  NNDB

 Charles Hermite Charles Hermite   (1822-1901; X1842)

After one year at  Polytechnique,  the military management dismissed him because of a congenitally deformed right leg.  Returning as a teacher, five years later, he contributed to number theory,  Ecole Polytechnique (X) orthogonal polynomials and elliptic functions.  He proved  e  transcendental in 1873.  Signature of 
 Charles Hermite

Encyclopedia Britannica   |   MacTutor   |   Wikipedia   |   Weisstein

 Louis Pasteur Louis Pasteur,  microbiologist   (1822-1895)

 Signature of 
 Louis Pasteur  Signature of 
 Louis Pasteur A chemist by training,  he separated chiral isomers by sorting the different crystals they produce.  He proved the  germ  theory of infectious diseases and invented  pasteurization.  Motto:  Fortune favors the prepared mind.

Director of ENS (1857-1867)   |   Pasteur Institute   |   Encyclopedia Britannica   |   Wikipedia   |   BBC   |   NNDB

 Gotthold Eisenstein Gotthold Eisenstein   (1823-1852)

His impoverished family had converted from Judaism to Protestantism before he was born.  Gauss  named Eisenstein one of the top three epoch-making mathematicians in history  (along Archimedes and Newton)  and  Weil  considered his approach paramount to modern mathematics.  He died at 29.

Ph.D. 1845  |  Eisenstein's lemma (1844)  |  Eisenstein integers  |  Diatomic sequence (1850)  |  McT  |  WP  |  W

 Leopold Kronecker Leopold Kronecker, algebraist   (1823-1891)

Famous for his credo "God made the natural numbers; all else is the work of man", Kronecker championed  constructivism.  He strongly opposed his former student Georg Cantor and the emerging nonconstructive Set Theory.

Ph.D. 1845  |  Legendre symbols   |   MacTutor   |   Wikipedia   |   Weisstein

 Gustav Kirchhoff Gustav Kirchhoff,  physicist   (1824-1887)

He formulated the basic laws of electrical circuits (1845)  and the  three fundamental laws of spectroscopy.  In 1858, he showed that, in  thermochemistry,  the  variation with temperature  of the heat of reaction is the difference between the heat capacities of the products and the reactants.

Ph.D. 1847  |  Blackbody radiation (1862)  |  Fluid dynamics (1877)  |  Diffraction (1883)  |  McT  |  WP  |  W  |  NNDB

 Baron Kelvin 
 of Largs

 Lord Kelvin Lord Kelvin   (1824-1907)

Born  William ThomsonLord Kelvin  was knighted in 1866 and raised to the peerage in 1892  (Baron Kelvin of Largs).  The SI unit of temperature is named after this mathematician noted for his engineering work (e.g., transatlantic telegraph).
 Signature of 
 Lord Kelvin, Professor of Natural Philosophy

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 Bernhard Riemann, 1863 Bernhard Riemann, mathematician  (1826-1866)

In 1851, his thesis introduced Riemann surfaces.  Riemann's habilitation lecture on the foundations of geometry (1854) stunned even Gauss.  Probing the distribution of primes with his  zeta function, he stated the Riemann Hypothesis in 1859.
 Signature of 
 Bernhard Riemann

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 Joseph Lister

 Joseph Lister Joseph Lister,  surgeon   (1827-1912)

Applying Pasteur's ideas, he introduced  antiseptic surgery  while working at the Glasgow Royal Infirmary.  Lister used  carbolic acid  (phenol)  to sterilize instruments and clean wounds.  This reduced post-operative infections and made surgery safer.  Baronet in 1883, he became a Baron in 1897.
 Signature of 
 Joseph Lister

Listerine (1879)  |  Lister Institute (1891)  |  Wikipedia  |  NNDB

 Marcellin Berthelot Marcellin Berthelot,  chemist   (1827-1907)

Pioneer of  synthetic organic chemistry.  He was opposed to atomist notations.  He signed his papers  P.E.M BerthelotCollège de France  (1865).  Académie des sciences  (1873).  Senator (1881).  French Minister of  education  (1886-87)  and  foreign affairs  (1895-96).  Académie française  (1901).

Thomsen-Berthelot principle (1854, 1864, obsolete)  |  Maximum work (1875)  |  Britannica  |  WP  |  NNDB

 Clerk Maxwell

 James Clerk Maxwell James Clerk Maxwell   (1831-1879)

In 1864, he devised Maxwell's equations which unify electricity and magnetism, by describing  electromagnetic  fields traveling at the speed of light.  In 1866, Maxwell proposed  (independently of Boltzmann)  the  Maxwell-Boltzmann  kinetic theory of gases.
 Signature of 
 James Clerk Maxwell

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 Richard Dedekind 
 Courtesy of the Library of the Swiss Federal Institute of Technology, Zurich Richard Dedekind,  mathematician   (1831-1916)

Julius Wilhelm Richard Dedekind  was the last doctoral student of Gauss (1852) but he also learned much from Dirichlet after his doctorate.  On 24 November 1858, he defined every  real number  as a Dedekind cut  of rationals.  In 1871, he introduced algebraic ideals.

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 Mendeleev arms

 Dmitri Mendeleev Dmitri Mendeleev, chemist   (1834-1907)

In 1869, he presented a classification of chemical elements (based mostly on atomic masses) which showed periodic patterns in their chemical properties.  He predicted the properties of 3 unknown elements which were discovered shortly thereafter:  Ga (1871), Sc (1879) and Ge (1886).
 Shape of the periodic table of elements

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 Eugenio Beltrami Eugenio Beltrami,  Italian geometer  (1835-1900)

Bringing to a great conclusion the works of  GaussBolyai, Lobachevski and Riemann on non-Euclidean geometry, he showed that geodesics matched straight lines on the plane only for surfaces of  constant curvature.  His  pseudosphere  (generated by rotating a tractrix)  is the key example (1868).

Ph.D. 1856   |   Beltrami-Klein disk   |   Beltrami-Poincaré disk   |   Houël translation   |   MacTutor   |   Wikipedia

 Johannes Diderik van der Waals

 Van der Waals Johannes van der Waals  (1837-1923)

Johannes Diderik van der Waals  obtained a doctorate in his native town of  Leiden  only when classical languages requirements were lifted in Science  (he was 36).  At a time when the very existence of molecules was doubted, his thesis showed how molecule interactions explain gas liquefaction.

Ph.D. 1873   |   Nobel 1910   |   Van der Waals forces   |   Equation of state (1873)   |   Wikipedia   |   NNDB

 Camille Jordan M. E.  Camille Jordan  (1838-1922; X1855)

A universal mathematician and one of the greatest teachers of the 19-th century,  he inspired  LieKleinBorel  and  Lebesgue Ecole Polytechnique (X) He invented the topological concept of homotopy (1866).  Camille Jordan  was appointed professor of Analysis at  Polytechnique  in 1876.

Ph.D. 1860  |  Jordan curve theorem  |  Jordan normal form  |  Jordan-Hölder theorem  |  Britannica  |  McT  |  WP

 Ernst Mach Ernst Mach,  physicist   (1838-1916)

Mach would only consider relative motion between objects, irrespective of absolute Newtonian space.  He studied the shockwaves produced by fast projectiles  (the  Mach number  of a projectile is the ratio of its speed to the speed of sound in the surrounding fluid).  Mach was Pauli's godfather.
 Signature of 
 Ernst Mach

PhD 1860  |  Mach's principle  |  Stanford  |  WP  |  W  |  NNDB

 Josiah Willard Gibbs Josiah Willard Gibbs, Jr.   (1839-1903)

Son of a philology professor at Yale,  Gibbs earned the first American doctorate in Engineering (1863).  His work in statistical mechanics and thermodynamics transformed much of chemistry into a deductive science.  The great importance of his contributions was only acknowledged after his death.

Ph.D. 1863  |  Heterogeneous Equilibria (1876)  |  Overshoot  |  McT  |  WP  |  Weisstein  |  NNDB

 Ernst Abbe Ernst Abbe,  optician  (1840-1905)

Founder of modern optics.  His industrial commitments to the instrument-maker Carl Zeiss (1816-1888) and the glassmaker Otto Schott (1851-1935) prevented Abbe from accepting a professorship at Berlin  (offered by Helmholtz).

Ph.D. 1861, 1863  |  Numerical aperture  |  Abbe sine condition  |  Abbe number  |  McT  |  WP  |  Weisstein

 Gaston Darboux Gaston Darboux,  geometer  (1842-1917)

He tied his definition of integrals (1870) to that of Riemann in 1875.  The  Darboux formulas  define the normal and geodesic curvatures as well as the geodesic torsion for a curve drawn on a surface.  He was a biographer of Poincaré. Darboux was elected to the  Académie des Sciences  in 1884.

Ph.D. 1866  |  Darboux sums (1875)  |  Darboux-Ribeaucour trihedron  |  Britannica  |  McT  |  WP  |  Weisstein

 Coat of arms of
 John William Strutt, 
 Lord Rayleigh

 Lord Rayleigh John Strutt,  Lord Rayleigh  (1842-1919)

He's the man who explained why the sky is blue  (Rayleigh scattering).  He described  surface acoustic waves  (SAW or  Rayleigh waves, 1885)  before they were observed in earthquakes.  He earned the Nobel prize (1904) for his 1892 discovery of Argon.  Rayleigh was J.J. Thompson's advisor.

Rayleigh's criterion  |  Ph.D. 1868  |  Nobel 1904  |  Encyclopedia  |  Britannica  |  McT  |  WP  |  Weisstein

 Sophus Lie Sophus Lie,  mathematician   (1842-1899)

With  Felix KleinSophus Lie  originated the investigation of the continuous groups of symmetry now named after him.  The study of  Lie groups  and the related  Lie algebras  would become a major branch of 20-th century mathematics, with applications to  quantum mechanics.

Ph.D. 1872   |   MacTutor   |   Britannica   |   Wikipedia   |   Weisstein   |   Facebook

 Ludwig Boltzmann Ludwig Boltzmann,  physicist   (1844-1906)

A proponent of  atomic theory  and the father of  statistical physics.  We call  Boltzmann's constant  the coefficient of proportionality between  entropy  (in J/K)  and the natural logarithm of the number  W  of allowed physical states.
 Signature of 
 Ludwig Boltzmann

Dangerous Knowledge 4 | 4 | 5 | 6  |  Arrow of Time  |  McT  |  WP  |  W  |  FB  |  NNDB

 Georg Cantor Georg Cantor,  mathematician   (1845-1918)

Cantor's diagonal argument shows that the points of a line are not countable.  More generally, Cantor's Theorem  states that no function from a set to its  powerset  can possibly be  surjective,  which establishes an infinite sequence of increasing  infinities.
 Signature of 
 Georg Cantor

Dangerous Knowledge 1 | 2 | 3   |   MacTutor   |   Wikipedia   |   Weisstein   |   Facebook Fans

 William Clifford by John Collier William Clifford,  geometer   (1845-1879)

Like Cavendish, Sylvester, Kelvin and Maxwell before him,  Clifford was  Second Wrangler  at Cambridge  (in 1867).
"On the Space-Theory of Matter" (1864-1876)
Clifford algebrasClifford-Klein forms.
 Signature of 
 William Clifford

Ph.D. 1868   |   Geometric algebra (1876)   |   MacTutor   |   Wikipedia   |   Weisstein

 Thomas Alva Edison Thomas Edison,  inventor   (1847-1931)

The most successfull inventor ever.  His 1093 US patents cover the phonograph, light-bulb, motion picture camera...  In 1876, he created the first industrial research laboratory at Menlo Park, NJ.  He favored DC current, which lost out to Tesla's AC generation and distribution of electric power.

"Hello" (1877)   |   Edison Birthplace Museum   |   Edison's homepage  by  Gerald Beals   |   Wikipedia   |   NNDB

 Wilhelm Killing Wilhelm Killing   (1847-1923)

Investigating  Lie groups  independently of Lie and Klein, he fully classified  simple Lie groups  in 1887  (as confirmed by Cartan in 1894):  5 exceptional Lie groups  (E,  E,  E,  G,  F)  and three regular families:  special linear groups SL(n),  orthogonal groups O(n),  symplectic groups Sp(2n).

Ph.D. 1872   |   Killing field   |   Killing spinor   |   Britannica   |   Mactutor   |   Wikipedia

 Christian Felix Klein C. Felix Klein,  mathematician   (1849-1925)

Born on 1849-4-25  (432, 22, 52 )  to a Prussian government official,  he married the granddaughter of Hegel in 1875.  The noncyclic group of order 4 bears his name.  As first president of the ICMI (1908) he was instrumental in bringing Calculus (back) to secondary schools worldwide.

Ph.D. 1868  |  Erlangen program (1872)  |  Klein bottle  |  Klein group  |  MacTutor  |  Wikipedia

 F. Georg Frobenius F. Georg Frobenius   (1849-1917)

In 1892, Weierstrass made him succeed Kronecker in Berlin, upholding traditions that would lose out to what flourished at Göttingen under Klein.  He contributed to pure mathematics in group theory (character theory),  differential equations, etc.  He proved the Cayley-Hamilton theorem in 1878.

Frobenius method  |  Frobenius map  |  Frobenius-Stickelberger formulae  |  Ph.D. 1870  |  MacTutor  |  Wikipedia

 Korvin arms

 Sofia Vasilyevna Kovalevskaya Sofia Kovalevskaya   (1850-1891)

Sofia Vasilyevna Kovalevskaya  was born  Sonya Korvin-KrukovskayaWeierstrass tutored her privately (1870-1874) and helped her Caution sign become the first female professor at a European university  (Stockholm, 1889)  since the days of Laura Bassi (1776) or Maria-Gaëtana Agnesi.
 Signature of 
 Sofia Kovalevskaya

Ph.D. 1874  |  Cauchy-Kovalevskaya theorem (1874)  |  MacTutor  |  WP  |  Weisstein

 Oliver Heaviside Oliver Heaviside   (1850-1925)

His innovations, which made higher-mathematics easier to use, include operational calculus and vector calculus  (which reduced to 4 the number of Maxwell's equations). In 1902, he predicted the Kennelly-Heaviside layer of the ionosphere, whose detection (1923) got Appleton a Nobel prize, in 1947.

Electromagnetic terms  |  Lorentz-Heaviside units  |  Heaviside step function  |  MacTutor  |  Wikipedia  |  NNDB

 van 't Hoff coat-of-arms

 Jacobus van 't Hoff 
 (Perscheid 1904) Jacobus Henricus van 't Hoff  (1852-1911)

Founded  physical chemistry.  Earned the first Nobel Prize in chemistry (1901)  for his work on equilibrium, reaction rates and osmotic pressure.  His first paper (1874) introduced  stereochemistry  (independently of Le Bel).  Van 't Hoff's equation (1884)  says how equilibria depend on temperature.

Ph.D. 1874  |  Nobel 1901  |  Osmosis (1886)  |  Arrhenius equation (1889)  |  Britannica  |  Wikipedia  |  NNDB

 Ecole Polytechnique (X)

 Antoine Henri Becquerel A. Henri Becquerel   (1852-1908; X1872)

His grandfather, father and son had the same career path as himself:  Polytechnician (*), physics chair at the Muséum national d'histoire naturelle and member of the Académie des sciences.  For his  re-discovery of radioactivity (1896-03-01)  he shared a Nobel Prize with Pierre and Marie Curie.

(* Edmond, his father, didn't attend Polytechnique)   |   Nobel 1903   |   SI unit of activity (Bq)   |   Wikipedia   |   NNDB


 Gregorio Ricci-Curbastro Gregorio Ricci-Curbastro   (1853-1925)

In 1884, he started the investigations of  quadratic differential forms  which led him to invent  tensor calculus  (1884-1894).  The text he published about that with  Tullio Levi-Civita in 1900 would enable Einstein to formulate General Relativity in 1915.
 Signature of 
 Gregorio Ricci-Curbastro

Ph.D. 1873   |   Britannica   |   MacTutor   |   Wikipedia   |   Weisstein

 Hendrik Antoon Lorentz Hendrik A. Lorentz,  physicist   (1853-1928)

Among the  many  contributions of  H.A. Lorentz  is the coordinate transformation which is the cornerstone of  Special Relativity.  In 1892, Lorentz proposed a theory of the  electron  (discovered by Perrin in 1895 and J.J. Thomson in 1898).
 Signature of H.A. Lorentz

Nobel 1902   |   MacTutor   |   Wikipedia   |   Weisstein   |   Facebook Fans

 Ecole Polytechnique (X)

 Jules Henri Poincare J. Henri Poincaré   (1854-1912; X1873)

Doctoral student of Hermite  (1879)  and last  universal  genius.  Quintessential absent-minded professor  (cf.  Savant Cosinus  comic strip).  Poincaré conceived Special Relativity before Einstein did.  His mathematical legacy includes  Signature of 
 Henri Poincare chaos theory  and contributions to topology.

MacTutor   |   Wikipedia   |   Weisstein   |   Bruce Medal 1911   |   Fans

 Nikola Tesla Nikola Tesla   (1856-1943)

He was originally trained as a  mechanical  engineer.  At least 272 patents were awarded to Tesla in 25 countries.  His work is the basis of modern  alternating current  (AC) electric power distribution.  In 1960, the SI unit of  magnetic induction  (magnetic flux density)  was named after him.
 Signature of 
 Nikola Tesla

Visions  |  Master of Lightning  |  Tesla coil  |  Teslamania  |  Weisstein  |  WP  |  NNDB

 Coat-of-arms of Heinrich Hertz

 Heinrich Hertz Heinrich Hertz  (1857-1894)

In 1887,  Heinrich Rudolf Hertz  discovered the  photoelectric effect, whose explanation by Einstein, in 1905, would establish the existence of photons.  In 1888,  he made the first transmission of a signal by  radio waves.  The SI unit of frequency  (symbol Hz)  was named after him, in 1960.  Signature of 
 Heinrich Hertz

Founder of  contact mechanics  (1882)   |   Uncle of Gustav Hertz  (Nobel 1925)   |   WP   |   NNDB

 Paternal coat-of-arms of Max Planck

 Max Planck 
 (1858-1947) Max Planck,  physicist   (1858-1947)

Planck combined the formulas of Wien (UV) and Rayleigh (IR) into a unified expression for the blackbody spectrum.  On Dec. 14, 1900, he justified it by proposing that exchanges of energy only occur in discrete lumps, dubbed  quanta.
 Signature of Max Planck 
 at 10 years of age

Ph.D. 1879  |  Nobel 1918  |  Wikipedia  |  MacTutor  |  FB  |  NNDB

 Giuseppe Peano 
 (1858-1932) Giuseppe Peano,  logician   (1858-1932)

In 1880, Peano joined the staff at Turin where he succeeded  Angelo Genocchi (1817-1889)  to the chair of Calculus, in 1890.  Peano defined the integers axiomatically (1889) and found a  space-filling curve (1890).  He invented  symbolic  logic (1895) and devised a new natural language (1903).

Peano axioms (1889)  |  Formulario (1895-1908)  |  Latino sine flexione (1903)  |  Britannica  |  WP  |  McT  |  NNDB

 Otto Hölder 
 (1859-1937) Otto Ludwig Hölder   (1859-1937)

Like his mentor  Paul du Bois-Reymond  (a student of KummerOtto Hölder  argued against  formalism  in foundational mathematics,  as championed by Cantor, Hilbert or  Robert Grassmann, of whom he was most critical (1892).  His  intuitionism  resembled Poincaré's  (not Brouwer's).

Sc.D. 1882  |  Jordan-Hölder theorem  |  Hölder mean  |  Hölder condition  |  Hölder's inequality (1884)  |  WP  |  McT

 David Hilbert 
 (1862-1943) David Hilbert,  mathematician   (1862-1943)

One of the most powerful mathematicians ever, David Hilbert gave a famous list of 23 unsolved problems in 1900.  Quantum Theory  is based on the complex normed vector spaces which are named after him.  In 1931,  Gödel shattered the dream Hilbert had voiced in 1930  ("we will know").
 Signature of David

Hilbert's List (1900)  |  Hilbert's radio address (1930)  |  WP  |  McT  |  FB  |  NNDB

 Minkowski family arms

 Hermann Minkowski 
 (1864-1909) Hermann Minkowski   (1864-1909)

Pioneering convex geometry, he proved an early version of the  separation theorem  (of Hahn-Banach) and called  A+B  the set of all sums with one addend in A and the other in B.  His name was given to the  Lp  triangular inequality  (1896)  and to the  relativistic  scalar product  in  spacetime (1908).  Signature of 
 Hermann Minkowski

Brunn-Minkowski  |  Hasse-Minkowski  |  Functional  |  Wikipedia  |  MacTutor  |  FB

 Jacques Hadamard 
 (1865-1963) Jacques Hadamard,  analyst   (1865-1963)

In 1892, he obtained his doctorate and was awarded the French Academy's  Grand Prix  for completing the work of Riemann on the  Zeta function.  He authored one of the first two proofs of the Prime number theorem in 1896.  He gave functional analysis its name in 1910.  Deeply influential.
 Signature of 
 Jacques Hadamard

1887  |  Ph.D. 1892  |  Hadamard matrices (1893)  |  Wikipedia  |  MacTutor  |  NNDB


 Marie Curie 
 (1867-1934) Marie Curie, physical chemist  (1867-1934)

Madame Curie  (née  Maria Salomea Sklodowska )  was the first woman to earn a Nobel prize and the first person to earn two.  In 1898, she isolated two new elements (polonium and radium) by tracking their  ionizing radiation,  using the electrometer of Jacques and Pierre Curie  (her husband).
 Signature of 
 Marie Curie

Nobel 1903 (Physics)   |   Nobel 1911 (Chemistry)   |   Wikipedia   |   AIP   |   Facebook Fans

 Henrietta Swan Leavitt 
 (1868-1921) Henrietta S. Leavitt,  astronomer  (1868-1921)

In 1908,  Henrietta Swan Leavitt  published the period-luminosity relationship for Cepheid variable stars,  which reveals their actual distances, even when stellar parallax is undetectable.  This paved the way for the first measurement of the  expansion of the Universe  by Edwin Hubble (1929).

1777 Variables in the Magellanic Clouds (1908)   |   Calibration by Hertzsprung (1913)   |   Wikipedia   |   NNDB

 Felix Hausdorff 
 (1868-1942) Felix Hausdorff,  topologist   (1868-1942)

In a Hausdorff space (1914) two distinct points are always disconnected.  In 1919, he introduced fractional dimensions and defined  d-dimensional  measures.  Hausdorff published literary work as  Paul Mongré.  Unable to escape the Nazis, he committed suicide with his wife and sister-in-law.

Ph.D. 1891  |  Hausdorff gap (1909)  |  Hausdorff distance  |  Hausdorff dimension  |  Hausdorff measure  |  McT  |  WP

 Elie Cartan 
 (1869-1951) Elie Cartan,  mathematician   (1869-1951)

In 1913, Cartan established, from a purely geometrical standpoint, the relations that lead to the quantization of spin.  He developed exterior calculus and published his  Theory of Spinors  as a textbook in 1935.  Godfather of  Bourbaki  and father of key Bourbakist  Henri Cartan (1904-2008).

Ph.D. 1894   |   MacTutor   |   Wikipedia   |   Weisstein   |   FB   |   NNDB

 Emile Borel 
 (1871-1956) Emile Borel,  mathematician   (1871-1956)

Sainte-Barbe  bursar,  he ranked first in the top three French academic competitions of 1889:  Concours Général, PolytechniqueEcole Normale.  He chose to enter the latter.  Borel developed point-set topology and founded Measure theory.  Elected to the  Académie des Sciences  in 1921.

Ph.D. 1893  |  Heine-Borel criterion  |  Borelian tribe (1898)  |  Divergent series (1899)  |  McT  |  WP  |  Weisstein

 Lord Rutherford of Nelson

 Ernest Rutherford Ernest Rutherford   (1871-1937)

British physicist born in Nelson, New Zealand.  His investigations of alpha and beta decay  (which he so named)  earned him a Nobel prize before he moved to Manchester, where he supervised the Geiger-Marsden experiment (1909) and inferred the planetary model of the atom (1911).
 Signature of 
 Ernest Rutherford

Nobel 1908   |   Nuclear Physics  |  Wikipedia  |  Weisstein  |  John Campbell (NZ)

 Constantin Caratheodory 
 (1873-1950) Constantin Carathéodory   (1873-1950)

Greek mathematician with a doctorate from Göttingen  (under Minkowski).  He made contributions to the calculus of variations  and founded  axiomatic  thermodynamics.  In measure theory, Carathéodory's criterion  characterizes measurability.  He corresponded with Einstein (1916-1930).

Ph.D. 1904  |  Outer measure  |  Axiomatic thermodynamics (1909)  |  Wikipedia  |  Weisstein  |  MacTutor

 René Baire (1874-1932) René Baire, French analyst   (1874-1932)

Entered  ENS  at  17,  by derogation (1892).  Agrégé  at 20.  The  Baire space is the set of all infinite sequences of natural integers, endowed with the Tychonoff topology.  It's  homeomorphic  to the subspace of the  interval  [0,1]  consisting of  irrational  numbers  (cf. continued fractions).

Ph.D. 1899   |   Teaching career (French)   |   Baire property   |   Baire spaces  vs.  Baire space   |   WP   |   McT

 Henri Lebesgue 
 (1875-1941) Henri Lebesgue, French analyst   (1875-1941)

Building on the work of  Jordan  and  Borel  (his advisor)  he laid the goundwork of  measure theory  in 1901 and went on to revolutionize the notion of definite integration in his doctoral dissertation (1902).  Lebesgue was elected to the  Académie des Sciences  on 29 May 1922.

Ph.D. 1902   |   Lebesgue spaces   |   Wikipedia   |   Weisstein   |   MacTutor

 G.H. Hardy 
 (1877-1947) G.H. Hardy,  pure mathematician   (1877-1947)

Known only by his initials G.H.  (for Godfrey Harold)  Hardy  was asexual, entirely devoted to mathematics and cricket  (a  nonpractising homosexual,  said Littlewood).  His collaboration with Littlewood is legendary.  So is the way Hardy recognized and guided Ramanujan's raw genius.

M.A. 1903  |  A Mathematician's Apology (1940)  |  Divergent Series (1949, posthumous)  |  McT  |  WP  |  NNDB

 Lise Meitner 
 (1878-1968) Lise Meitner,  physical chemist   (1878-1968)

A student of Ludwig Boltzmann, she became a collaborator of  Otto Hahn  who was awarded a Nobel prize (1944) for their joint work.  With  Otto Frisch  (her nephew)  Lise Meitner gave  nuclear fission  its name  (Kernspaltung).  She correctly explained the related  mass defect  (1938).  Signature of 
 Lise Meitner

Ph.D. 1906  |  Otto Hahn's Nobel Lecture  |  WP  |  Weisstein  |  Meitnerium (1997)

 Albert Einstein 
 (1876-1955) Albert Einstein,  physicist   (1879-1955)

In 1905, Einstein published on Brownian motion (existence of atoms) the photoelectric effect (discovery of the photon) and his own Special Theory of Relativity, which he unified with gravity in 1915 by formulating the General Theory of Relativity.  In 1916, he discovered what led to  lasers.
 Signature of 
 Albert Einstein

PhD 1905  |  Nobel 1921  |  EPR 1935  |  McT  |  WP  |  Bonn  |  W  |  AIP  |  NNDB

 Bertus Brouwer 
 (1881-1966) L.E.J. Brouwer,  mathematician   (1881-1966)

Early in his career,  Bertus Brouwer  founded modern topology.  He later championed the incompatible philosophy of  intuitionism  which considers only sets whose elements can be shown to belong in finitely many steps.  As topology  isn't  intuitionistic, he wouldn't teach it at all!

Ph.D. 1907  |  Fixed-point theorems  |  Domain invariance (1912)  |  Topological spaces (1913)  |  McT  |  WP  |  W

 Karman Todor 
 (1881-1963) Theodore von Kármán,  engineer   (1881-1963)

Born in Budapest.  Visiting Paris in March 1908, he saw early aviation flights and decided he'd apply mathematics to aeronautics.  He became director of the Aeronautical Institute at  Aachen  in 1912.  He emmigrated to the US in 1930 and received the  first  National Medal of Science, in 1963.

Ph.D. 1908  |  Kármán's vortex street (1911)  |  Kármán line (Andrew G. Haley, 1963)  |  Britannica  |  McT  |  WP  |  W

 Emmy Noether 
 (1882-1935) Emmy Noether,  mathematician   (1882-1935)

Emmy Noether discovered the remarkable equivalence between symmetries in physical laws and conserved physical quantities  (Noether's theorem, 1915).  Her considerable legacy also includes three Isomorphism Theorems named after her (1927).   [ ]

Ph.D. 1907  |  1918 Paper  |  Noether's theorem & Proof  |  MacTutor  |  Wikipedia  |  FB  |  Video (2015)

 John E. Littlewood 
 (1885-1977) John E. Littlewood,  analyst  (1885-1977)

Littlewood  had 22 doctoral students but, like Hardy, never bothered to take a doctoral degree himself.  In 1910 or 1911, he started a prolific collaboration with G.H. Hardy which spanned 35 years.  He was so discreet that rumors once circulated that he was just a figment of Hardy's imagination.

Senior Wrangler 1905  |  MA 1910  |  FRS 1916  |  Rouse Ball professor, 1928  |  Miscellany (1953,1986)  |  McT  |  WP


 Niels Bohr 
 (1885-1962) Niels Bohr,  physicist   (1885-1962)

In 1913, Bohr started the quantum revolution with a model where the  orbital angular momentum  of an electron only has discrete values.  He later spearheaded the  Copenhagen interpretation  (i.e., probabilistic measurements cause the  collapse  of otherwise linearly-evolving quantum states).  Signature of Niels Bohr

Ph.D. 1911 (Copenhagen)  |  Nobel 1922  |  Wikipedia  |  Facebook Fans

 Hermann Weyl 
 (1885-1955) "Peter" Hermann Weyl   (1885-1955)

In 1908, Weyl obtained his doctorate from Göttingen under Hilbert.  He was enthralled by  symmetry  in mathematical physics.  In 1913, Weyl became a colleague of Einstein's at the ETH Zürich.  He befriended Schrödinger in 1921.  Weyl introduced compact groups (1923-1938).  Signature of 
 Hermann Weyl

Ph.D. 1908   |   Weyl algebra   |   Symmetry (1952)   |   WP   |   McT   |   FB

 Erwin Schroedinger 
 (1887-1961) Erwin Schrödinger,  physicist   (1887-1961)

In 1926, Schrödinger matched observed quantum behavior with the properties of a continuous nonrelativistic wave obeying the Schrödinger Equation.  In 1935, he challenged Bohr's   Copenhagen Interpretation,  with the famous tale of Schrödinger's cat.  He lived in Dublin from 1939 to 1955.
 Signature of 
 Erwin Schroedinger

Nobel 1933 (lecture)  |  What is Life? (1944)  |  WP  |  McT  |  NNDB

 Srinivasa Ramanujan 
 (1887-1920) Srinivasa Ramanujan   (1887-1920)

Ramanujan lacked a formal mathematical education but, in 1913, a few of his early results managed to startle  G.H. Hardy (1877-1947)  and  J.E. Littlewood (1885-1977)  who invited him to Cambridge in 1914.  Ramanujan has left an unusual legacy of brilliant unconventional results.
 Signature of 
 Srinivasa Ramanujan

Degree 1916  |  FRS 1919  |  Wikipedia  |  MacTutor  |  FB Fans  |  NNDB

 Louis J. Mordell 
 (1888-1972) Louis J. Mordell   (1888-1972)

Born in Philadelphia to Lithuanian parents,  he was inspired by second-hand textbooks and conceived the  mad  project of competing for a Cambridge scholarship.  Against all odds, Mordell placed first (1906).  His results would set the tone for modern views of number theory  (cf. elliptic curves).

Degree  |  Tau (1917)  |  Mordell's theorem (1922)  |  Falting's theorem (1922 conjecture)  |  Wikipedia  |  MacTutor

 Stefan Banach

 Stefan Banach
 (1892-1945) Stefan Banach   (1892-1945)

Pioneer of functional analysis  (Théorie des opérations linéaires, 1932).  His name was given to the main backdrop (Banach spaces) and the 3 fundamental theorems:  Hahn-Banach  (linear extension & separation),   Banach-Steinhaus  (uniform boundedness),  Banach-Schauder  (open map).

home   |   Ph.D. 1920  (Banach spaces)   |   Wikipedia   |   MacTutor

 de Broglie

 Louis de Broglie
 (1892-1987) Louis de Broglie,  physicist   (1892-1987)

In 1923, he proposed that any particle could behave like a wave of wavelength inversely proportional to its momentum  (this helps justify Schrödinger's equation).  He predicted  interferences  for an electron beam hitting a crystal.
 Signature of Louis de Broglie (1970)

Nobel 1929   |   1967   |   Wikipedia   |   MacTutor   |   NNDB

 Carl Ludwig Siegel
 (1896-1981) Carl L. Siegel,  mathematician   (1896-1981)

In 1978, Siegel became the first recipient (oldest to date) of the  Wolf Prize  for his work in celestial mechanicscomplex variables and  transcendental numbers :  Siegel's lemma (1929).  Siegel modular forms (1935).  Mass formula (1935).  Siegel-Weil formula (1951).  Thue-Siegel-Roth.
 Signature of Carl Ludwig Siegel

Ph D 1920   |   Greatness (forum)   |   MacTutor   |   Wikipedia

 Emil Artin 
 (1898-1962) Emil Artin,  mathematician   (1898-1962)

Born in Austria, he fled the Nazis in 1937.  Artin is credited for modernizing Galois theory.  He passed on his interest in subassociativity to his student Max Zorn  (of lemma fame).  Emil Artin was also the doctoral advisor of two  BourbakistsJohn Tate (Abel prize, 2010) and Serge Lang.

Ph D 1921  |  Reciprocity & Artin's constant (1927)  |  Artin-Zorn theorem (1930)  |  Gamma (1931)  |  McT  |  WP

 Helmut Hasse 
 (1898-1979) Helmut Hasse,  mathematician   (1898-1979)

The Hasse-Minkowski theorem (1921) transfers arithmetical questions to local fields.  The  Hasse invariant  of a non-singular algebraic curve over a finite field is the rank of its Hasse-Witt matrix.  In 1937, Hasse's application to the Nazi party was denied because he had a Jewish great-grandmother.

Local-global principle (1920)  |  Ph D 1922  |  Artin-Hasse exponential (1928)  |  Hasse bound (1933)  |  McT  |  WP

 Wolfgang Pauli 
 (1900-1958) Wolfgang [Ernst] Pauli,  physicist   (1900-1958)

In 1925, Wolfgang Pauli formulated the  exclusion principle  which explains the entire table of elements.  His Godfather was Ernst Mach.  Pauli's sharp tongue was legendary; he once said about a bad paper:  "This isn't right; this isn't even wrong."
 Signature of Wolfgang Pauli

Ph.D. 1921  |  Nobel 1945  |  great-grandfather  |  Wikipedia  |  Video Tribute  |  NNDB

 Enrico Fermi 
 (1901-1954) Enrico Fermi,  physicist   (1901-1954)

In 1926, Fermi helped formulate the Fermi-Dirac statistics obeyed by what we now call  fermions.  He identified the  neutrino  in beta-decay.  He discovered slow neutrons and the radioactivity they  induce.  On December 2, 1942, Fermi produced the first self-sustaining nuclear chain reaction.  Signature of Enrico Fermi

Fermions (1926)  |  "Neutrino" (1933)  |  Nobel 1938  |  Fermilab (1969)  |  WP  |  NNDB

 Werner Heisenberg 
 (1901-1976) Werner Heisenberg,  physicist  (1901-1976)

In 1925, Werner Heisenberg replaced Bohr's semi-classical orbits by a new quantum logic which became known  as matrix mechanics  (with the help of Born and Jordan).  A consequence of the noncommutativity so entailed is  Heisenberg's uncertainty principle.
 Signature of 
 Werner Heisenberg

Ph.D. 1923   |   Nobel 1932   |   Patriot   |   MacTutor   |   Wikipedia   |   NNDB

 Alfred Tarski

 Alfred Tarski 
 (1902-1983) Alfred Tarski,  logician   (1902-1983)

In 1924, he gave a nice  definition of infinite sets.  Also due to him are the  Banach-Tarski Paradox  and the  Tarski-Grothendieck set theory.  His  axioms for  elementary  Euclidean geometry (1959) form a system (unlike anything covering arithmetic) where every true statement is provable.

Ph.D. 1924   |   Tarski's undefinability theorem   |   Stanford    |   MacTutor    |   Wikipedia   |   Weisstein   |   NNDB

 Paul Adrien Maurice 

 Paul Dirac 
 (1902-1984) Paul Adrien Maurice Dirac   (1902-1984)

In 1925, Paul Dirac came up with the formalism on which quantum mechanics is now based.  In 1928, he discovered a relativistic wave function for the electron, predicting the existence of  antimatter  (observed by Anderson in 1932).  He coined the name for  quantum electrodynamics  (QED).
 Signature of P.A.M. Dirac (Bodensee, 1962)

Family  |  Ph.D. 1926  |  Nobel 1933  |  FSU  |  Large numbers  |  FB  |  WP  |  NNDB

 Andrey Nikolaevich Kolmogorov (1903-1987) Andrey Nikolaevich Kolmogorov  (1903-1987)

He constructed functions whose Fourier series diverge almost everywhere (1922) or everywhere (1926).  In 1933, he laid the foundations of  axiomatic probability theory.  Based on his 1954 work, the long-term stability of the solar system can  almost  be established  (KAM theorem).

Ph.D. 1925   |   algorithmic complexity   |   Trennung (T0 axiom)   |   Britannica   |   WP   |   McT   |   W

 Alonzo Church (1907-1989) Alonzo Church,  logician   (1903-1995)

He had 35 doctoral students, including Turing.  He invented lambda-calculus and amended it, in 1936, with his student J. Barkley Rosser, Sr. (1907-1989) to describe all effective computations.  (The equivalence with Turing machines became the basis for the generalized Church-Turing thesis.)

Ph.D. 1927  |  Church's theorem  |  Church-Rosser theorem (1936)  |  Britannica  |  WP  |  McT  |  NNDB

 John von Neumann

 John von Neumann (1903-1957) 
 at Los Alamos Jancsi "John" von Neumann  (1903-1957)

He is credited with the  stored program architecture  (1946)  whereby a computer uses its primary memory space to store both the data it operates on and the  codes  for the programs it executes.  Von Neumann  pioneered  game theorydecision analysisautomata theory  and  fault-tolerant systems.
 Signature of 
 John von Neumann

NBG  |  FB  |  video (1966)  |  The Scientific 100  |  McT  |  WP  |  NNDB

 Henri Cartan 
 (1904-2008) Henri Cartan,  mathematician   (1904-2008)

Son of Elie Cartan (1869-1951).  A key founder, with Weil,  of the Bourbaki group (1935)  which would consume a large part of his research activities.  He was the leading professor at ENS for several decades.  Cartan was instrumental in reconciling French and German mahematics after WWII.

Ph.D. 1928   |   Caen (1928-1929)   |   Bourbaki (1935-)   |   Wikipedia   |   MacTutor

 Tommy Flowers 
 (1905-1998) Tommy Flowers,  engineer   (1905-1998)

In 1944, Thomas Harold Flowers  built the first large-scale electronic computer  (Colossus)  at  Bletchley Park.  As the accomplishment remained classified for decades, Flowers was deprived of the glory which went instead to Mauchly and Eckert for the ENIAC (Philadelphia, 1946).

Wikipedia   |   Bletchley Park   |   The design of Colossus by Thomas H. Flowers

 Kurt Goedel 
 (1906-1978) Kurt Gödel,  logician   (1906-1978)

The  completeness  theorem in his dissertation  (1929)  states that a statement true in  every  model  of an axiomatic system is provable in it.  His more famous  incompleteness  theorem  (1931)  says that, in any model of a set of axioms covering arithmetic, some true statements are not provable.
 Signature of 
 Kurt Goedel

NBG  |  Ph.D. 1929  |  Grave  |  Centenary  |  Conway  |  IAS  |  WP  |  McT  |  FB  |  NNDB

 Andre Weil 
 (1906-1998) André Weil,  mathematician   (1906-1998)

Brother of the philosopher Simone Weil (1909-1943)  but unrelated to the politician Simone Veil (1927-2017).  He was the leading founder of  BourbakiWeil  established the field of  algebraic geometry  and, arguably, charted the course of much  abstract mathematics  in the  twentieth century.

D.Sc. 1928   |   Uniform spaces (1937)   |   Weil conjectures (1949)   |   Wikipedia   |   MacTutor   |   ams

 Ettore Majorana 
 (1906-1938) Ettore Majorana,  physicist  (1906-1938?)

Arguably the most brilliant of a dozen Via Panisperna boys selected by Fermi  (including the likes of Wick and Segrè).  Majorana published only 9 scientific papers but left a huge 10,000-page legacy of notebooks written between 1927 and 1932.  He organized his own disappearance in March 1938.

French video by Etienne Klein   |   Via Spanisperna   |   Majorana fermion   |   Wikipedia

 H.S.M. Coxeter 
 (1907-2003) Donald Coxeter,  geometer   (1907-2003)

Harold Scott MacDonald Coxeter  was a British-born Canadian mathematician teaching at Toronto.  He put forth  reflection groups.  He wrote  Introduction to Geometry (1961)  and  Regular Polytopes (1963).  A correspondant of Martin Gardner, he inspired Bucky Fuller and M.C. Escher.

Senior Wrangler 1928  |  Ph.D. 1931  |  Coxeter groups  |  The man who saved geometry  |  Wikipedia  |  MacTutor

 Alan M. Turing

 Alan Turing 
 (1912-1954) Alan Turing,  logician   (1912-1954)

Top code-breaker of  Bletchley Park  (WWII).  A  Turing Machine  is a finite automaton endowed with an infinite read/write tape on which it can move back and forth, one step at a time.  Turing showed that such a machine is capable of computing anything that any other machine could.  Signature of Alan Turing

PhD 1938  |  Bio  |  |  Copeland  |  BBC  |  WP  |  McT  |  FB  |  NNDB

 Paul Erdos 
 (1913-1996) Paul Erdős,  mathematician   (1913-1996)

Paul Erdös  wrote over 1500 papers with 511 collaborators.  He contributed many conjectures and proved some great ones.  Faced with antisemitism, he left Hungary in 1934 and spent the rest of his frugal life on the road, touring mathematical centers.

Pronounce it right  |  Ph.D. 1934  |  Erdös number  |  Wikipedia  |  MacTutor  |  Facebook Fans  |  NNDB

 Fields Medal

 Laurent Schwartz Laurent Schwartz   (1915-2002)

"One night in 1944", he figured out that the  distributions  used in theoretical physics  (including Dirac's delta)  weren't pointwise functions but linear forms over a restricted set of smooth  test functions.  The  Fourier transform  turns out to be a  linear automorphism  among  tempered distributions.

Ph.D. 1943  |  Bourbakist  |  Fields Medal 1950  |  Wikipedia  |  MacTutor  |  Convolutions & Distributions

 Claude E. Shannon Claude Elwood Shannon,  engineer  (1916-2001)

Known as the  father of information theory
A Mathematical Theory of Communication (1948).
Shannon-Hartley channel capacity theorem
Nyquist-Shannon sampling theorem

Ph.D. 1948  |  Statistical entropy (1948)  |  Information unit (Sh)  |  Video  |  Britannica  |  WP  |  McT  |  W  |  NNDB

Fields Medal

 Atle Selberg 
 (1917-2007) Atle Selberg,  mathematician  (1917-2007)

Norwegian-born.  He furthered the sieve methods of his countryman  Viggo Brun (1885-1978)  and proved major results on the  Riemann zeta function.  With  Erdös,  Selberg gave an elementary proof of the  prime number theorem  and  generalized it to  primes in arithmetic progression.

Ph.D. 1943  |  Fields Medal, 1950  |  Selberg's eigenvalue conjecture (1965)  |  Britannica  |  MacTutor  |  Wikipedia

 Bill Tutte Bill Tutte,  graph-theorist   (1917-2002)

During WW2, William T. Tutte (pronounced Tut) broke the Lorenz cipher.  His algorithms motivated Flowers' Colossus.  He developed Whitney's (1935) matroids.  The Tutte graph (1946) disproved Tait's conjecture (1884).  In 1948, Coxeter invited him to Canada, where he remained.

Ph.D. 1948  |  Tutte polynomial  |  Tutte theorem  |  Homotopy theorem (1958)  |  Spring theorem (1963)  |  WP  |  McT

 Richard P. Feynman 
 (1918-1988) Richard P. Feynman,  physicist   (1918-1988)

In 1949, he introduced  Feynman diagrams  to describe the relativistic quantum theory of electromagnetic interactions known as  Quantum electrodynamics  (QED)  using  perturbation theory.  This has helped visualize all other types of fundamental interactions ever since.

Ph.D. 1942  |  Nobel 1965  |  1972 Interviews  |  1979 Lectures  |  1988  |  FB  |  MacTutor  |  WP  |  NNDB

 Abraham Robinson 
 (1918-1974) Abraham Robinson   (1918-1974)

Robinson's  non-standard analysis (1961)  gave a rigorous footing to the  infinitesimals  introduced by Leibniz (1675)  thus providing an alternative basis for  analysis  (competing with the approach made standard by  Cauchy  in 1821).  This was an early application of  Model theory.

Ph.D. 1949   |   Hyperreal numbers   |   Non-standard analysis   |   MacTutor   |   Wikipedia

 C.N. Yang Franklin Chen-Ning Yang,  physicist   (1922-)

With  Robert Mills (1927-1999)  in 1954,  Frank Yang  generalized the  gauge theories  of  Weyl  (1919).  Yang-Mills theory,  is now the paradigm for the modern description of all interactions.  With  T.D. Lee  and  Chien-Shiung Wu (1912-1997)  Yang  found beta-decay to violate parity (1956).

Ph.D. 1948  |  Nobel 1957  |  Yang-Mills theory  |  Fiber bundle  |  Millennium problem  |  2006-05-18  |  WP  |  NNDB

Freeman DysonFreeman J. Dyson   (1923-)

Born in England, Dyson went to Cornell as a student (1947) and went on to replace Feynman there, without ever getting a doctorate.  In 1949, he showed Feynman's  QED  diagrams to be equivalent, to the methods of Schwinger or Tomonaga. Dyson joined the IAS in Princeton in 1953 and never left. 

Dyson series  |  Orion Project (1957-1961)  |  Birds & Frogs (2009)  |  Climate (2015)  |  Religion  |  IAS  |  WP  |  NNDB

 Benoit Mandelbrot 
 (1924-2010) Benoît Mandelbrot,  mathematician  (1924-2010)

Nephew of the founding  Bourbakist  Szolem Mandelbrojt (1899-1983).  His family emigrated from Poland to France in 1936 and he was educated at  Ecole Polytechnique (X) Polytechnique.  He founded fractal geometry  and discovered the  Mandelbrot set.
 Signature of Benoit Mandelbrot

Ph.D. 1952   |   Fractals and Roughness   |   Wikipedia   |   MacTutor   |   NNDB

 Fields Medal

 Jean-Pierre Serre 
 (1926-) Jean-Pierre Serre,  mathematician  (1926-)

Bourbakist  noted for broad contributions in fields like topology, group theory and number theory  (particularly Galois representations and modular forms).  First prize for mathematics in Concours Général (1944).  Youngest Fields medalist (in 1954) and first  Abel prize  recipient (2003).

Ph.D. 1951   |   Collège de France (1956-1994)   |   Conjecture II   |   Abel prize   |   WP   |   McT   |   Video

 Fields Medal

 Alexandre Grothendieck Alexander Grothendieck   (1928-2014)

Visionary mathematician.  Student of  Schwartz,  advisor of Deligne.  Championing categories,  he advocated  Schemes  and  Motives.  Having given up research in 1972, he retired in 1988.  In 1991, he chose to live as a recluse in Ariège  (09230 Lasserre, pop. 211; 16 km North of Saint-Girons).
 Signature of 
 Alexander Grothendieck

Ph.D. 1953  |  Grothendieck Circle  |  Cartier  |  WP  |  McT  |  NNDB

 John F. Nash John Forbes Nash, Jr.   (1928-2015)

In his 1950 thesis about  non-cooperative games)  The notion of a  Nash equilibrium  makes  game theory  relevant to many real-life situations.  Nash battled schizophrenia for decades, but   willed it off  before receiving the Nobel prize in economics, at 66, and the Abel prize, at 86  (2015).

Ph.D. 1950  |  Embedding  |  Nobel Prize, 1994  |  Brilliant madness  |  A Beaufiful Mind  |  RI  |  WP  |  McT  |  NNDB

 John S. Bell John S. Bell,  Irish physicist  (1928-1990)

John Stewart Bell earned his PhD in nuclear physics at Birmingham in 1956.  In 1960, he and his wife (Mary Ross) gave up tenured positions to work at CERN for the rest of their careers.  After a year-long sabbatical from CERN, John published his masterpiece:  "On the EPR paradox" (1964).

Bell's inequality (1964)  |  The most profound discovery in Science  |  WP  |  McT  |  NNDB

 Fields Medal

 Michael Atiyah 
 (1929-) Michael Atiyah,  mathematician  (1929-)

In algebraic geometry,  the  index theorem (1963)  equates the  topological index  of an elliptic differential operator,  on a compact manifold,  to its  algebraic index  (pertaining to the dimension of the space of solutions).  This very general theorem has many specializations and applications.

Ph.D. 1955  |  Atiyah-Singer index theorem (1963)  |  Abel Prize, 2004  |  MacTutor  |  Wikipedia  |  FB Fans  |  NNDB

 Murray Gell-Mann 
 (1929-) Murray Gell-Mann,  physicist  (1929-)

An early proponent of the chirality of weak interactions  (1958)  he dubbed  strangeness  one  flavor  they don't conserve.  Gell-Mann gave  "quarks"  their name and called  color  what they trade.  The same scheme was independently proposed by  George Zweig (1937-)  using the word  aces.

Ph.D. 1951  |  Gell-Mann-Okubo (1961)  |  Yuval Ne'eman & Eightfold Way (W-, 1964)  |  Nobel 1969  |  WP  |  NNDB

 Roger Penrose 
 (1931-) Sir Roger Penrose,  cosmologist   (1931-)

His father, Lionel, was a geneticist.  His mother, Margaret, was a physician.  His older brother, Oliver, became a professor of mathematics.  His younger brother, Jonathan, was 10 times  British Chess Champion,  perhaps the most talented ever.  Roger penrose put forth  twistors in 1967.

Ph.D. 1958  |  Penrose diagram  |  Kites & Darts (1977)  |  Why did our universe begin?  |  2016  |  WP  |  McT  |  NNDB

 Steven Weinberg 
 (1933-) Steven Weinberg,  physicist   (1933-)

In 1967, he formulated the  electroweak  unification of the weak nuclear force and electromagnetism, predicting a massive neutral messenger particle  (the Z boson)  which was first observed in 1979.  Steven Weinberg gave the  Standard Model  its name.  ["To Explain the World", 2015.]

Ph.D. 1957  |  home  |  video  |  Nobel 1979  |  Wikipedia  |  Emperor Has No Clothes Award  |  FB Fans  |  NNDB

 Fields Medal

 Paul Cohen Paul Cohen,  logician   (1934-2007)

His invention of the technique of  forcing  revolutionized logic and allowed him to prove, in 1963, the undecidability of Cantor's  continuum hypothesis  (CH):  Gödel had shown  CH  to be compatible with the  axioms of set theory  and  Cohen  proved the same for the negation of CH...

Ph.D. 1958 (on U-Sets)  |  CH (1963)  |  Fields medal (1966)  |  The Story of Mathematics  |  MacTutor  |  Wikipedia

 Glider in Conway's 
 Game of Life

 John Horton Conway 
 (1937-) John H. Conway   (1937-)

In 1970, Conway found the simple rules of a cellular automaton  (the  Game of Life)  capable of self-replication and universal computation.  His many other original contributions include the ultimate extension of the ordered number line:  surreal numbers (1973).

Ph.D. 1967  |  bibliography  |  New York Times  |  The 3 Conway sporadic groups  |  Wikipedia  |  MacTutor  |  NNDB

Caution sign

 Donald E. Knuth (1938-) Don Knuth,  computer scientist   (1938-)

Donald Ervin Knuth  made the rigorous analysis of algorithms a key aspect of computer science.  Complexity theory  studies the best possible  asymptotic  performance of all procedures that can solve a given problem  (running time and/or memory-space used, as functions of input data size).

Ph.D. 1963 (Caltech)   |   home   |   The Art of Computer Programming  |  Advice  |  McT   |   WP   |   NNDB

 Stephen Hawking (1942-) Stephen W. Hawking,  cosmologist   (1942-)

Diagnosed with  ALS at age 21,  he wasn't expected to reach his 25th birthday,  but went on to establish the pointlike nature of the Universe's origin.  Now communicating via one cheek muscle,  he retains a  legendary status  in the public eye.  Hawking's fame in physics is second only to  Einstein's.

Ph.D. 1966  |  home, bio  |  10 facts  |  No-hair  |  Hawking radiation (1973)  |  Information paradox  |  WP  |  FB  |  NNDB

 Professor Dame Susan Jocelyn Bell Nurnell (1943-) Susan Jocelyn Bell,  astrophysicist   (1943-)

Dame Jocelyn Bell Burnell  discovered the first  pulsar  (neutron star)  in July 1967 and the next three shortly thereafter.  She was then a Ph.D. student supervised by  Antony Hewish  (who would be awarded a Nobel prize in physics, in 1974, for their subsequent joint work).

Little Green Men (LGM 1,2,3,4)   |   Encyclopedia Britannica   |   Wikipedia   |   NNDB

 Gerard 't Hooft Gerard 't Hooft,  physicist   (1946-)

With Veltman, he devised dimensional regularization and proved Yang-Mills theories to be renormalizable (1972).  He anticipated asymptotic freedom in QCD and paved the way for the description of strong interactions by  Gross, Wilczek and Politzer.  He originated the holographic principle.

Ph.D. 1972   |   Nobel 1999   |   Become a GOOD theorist,  or a bad one   |   Beyond quantum?   |   WP   |   NNDB

 Fields Medal

 Bill Thurston (1946-2012) Bill Thurston,  3D topologist   (1946-2012)

His  Geometrization conjecture (1982)  was famously proved,  in 2002,  by  Grigori Perelman (1966-).  It implies  Thurston's own  Elliptization conjecture  and  Poincaré's conjecture (1904).  Thurston's thorough investigation of foliations nearly  killed  the subject.  Fields medallist (1982).

Ph.D. 1972  |  MathOverflow  |  Not Knot  |  Narnia  |  Outside In (1994)  |  2010-06-08  |  2013  |  3D  |  McT  |  WP

 Alan Guth (1947-) Alan Harvey Guth,  cosmologist   (1947-)

Alan Guth  (MIT)  came up with the idea of  cosmic inflation  in 1980 to explain the extremely even distribution of the contents of the Universe at the beginning of the  Big Bang.  For this, he shared the  2002 ICTP Dirac Medal  with Andrei Linde (Stanford)  and  Paul Steinhardt (Princeton).

Ph.D. 1972   |   Cosmic Inflation   |   Inflationary Epoch   |   Britannica   |   Wikipedia   |   NNDB

 Fields Medal

 Edward Witten Ed Witten,  theoretical physicist   (1951-)

He was awarded a Fields Medal (1990) for his mathematical contributions to a physical theory  (String Theory)  which captured the hearts of generations of physicists without any empirical support.  In 1995, Witten unified the 5 or 6 flavors of that theory under a single umbrella he called  M-Theory.

Ph.D. 1976   |   M-Theory   |   Weinberg-Witten theorem   |   Britannica   |   MacTutor   |   Wikipedia   |   NNDB

 Coat-of-arms of Andrew Wiles (1953-)

 Andrew Wiles Andrew Wiles,  number theorist   (1953-)

He worked secretly on a  proof of Fermat's last theorem  for seven years before offering it for publication in 1993.  A flaw discovered by Nick Katz required new insights and the collaboration of Richard Taylor.  By resolving the issue on  1994-09-19,  Andrew Wiles  achieved worldwide fame!

Ph.D. 1979  |  Modularity  |  Clay Math 2001  |  Abel prize 2016.  |  Interview.  |  Britannica  |  McT  |  WP  |  NNDB

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