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].

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

He founded metaphysics
and argued that nothing remains still,
which led him to a Mach-like principle of Relativity.
Dubbed the weeping philosopher
(while Democritus is the laughing philosopher).
He called Pythagoras a fraud.

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).

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.

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.

He put Pythagoreanism
in writing (including numerology).
He is credited with the
first astronomical system
where the Earth wasn't at the center of the Universe.
After a second fire destroyed the Pythagorean campus at
Croton
(c. 454 BC) Philolaus fled
to Lucania
and Thebes.
He taught Archytas.

A 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.

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".

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

Mathematician, statesman, staunch Pythagorean.
Student of Philolaus
and teacher of Eudoxus.
Invented the pulley and the screw.
Archytas considered surfaces generated by rotating curves and could
double the cube
by intersecting three of those (defining the
Archytas curve in the process).

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.

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.

In 338 BC, he was (narrowly) elected third rector of the
Academia
(suceeding Plato's nephew Speusippus of Athens).
Unlike other atomists, he
envisioned the ultimate constituents of matter as lines; not corpuscules.
Xenocrates may thus be construed as the first string theorist...

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.

Following Democritus,
he believed only matter existed, consisting of atoms and void. Unlike
Pythagoras or Plato
he didn't believe in an immortal soul and argued that death shouldn't be feared.
His philosophy and physics (causality and conservation laws) inspired
Lucretius and Newton.

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

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).

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).

Also known as Philo Mechanicus, he was an engineer
who journeyed to Rhodes and Alexandria.
He is credited for inventing the
escapement,
the water mill and the
gimbal suspension (described by Cardano).
Philon constructed the Delian constant
by intersecting a circle and an hyperbola.

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.

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.

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-will.
Rutherford's motto is a quote from Lucretius.

Lucius Annaeus Seneca the Younger served as
Nero's tutor and an advisor early in his
reign. He retired from public life in 62.
He reflected on comets, meteors, meteorological optics, thunder and the colors produced by
glass corners. Forced to commit suicide as a suspect in a
plot against Nero.

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

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).

Earliest female experimentalist on record (signing
Miriam the prophetess, sister of Moses).
The tribikosstill
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.

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.

A leading member of the late Pythagorean School.
His Introduction to Arithmetic
(Arithmetike eisagoge, c. AD 100) was the standard arithmetic text for more than 1000 years but it
contains no proofs and has several elementary mistakes in it.
He knew only 4 perfect numbers (6, 28, 496 and 8128).

A resident of Rome who spent his youth in Alexandria,
he recognized geodesics on a curved surface
as analogs 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.

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.

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.

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.

A 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.

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.

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.

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.
Hypatia's murder marks the beginning of the Dark Ages in the West.

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...

Ioannis Grammaticus was one of the last to hold the chair of philosophy in
Alexandria.
Controversial in his time,
he was the only writer in late antiquity to point out that the duration of a body's free fall doesn't depend on its weight
(contra Aristotelem ). Galileo would give him credit for that.

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 celebrated
formula
for the area of a quadrilateral is only valid
for cyclic quadrilaterals.

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.

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.
The quadratic formula is due to
Al Kwarizmi.

Born in the Cuba City of
Transoxiana
(Ferghana region of far-eastern Uzbekistan).
Worked in Baghdad and died in Egypt.
Alfraganus summarized and perfected ptolemaic astronomy in
The book of 30 chapters (c. 833). Messed-up the al-Ja'fari
branch of the Nahrawan Canal
near Samarra.

A Sabian, not a Muslim,
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.
His remark that there are as many integers as even ones
helped Dedekind characterize infinite sets
(as equipollent to a proper subset).

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.

Precursor of Alhazen
largely ignored before 1993
(Roshdi Rashed).
First Muslim known to have studied Ptolemy's Optics.
In Burning Mirrors and Lenses (c.984) he
first stated the
proportionality of sines in a refracted ray
(Snell's law) and
worked out the exact shapes of anaclastic lenses.

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.

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).

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 state the limitation of
Brahmagupta's simplified formula
for areas of quadrilaterals.

Abu Alî al-Hosain ibn Abdallâh ibn Sîna is also known as Pur Sina,
the Prince of physicians.
He was a child prodigy born on 980-08-23 in the Persian city of Afshaneh,
near Bukhara.
7 centuries before Newton,
he held that motion in a vacuum would be self-sustaining
(first law of dynamics).

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

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.

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.

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...

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 Grosseteste, Roger Bacon became the
most active early proponent of the scientific method in Europe.

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.

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).

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.

Star student of Jean Buridan,
Nicolas 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...

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 later, in the West.

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.

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).

A 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".

Lecturer in arithmetic and geometry since 1496 at
Bologna,
Pacioli visited in 1501-02 and somehow inspired
the private solution of the cubic equation in depressed
form (quadratic term suitably removed)
passed by Ferro to his son-in-law and successor (1526) Hannibal della Nave.

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.

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.

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).

Born into a noble
Calabrian family,
he studied in Milan, Rome and
Padua.
He left the universities in 1535, without a doctorate.
Once married (1553) he went back home to
Cosenza
and reorganized what became the
Cosentian Academy.
He revolted against Aristotelian doctrines.

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).

Breaking with the precepts of Galen,
Andreas 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.

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.

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.

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).

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).

Harriotre-discovered
the law of refraction in July 1601
(before Snell and 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.

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 (1609).

He found vision comes from inverted images formimg on the retina.
His 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.

Inventor of the slide rule (1630).
The symbols × for multiplication and ::
for proportionality are due to him.
Ordained in 1603, vicar of Shalford in 1604, rector of Albury (1610-1660).
For half a century, he mentored many mathematicians, including John Wallis (1616-1703).

Founder of pneumatic chemistry and biochemistry,
who coined the word gas (1632).
He famously proved that plant bulk doesn't come from soil by weighing a potted
willow tree after 5 years.
His chemical work was published in 1640 by his son,
Franciscus
Van Helmont (1614-1698).

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.

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.

Building on the fundamental results of Pappus,
Desargues 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.

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).

In Pisa, Cavalieri was mentored by
Benedetto Castelli (1578-1643)
who put him in touch with Galileo.
Cavalieri'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...

Orphan. Assistant to Castelli, then Galileo.
Torricelli invented the barometer in 1644: He
figured out that the rarefied mercury vapor above the mercury is nearly a vacuum.
What pushes the liquid up the tube
is the (variable) atmospheric pressure.
Gabriel's horn (1643).

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.

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).

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.

In 1660 (as assistant of
Robert Boyle)
his law of elasticity affirmed the notion of force.
After the Great Fire (1666)
he surveyed half of London and designed many new buildings.
For 40 years, he produced new experiments weekly for the Royal Society.
He was a microscopic & telescopic observer.

The Japanese Newton.
Second son of a Samurai warrior.
Adopted by a technocrat (Gorozaemon SEKI )
whose name he took.
Some of his findings predate their Western discoveries:
Determinants (1683)
Bernoulli numbers, etc.
He was the teacher of Katahiro TAKEBE (1664-1739).

Also known as Lucrezia Piscopia,
Elena 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.

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).
It was first called "Rolle's theorem"
by Drobisch (1834)
and Bellavitis (1846).

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

Chemist, astronomer and electrician.
In 1729 (well before
Du Fay)
he realized that electricity could flow through conductors
but not insulators (both names were coined by
Desaguliers in 1742).
Gray was the first recipient of the Copley Medal (1731).
He died a pauper.

French Huguenot, tutored by
Jacques Ozanam (1640-1718) in 1684-85.
He fled to England shortly after 1685,
eking out a living as a tutor and actuary.
He befriended the likes of
Halley and Newton
and entered all major mathematical societies: London (1697), Berlin
(1735) and...
Paris (1754).

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.

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 divergentasymptotic series.

Attempting to detect stellar parallax
(which Bessel observed in 1838) he discovered
the aberration of light and obtained a good estimate of the speed of light (1728).
Bradley later found the nutation of the Earth's axis (1742). He was both
Savilian Professor (1721-)
and Astronomer Royal (1742-).

Having entered the University of
Glasgow at age 11, he was granted an MA three years later for a thesis entitled
The Power of Gravity. He then read divinity
until elected professor of mathematics at 19, in
Marischal College,
after a 10-day competition.
(That record would hold until 2008.)

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.

Independently of
Watson
(1746) Franklin discovered the conservation
of charge by positing opposite signs for what
Du Fay
(1733) had called resinous (-) and vitreous (+)
electricity.

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.

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.

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.

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.

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
Pope Benedict XIV
but she never went there (the first woman to hold
a chair in Europe was thus Laura Bassi, in 1776).

CambridgeDon.
He invented the torsion balance
(before Coulomb) and
found the inverse square law for magnetic poles (1750).
Pioneered seismology (1760).
Detected radiation pressure.
Conceived, before Laplace, of dark stars
with escape velocities exceeding the speed of light.

Etienne Montucla was a mathematician and a 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).

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 geometry.
Bézout's
little theorem says (x-a) divides the polynomial
P(x)-P(a).

Dutch-born British physician who discovered the principles of
photosynthesis.
Building on the work of
Joseph Priestley (1771)
Ingenhousz showed that green plants do require sunlight to produce
oxygen (1779). He was honored by a
Google Doodle
on his 287-th Birthday (2017-12-08).

Né Friedrich Wilhelm Herschel in
Hanover,
where he followed his father as a military musician, before emigrating to England (1757).
He built his first large telescope in 1774.
He discovered the planet Uranus on 1781-03-13.

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.

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.

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

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 (his 1765 drafting method).

Initiated to mathematics, in
Caen, by
Christophe
Gadbled
and Pierre Le Canu,
Laplace 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).

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.

Because of typhus,
she only grew to be 4'3'' (1.295 m)
and wasn't expected to marry. She was denied an education until she joined
the household of her brother (1772) with whose help
she became an award-winning astronomer; the first woman to receive an official salary
as a scientist (1787).

A student of l'abbé Marie (1738-1801)
Legendre grew to be 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).

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.

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).

Quaker schoolteacher. His first paper was on the genetic
red-green color blindness (Daltonism)
which affected him and 8% of European boys but only 0.64% of the girls.
Studying meteorology, he found the law of partial pressures (1801)
which supported his celebrated atomistic views of chemistry.

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).

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.

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.

Expelled from
Mezières
for shady reasons (1793)
he became a student at Ecole Polytechnique upon its creation (1794).
Malus discovered the polarization of light by reflection off non-metallic surfaces (1809)
and by double-refraction (1810)
which brought him multiple honors.

At 13, she was inspired by
Montucla's tale of the death
of Archimedes.
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).

Lorenzo Romano Amedeo Carlo Avogadro, Conte de Quaregna e di Cerreto
was born in Turin to a noble family of
Savoy-Sardinia.
In 1820, he accepted the first chair of mathematical physics at the
University of Turin, which
had to close in 1822. Avogadro got the chair back in Nov. 1834.

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 19, his breakthrough about
constructible polygons helped him choose
a mathematical career.
Honored by a Doodle on 2018-04-30.

Perfecting the ideal gas law, Gay-Lussac formulated
the isochoric law in 1802.
With Humboldt (1805) he figured
that water is evolved from one volume of oxygen and two volumes of hydrogen.
His generalizations to other gaseous reactants (1809) prompted
Avogadro's law (1811).

Née Fairfax.
Two sons
from first marriage (1804) to Samuel Greig (1778-1807).
4 children from second marriage (1812) to
William Somerville (1771-1860).
Her study of Uranus (1836) paved the way for the
discovery of Neptune (1846).
She and Caroline Herschel,
were the first women in the RAS.

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

In 1799, he left school at the age of 14 to become an import-export apprentice,
studying various subjects on his own time. His first astronomical paper (1804)
eventually led to academic appointments and an honorary doctorate (1810).
He found the first distances to stars using
parallax (1838).

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 1848 and was instrumental in abolishing slavery in the
French Colonies (1848).

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).

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
whose two polarizations don't interfere with each other.
He invented
Fresnel lenses for use in lighthouses.

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

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 made analysis rigorous.
He originated the calculus of residues (1826) and
complex analysis (1829).

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.

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).

He gave the terms
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.

Green worked in his father's bakery and mill.
He entered Cambridge
at the age of 40 (in 1833) 5 years after self-publishing his best work
(extending the work of Poisson in electricity and magnetism)
using self-taught mathematical physics.
Green coined the word potential.

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.

He found the law of induction independently of
Faraday (mutual inductance)
and discovered self-inductance (1832).
The SI unit of inductance
was named after him in 1960.
His relay (1835) made practical the
electrical telegraph devised by
Schilling (1832) and patented by
Morse (1847).

Born in Lyme Regis, she first collected fossils for
tourists from the nearby cliffs during winter storms, before the Sea could reclaim them.
At age 12 (1811) she found the skull of the first properly idenfified
Ichthyosaur
(Blainville, 1835).
She later helped promote the notion of extinction.

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.

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.

A pupil of Lhuilier in
Geneva,
he earned a top prize with Colladon
for measuring the speed of sound in water (1826-27). They both moved to Paris.
Teacher at Rollin (1830).
French citizen (1833). He succeeded Ampère at
Académie des sciences (1836)
and Poisson at Polytechnique (1840).

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.

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.

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.

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.

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

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).

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.

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-hypersphere.
Schläfli also classified
allregular polytopes.

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 Assembly.
Catalan's conjecture (1843)
saying that the only solution of
1+x^{m }= y^{n} is 1+2^{3 }= 3^{2},
was proved in 2002.

Julius Robert Mayer was ennobled on 1867-11-05
(in Württemberg)
for his founding rôle in thermodynamics:
In 1841, he gave a preliminary version of the
first law (energy is conserved).
He identified oxidation
as the main source of energy for living organisms (1842).

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.

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 ]

By measuring the mechanical equivalent
of heat, his paddlewheel experiment (1845)
established the first law of thermodynamics,
whereby the total energy (heat and mechanical energy) is conserved.
The SI unit of energy was called joule
(J) in his honor in 1889, shortly before he died.

He could only gain access to books (and a self-education) by becoming a
janitor at the museum of the
Andersonian Institute
in Glasgow (1859-67). Once amended for Northern dominance by
Milankovic, his
proposed astronomical causes for climate variations would be vindicated in 1976.

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.

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.

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).

Clausius formulated the second law of thermodynamics.
He coined the word entropy (1865) for which he introduced
the deprecated clausius unit
(1 Cl = 1 cal/°C = 4.184 J/K).
His only doctoral student was
Carl von Linde (1842-1934)
of gas liquefaction fame.

Father of genetics.
Mendel communicated his results to
Karl von Nägeli (1817-1891)
who expressed contempt for them and was instrumental in burrying them for three decades.
Mendel's laws of heredity were rediscovered in the 1890s by
Hugo de Vries (1848-1935).

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,
orthogonal polynomials and elliptic functions.
He proved e transcendental in 1873.

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.

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.

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.

Born William Thomson, Lord 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).

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.

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

In 1865, Kekulé had a revelation of the
cyclic structure of benzene in a daydream where he saw
snakes biting their own tails.
He first proposed a planar molecule of trigonal symmetry,
with alternating single and double bonds
(instead of the currently accepted perfect hexagonal symmetry).

In 1864, his equations
unified electricity and magnetism, by describing electromagnetic
fields traveling at the speed of light.
In 1866, he proposed (independently of
Boltzmann) the Maxwell-Boltzmann
kinetic theory of gases. In 1867,
Maxwell's Demon helped equate entropy and information.

Julius Wilhelm Richard Dedekind was
the last doctoral student of Gauss
(1852)
but he also learned much from Dirichlet
after his doctorate. In 1858, he defined every real number
as a Dedekind cut
of rationals (as Bertrand has done in 1849).
In 1871, he introduced algebraic
ideals.

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).

Born in Canada. In 1861,
he received a commission in the corps of professors of mathematics in the US Navy.
He reached the mandatory retirement age for captains in 1897,
but was promoted to rear-admiral so he could remain in the service.

Bringing to a great conclusion the works of
Gauss,
Bolyai,
Lobachevsky 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).

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 molecular interactions explain gas liquefaction.

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

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.

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.

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).

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.

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. Thomson's advisor.

Founder of modern bacteriology.
He identified the etiologic agents of
anthrax (1876),
tuberculosis (1882)
and cholera (1884).
His Google Doodle
(2017-12-10) shows the potato slices he first used for bacterial growth and the
Petri dish invented by his assistant
Julius Petri (1852-1921).

With Felix Klein,
Sophus 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.

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.

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.

He received the first Nobel prize in physics (1901) for his discovery of
X-Rays, on
1895-11-08.
In his honor, element 111 was named
Roentgenium (Rg) in 2004.

Swedish mathematician who founded
Acta Mathematica in 1882
and served as chief editor for 45 years.
His own research specialized in what was then called the theory of finctions
(complex analysis). A major theorem in the field
is due to him, so is a key function
for fractional calculus.

With two early railway patents
(frog and
car replacer, 1867) he financed a major one: air brakes (1869)
which he'd make failsafe (1873) and responsive (1876).
He distributed natural gas and AC electricity (with transformers)
prevailing over Edison's DC.
He made Saturday a half-holiday (1881).

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.

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_{6 },
E_{7 },
E_{8 },
G_{2 },
F_{4 })
and three regular families:
special linear groups SL(n),
orthogonal groups O(n), symplectic groups Sp(2n).

Born on 1849-4-25 (43^{2}, 2^{2}, 5^{2 })
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.

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

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.

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 1897,
who measured the mass-to-charge ratio).

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

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.

Picard's little theorem (1879) says that any nonconstant entire function
takes any value infinitely often, with at most one exception (dubbed lacunary).
His great theorem says that, about an
essential singularity, an
analytic function takes every value infinitely often, with one possible exception.

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.

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.

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 symboliclogic (1895) and
devised a new natural language (1903).

Like his mentor
Paul du Bois-Reymond
(a student of Kummer)
Otto 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).

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").

Barred from higher education as a woman, she accessed
scientific litterature through her younger brother Friedrich
(PhD 1889)
and was helped by Rayleigh once she sent
him her research on surface tension.
Her homemade apparatus paved the way for the
Langmuir-Blodgett trough.

Polytechnicien (X1880). He held the chair of Professor of Geometry (1912-1937)
at Polytechnique, preceeding Gaston Julia.
Credited for the (lost) science of
nomography (1884) in spite of the key rôles of
Charles Lallemand (1857-1938; X1874)
and Rodolphe Soreau (1865-1935; X1885).

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 L^{p}triangular inequality (1896)
and to the relativisticscalar product
in spacetime (1908).

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.

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).

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

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.

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).

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

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).

His papers on the astronomical consequences of
Einstein's general relativity
(1916-17) stirred early interest. De Sitter argued for an
expanding Universe well before Hubble
found any evidence for it.
He also gave an acceleratingsolution
for early and late regimes where matter is negligible.

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

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.

Last student of Ludwig Boltzmann, she collaborated with
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 in German).
She correctly explained the related
mass defect (1938).

He improved upon the forgotten climate model of James Croll
using new geological data and a better mathematical insight that the
key to climate change is the Summer melting of the Northern ice cap over land masses,
rather than the growing of either ice cap over water in the cold season.

A student of Ludwig Boltzmann in
Vienna.
In 1901, he was sent for 18 months to
Göttingen
where he met Tatyana, the Russian student
he'd marry after getting his doctorate, back in Vienna (1904).
He mentored many rising stars, from
Gregory Breit (in 1921)
to Jan Tinbergen (Nobel 1969).

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!

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 firstNational Medal of Science, in 1963.

Sierpinski was the first person to lecture on set theory
(1908).
After WWI, he organized mathematics in Poland around
set theory & logic,
topology and real analysis.
He wrote about 600 papers on those topics. Later in life,
he produced about 100 more papers on number theory.

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

He coined the term quantum mechanics%nbsp; in 1924.
Born's probabilistic interpretation of Schrödinger's wave function
ended determinism in physics but provided a firm ground for
quantum theory.
Irene Born, the eldest of his 3 children, is the mother of
Olivia Newton-John.
Doodled
on 2007-12-11.

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.

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).

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.

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.

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).

In 1929, with sketchy observational data, he saw that
galaxiesrecede at speeds proportional
to their distances from us. The coefficient of proportionality Ho
(Hubble's constant) varies inversely as the age of the Universe
(thus proved to be expanding,
by the cosmological principle).

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.

Normalien (1911).
He lost his nose in combat (1915).
His 199-page memo on the iteration of rational functions (1918)
won a Grand prix
which made him famous (groundwork of Mandelbrot's
fractals).
In 1937, Julia suceeded
Maurice d'Ocagne to lead mathematics at
Polytechnique, with Lévy.

Jesuit Catholic priest (1923). Father of the Big Bang theory (1927)
which he called the primeval atom.
First proponent of Hubble's law.
Lemaître passed away on June 20, 1966, shortly after his theory had been vindicated experimentally by the
discovery of the
CMB in 1964 (Penzias & Wilson).

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.

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."

She was the first to propose (1925) that stars consist mostly of hydrogen and helium, the two
most abundant elements in the Universe.
She married her colleague Sergei Gaposchkin (1889-1984) in 1934 and had three children with him.
They met in Germany and she helped him join the Harvard faculty.

She obtained her Ph.D. from Oxford
in 1930, under G.H. Hardy
and Ted Titchmarsh.
She first met J.E. Littlewood as he was sitting in her jury.
With him, she would pioneer the use of
chaos theory in radio engineering (1945).
First female mathematician elected to the Royal Society (1947).

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.

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.

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).

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 theory,
decision analysis,
automata theory. fault-tolerant systems,
etc.

Son of Elie Cartan, son-in-law of
Pierre Weiss.
Key founder, with Weil, of
Bourbaki (1935) which consumed
a large part of his research activities. Leading professor at
ENS
for several decades.
Henri Cartan was instrumental in reconciling French and German mathematics after WWII.

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).

The completeness theorem in his dissertation (1929)
states that a statement true in everymodel 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.

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

He fled Germany in 1933, after losing his post at
Tübingen
because of his Jewish ancestry.
In 1935, he got a position at Cornell,
which he never left except for wartime work at MIT and
Los Alamos
(as head of the theoretical division).
Nobel prize for his work on nuclear fusion in
stars of all sizes.

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.

He conceived electronic television in 1922 (at the age of 14) applied for a patent in 1927
and first tested it on 1927-09-07.
His wife Elma Gardner "Pem" Farnsworth
(1908-2006)
was the first person to be televised. He demonstrated nuclear
fusion on a tabletop and held about 300 patents.

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.

He died (in a mountaineering accident) before Bourbaki was formed.
His close friend Chevalley (who, like him, became
normalien at a very young age)
made sure they took his views on logic into account.

Born in Johannesburg,
where his father was French Consul.
His parents wrote the Oxford Concise French Dictionary.
Normalien at the age of 17 (1926)
he would be the youngest founding Bourbakist (1935).
He revived Clifford algebras
and had a major impact in Group theory
and Ring theory.

Astrophysicist.
Chandra was the nephew of Raman
(1888-1970; Nobel 1930).
On Chandra's 107th birthday, Google's home page in 28 countries featured an animation illustrating the
Chandrasekhar limit (1.44 solar masses)
beyond which a star's death can only yield a
neutron star or a black hole.

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.

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.

Son-in-law of Paul Lévy.
"One night in 1944", he figured out that the distributions
used in physics (including Dirac's delta) were
continuous linear forms over a restricted set of
smooth test functions. He found the Fourier transform
to be a linear automorphism
among tempered distributions.

Got his PhD (1942) under Wheeler.
In 1949, he introduced Feynman diagrams
for the relativistic quantum theory of electromagnetism
(Quantum
electrodynamics = QED) using perturbation theory.
This has helped visualize all other types of fundamental interactions ever since.

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.

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).

Raised 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 QEDdiagrams to be equivalent,
to the methods of Schwinger or
Tomonaga.
He joined Princeton's IAS in 1953 and never left.

A 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 laureate (2003).

Father of modern cosmology.
Last doctoral student of Dirac (before he moved to Florida) with a thesis entitled
"On the Origin of Inertia". He served as thesis advisor to Stephen Hawking in 1966.

Joe Kruskal obtained his Ph.D. from Princeton in 1954, under
Lyndon and Erdös.
He was the younger brother of the statistician
William H. Kruskal (1919-2005)
and the physicist
Martin D.
Kruskal (1925-2006) who is known for the Kruskal principle,
used in magic.

In his 1950 thesis about non-cooperative games,
the notion of a
Nash equilibrium
made 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 (1994) and the
Abel prize, at 86 (2015).

John Stewart Bell earned his Ph.D. 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).

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.

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.

His father, Lionel,
was a geneticist. His mother, Margaret, was a physician.
His older brother, Oliver,
was a professor of mathematics. His younger brother,
Jonathan,
was 10 times British Chess Champion.
Roger penrose put forth twistors in 1967
and spin networks in 1971.
Nobel 2020.

Normalien at 18 (Ulm, 1951).
Founding father of soft matter
physics (French: matière molle)
including liquid crystals and polymers, where the dominant phenomena occur
at an energy scale comparable to thermal energy at room temperature
(where quantum aspects are negligible).

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.]

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...

Langlands is now a professor emeritus at the
IAS,
where he occupies Albert Einstein's former office.
The Langlands program, oulined in a letter to Weil (1967)
seeks to connect algebraic number theory (Galois groups) with automorphic forms and representations
over local fields and adele rings.

In 1970, Conway found the simple rules of a cellular automaton
(the Game of Life)
capable of self-replication and universal computation.
His other original discoveries include
the ultimate extension of the ordered number line
(surreal numbers, 1973)
and the free-will theorem (2006).

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).

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.
Communicating only via one cheek muscle,
he achieved a legendary status in the public eye. Hawking's fame in physics
is second only to Einstein's.

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).

Alan Guth (MIT) came up with the idea of cosmic inflation
in 1979 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).

Classifying the noncommutative structures underlaying any
foreseeable quantum theory (1973) he found an unavoidable evolution indicator
(modulo inner automorphisms)
looking like emergent time.
That paves the way for a quantum theory of spacetime, unifying gravity with all other forces.

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.

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!

Grigori Yakovlevich Perelman turned down the Fields Medal (2006)
and a million-dollar Clay prize (2010) for his 2002 proof of
Thurston's geometrization conjecture,
implying the legendary
Poincaré conjecture (1904).
Since 2005, Perelman has been living as a
recluse
in Saint-Petersburg.