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Numericana's  Biographies
© Copyright 2006-2017   by   Gérard P. Michon, Ph.D.

Numericana pages provide biographical information in three distinct ways:
1.   Direct links  to biographies published by others, most notably the remarkable collection of  MacTutor  biographies edited by  J.J. O'Connor  and  E.F. Robertson  at the  School of Mathematics and Statistics  of the  University of St Andrews  (Scotland). 
2.   50-word biographies  within Numericana itself, which usually provide  several  links to noteworthy online biographies.  They appear on a few pages dedicated to a very limited number of themes:  Web Authors, Giants of Science, Solvay Attendees...
3.   Orphan biographies  in no particular format or size, are regrouped on this page  (inaugurated on March 29, 2006 with notes about Evariste Galois).  Scientists of various notorieties are listed here  (in chronological order of birth)  as the need arises.

Babinet, Jacques
Bigourdan  Etienne
Cosserat  brothers
Drach, Jules
Dulong, Pierre Louis
Galois, Evariste
Gérardin, André
Glénisson, Yves
Houël, Jules
Laurent, Pierre
Le Verrier, Urbain
Lucas, Edouard
Mathieu, Emile
Midy, Etienne
Miquel, Auguste
Morton, Pierce
Padé, Henri
Petit, Paul
Poulet, Paul
Puiseux, Victor
Roch, Gustav
Tannery, Jules
Vernier, Pierre
Verron-Vernier, Hippolyte
Vessiot, Ernest
Yvon Villarceau, Antoine
Pierre Vernier

Pierre Vernier   (1584-1638)
MacTutor   |   Wikipedia   |   Galileo Project   |   Encyclopedia Britannica (1911)

French mathematician, military engineer and instrument-maker, born in Ornans (near Besançon, Franche-Comté, now in France)  where a collège is named after him  (so is a public institute  for technological innovation, located in Besançon).  Pierre Vernier served the King of Spain who was ruling  Franche Comté  at the time.  In 1623, he was awarded the title of citizen of Besançon for his work on the fortifications of the city.

In a treatise entitled  La Construction, l'usage, et les propriétés du quadrant nouveau de mathématiques  (Brussels, 1631)  Pierre Vernier published a description of the sliding scale named after him and used in quadrants, sextants, calipers and other precision measuring instruments.  Originally, he described a  quadrant  allowing angular measurements to a precision of one minute, using a main scale graduated in half-degrees and a movable sector divided into 30 equal intervals spanning 29 half-degrees.

The underlying idea can be traced to the  multiple fixed scales of the  nonius  invented by the Portuguese mathematician Pedro Nunes (1502-1578)  which Tycho Brahe (1546-1601) dismissed as unpractical  (the multiple scales were also difficult to engrave to the required precision).  Improvements were attempted by Jacob Curtius (1554-1594)  and by the Bavarian Jesuit  Christopher Clavius (  Schlussel,  1538-1612)  who is best remembered as the astronomer who engineered the modern  Gregorian calendar.
By replacing the full-length fixed scales of the  nonius  with a short movable scale,  Pierre Vernier  eliminated the need for auxiliary tables and invented a truly practical device  (which would become popular early in the eighteenth century).  That innovation was properly named after Vernier by Lalande in 1771, but the earlier etymology  (nonius)  survives in some languages.

In modern times, the most common Vernier scales are  decimal  ones, featuring  10  intervals spanning  9  intervals of the main scale.  If the two scales coincide precisely after  n  Vernier intervals, then the measurement exceeds by  n/10  whatever is indicated on the main scale  (just before the zero of the Vernier scale):

 Vernier scale

Etienne Midy   (c. 1773,  fl. 1846)
Midy's theorem (1835)   |   Midy à quatorze heures (Forum in French, 2010)

His name is spelled  Meidy  in some records.  He was probably already teaching when  Napoléon  instituted the  lycées,  in 1802.  Midy himself advertised he had taught  mathématiques spéciales  at Cahors and Orléans, before moving to Nantes.

At the  Collège Royal de Nantes  (future  Lycée Clémenceau)  Midy first taught  mathématiques élémentaires  from 1833 to 1837.  That post was entrusted to a young  normalien  (Alexandre Lepord, ENS 1834)  when Midy was promoted to teach  mathématiques spéciales  from 1837 to 1838  (after M. Dorveau resigned).  Midy would be replaced in this capacity by M. Gascheau  (previously, professor of physics)  when a ministerial decree  (1838-11-17)  allowed him to retire.

In Nantes,  Etienne Midy lived  3, rue Richebourg,  next to his workplace.

"De quelques propriétés des nombres et des fractions décimales périodiques" (Forest, Nantes, 1835). 21 pages.
"Du théorème de M. Sturm et de ses applications numériques" (Nantes & Paris, 1836)
After his retirement in 1838,  Etienne Midy published 15 times,  from 1842 to 1846,  in
Nouvelles Annales de mathématiques  (Journal des candidats aux écoles Polytechnique et Normale).
"La Conchoïde"  9, 2, pp. 281-292  (1843)   |   "Note sur le folium de Descartes"  1, 3, pp. 293-303  (1844)
"Analyse indéterminée du premier degré" pp. 146-   &   "Equations polaires" pp. 597-,  4  (1845)
"Sur une propriété des nombres"  pp. 640-646,  1, 5 (1846)

  Pierre Louis Dulong
Pierre Louis Dulong

Pierre Louis Dulong   (1785-1838; X1801)
Wikipedia   |   Encyclopedia Britannica (1911)

An only child born in Rouen and orphaned at the age of 4, Dulong was brought up by an aunt.  He was educated at Centrale-Auxerre and Centrale-Rouen.  He entered  Polytechnique  at the age of 16.
He became a physician and worked as a chemist with Berthollet in Arcueil.  Dulong discovered the explosive properties of  nitrogen chloride  in 1811, losing an eye and two fingers in the process.

He worked as a  répétiteur  (scientific coach)  at the  Ecole Normale Supérieure  and was a chemical technician at  Polytechnique  under  Louis Jacques Thénard (1777-1857)  a famous teacher who had invented  cobalt blue  in 1802  (that  pigment  is still known as  Thénard's blue  or  bleu de Thénard ).  Dulong was an examiner for the entrance exam of  Polytechnique  (1813).  He taught physics at the veterinary school of Maison-Alfort until 1827.

In 1820, Dulong and Berzelius determined that water was an oxide of hydrogen.

After the death of  Alexis Petit  (1791-1820)  Dulong held the chair of physics at  Polytechnique  from 1820 to 1829.  He was thus the third holder of the chair of physics at  Polytechnique,  following Hassenfratz (1794) and Petit (1815). 

A second chair of physics would be created for Jules Jamin (1818-1886) who taught at Polytechnique from 1852 to 1881.  The sixth holder of that second chair, from 1936 to 1969, was Louis Leprince-Ringuet (1901-2000; X1920N) who was instrumental in obtaining the creation, in 1958, of a third chair of physics at Polytechnique for Bernard P. Grégory (1919-1977; X1939) who would become director-general at CERN (from 1965 to 1970) after the retirement of Viki Weisskopf (1908-2002).

For his joint work with Petit  (including the formulation of the Dulong-Petit law, in 1819)  Dulong was elected to the physics section of the French  Académie des sciences  (of which he would become president, in 1828). 

Dulong was director of scientific studies at  Polytechnique  from 1830 to 1838.  His successor in this capacity was  Gustave Coriolis (1792-1843; X1808).

Maître de conférences à Normale (1830), il est professeur de chimie en Sorbonne (1832). Il fut membre de l'Académie de médecine. Les "Lois de Dulong" ont fondé l'analyse des minerais insolubles. Il étudie la force élastique des vapeurs et la loi de Mariotte, imagine le cathétomètre et le thermomètre à poids. Dulong et Arago formulent la loi sur les machines à vapeur demandée par le gouvernement en 1825.
--- Refer. : Dbf 12, 83 (bibliogr.) - Larousse 2, 992-3 (gr.) - LC 1, 269-85 (méd.)

  Jacques Babinet
Jacques Babinet

Jacques Babinet   (1794-1872; X1812)
Christian Nitschelm   |   Wikipedia

Jacques Babinet was born on 1794-03-05 in Lusignan (Vienne)  to Jean Babinet, mayor of Lusignan, and his wife Marie-Anne Félicité Bonneau du Chesne, daughter of a lieutenant-general.

He attended the  Lycée Napoléon  (formerly  Ecole Centrale du Panthéon,  currently  Lycée Henri IV)  where he studied under Jacques Binet (1786-1856; X1804)  to prepare for  Polytechnique,  which he duly entered in 1812.  (Babinet would later become an examiner there.)

After a one-year initial formation at Polytechnique, Babinet chose to specialize as an artillery officer and went through the Ecole militaire de Metz  (1813)  before being briefly assigned to the Fifth regiment of Artillery, in Strasbourg.

At the Restoration (1814) he left the Army to become a teacher.  He was professor of mathematics in Fontenay-le-Comte and professor of physics in Poitiers  (near his birthplace)  before being awarded the chair of physics at  Saint-Louis  in 1820.

From 1825 to 1828,  Babinet delivered a course of lectures on meteorology, including meteorological optics, at ???

In 1838, he succeeded  Félix Savary (1797-1841; X1815)  at the  Collège de France.  In 1840, Jacques Babinet was elected to the  Académie des sciences  (General Physics section).

The primary focus of his research was the study of  diffraction,  which he used to measure wavelengths more accurately than ever before.  In 1827, he proposed a standardization of the  ångstrom  based on the wavelength of the prominent red Cadmium line.  (Babinet's idea was used to define the meter, between 1960 and 1983, in terms of the wavelength of a ray in the spectrum of Krypton.)

He also constructed a hygrometer and improved the valves of air pumps to achieve a high vacuum.

Jacques Babinet achieved considerable fame as a popularizer of science, in public lectures and popular articles on a wide range of topics:  geology, mineralogy, astronomy, meteorology...  He passed away in Paris on 1872-10-21, at 78.

Jean Hippolyte Verron-Vernier   (1800-1875)
Thèse de mécanique (1824)

Hippolyte Vernier  made his mark as an elite teacher.  In particular, he was the  very first  mathematics instructor Evariste Galois ever had  (starting in February 1827).  At the time, Vernier was boldly shunning Euclidean tradition in favor of  Legendre's  textbook  Elements de Géometrie  (1794).

Verron-Vernier entered the  Ecole Normale Supérieure  in 1817.  (Well, it was just called  Ecole Normale  in those days.)  He was one of only three scientists to do so that year.  The other two were  Joseph Avignon (1799-1867)  and  [Henri]  Jean Adolphe Faure (1799-1879)  about whom very little is known.

Upon graduation,  in 1820,  he was named  agrégé en mathématiques élémentaires à Angers.  This was the year before the  agrégation  of French professors became a national competition  (it still is).  Vernier's direct appointment to teach high-school seniors indicates that he was highly esteemed.  His classmate,  Joseph Avignon  was likewise appointed in Caen at that same time, to teach science to high-school seniors and also physics to  mathématiques spéciales  students.  When Avignon moved on two years later (1822-11-09) Vernier succeeded him in that position at the  Collège Royal  of Caen, where he made time to write his doctoral dissertation.

In his doctoral thesis entitled  "Distribution de l'électricité à la surface des corps conducteurs"  (July 1824)  he made a modest extension to three spheres of a two-sphere result recently obtained by Poisson.  His doctoral examination committee comprised Poisson himself, Cauchy and Lacroix, among others.

By the time he was appointed to  Louis-le-Grand  (1826)  Vernier had made several other publications at the research level  (analysis, electrostatics, mechanics, astronomy).  A few months later, the young Galois walked into his class...

In October 1835,  Véron-Vernier  was promoted to the chair of  mathématiques spéciales  at  Henri IV  to replace M. Navarre  (himself  agrégé  in 1811 and promoted  inspecteur d'académie  for Paris).

Later in his career, Véron-Vernier became a popular writer of textbooks for primary and secondary education  (weights & measures, arithmetic, geometry).

He married M. Neveu in Paris, after 1850.  When he passed away in 1875, the official title of  Véron-Vernier was  inspecteur honoraire d'académie à Paris.  He had been  inspecteur d'académie  at Melun, covering  Seine-et-Marne.

According to a fantastic literary legend, possibly a hoax with some elements of truth, Hippolyte fathered a mysteriously plagiarized poet called Hugo Vernier (1836-1864)  born to Sarah Judith Singer on September 3, 1836 in Vimy.  Legend has it that Hugo Vernier secretly married (1863) Virginie Huet,  a beautiful pianist who was the younger sister of Honorine Huet,  a well-known overweight French spiritualist  (Théophile Gautier hired first Honorine then Virginie as preceptors for his daughters, Estelle and Judith).  Hugo Vernier died a few months before Virginie gave birth to a little Vincent, in Vernon, late in 1864...  The legend is still afloat to this day !

Pierce Morton   (1803-1859)
Proof of the focus-directrix characterization of conics, using Dandelin spheres   |   Genealogy

Pierce Morton  was born on 27 November 1803 in  County Cavan, Ireland.

At Cambridge, he was a pupil of  George Biddell Airy (1801-1892) who described him as "a clever gentlemanly man, and a high wrangler, but somewhat flighty".

Around 1825, he was appointed  Professor of Mathematics and Natural Philosophy  and also  Fellow of King's College  in Nova Scotia  (Canada). He left the Province suddenly in April 1826.

In the first volume of the  Cambridge Philosophical Transactions  (1829)  Morton published a new proof of the focus-directrix property of conic sections using Dandelin spheres.  Earlier on,  Hamilton (1805-1865)  had remarked that the circle where a Dandelin sphere touches the cone defines a plane whose intersection with the plane of section is a directrix of the curve.

On 1 June 1839, Pierce Morton married an Irish lady, Louisa Somerville (1808-1850) in St. Peter's Church  (Dublin, Ireland).  They had four children:

  • Frances Armytage Morton  was born in 1840.  She married  Henry Meredith Cruise  on 26 September 1857 in Anglesey, Wales  (they had a son, named  Meredith II, around 1860).  Widowed, she married Mr. Brown in 1878.  Later court documents  (Morton's Trusts, 3 March 1888, pp. 310-313)  refer to her as  Mrs. Frances McDonald Brown.  Her nickname was  Fanny.
  • Pierce Edward Morton  (a.k.a.  Pierce Junior )  was born on 3 February 1842, in  Le Havre  (France)  where his father was teaching.  He served as a Midshipman in the Royal Navy, before moving from Cape Town to Canada, in the autumn of 1860.  He was living in the household of his uncle  Dr. Edward Morton,  in East Gwillimbury, at the time of the 1861 Census.  He drowned with two other people on  August 12, 1861 in the shipwreck of the yacht  Wave  at "the Eastern Gap off the Island, Toronto"  (according to a note written by his cousin in the family bible).
  • John D'Arcy Morton  was born on 10 January 1843.
  • Arthur Pratt Winter Morton  was born in 1844 and died in 1871, leaving a widow and two children.

All four children were born in France as British subjects.  At the time of the 1851 census of Wales, they were living as wards in William Griffith's home  (in Holyhead, Anglesey).  Their father was living nearby at the time, but he was planning a move to South Africa...

Airy was instrumental in having  Pierce Morton  sent as Magnetic Assistant to the Cape Observatory.  Morton arrived in South Africa on November 27, 1851.  He passed away on April 18, 1859  and was buried in the Cape.

Pierce Morton  is listed as the head of the  Morton of Kilnacrott  family in Burke's Landed Gentry.  He was one of the  14  children of Charles Carr Morton and Charlotte Tatlow.  His paternal grandfather was the physician  Charles Morton (1716-1799)  principal librarian of the British Museum from 1776 to 1799.

In the orthodox blazoning style which forbids repetitions of tinctures,  the description of their coat-of-arms is quite convoluted  (the punctuation is mine):

Ermine, on a chevron, between three ogresses,
each charged with a martlet of the field,
as many mascles Or, a chief, Gules.

My understanding is that the field and the three martlets are Ermine, the ogresses are Sable, the chevron and the chief are Gules and the three mascles are Or.

Geometry, Plane, Solid, And Spherical, In Six Books (1830)   by Pierce Morton & S.W. Waud.

Etienne Bigourdan   (1804-1865)

Etienne Bigourdan  was born on 10 December 1804 in  Fleurance,  Gers. 
He died in 1865, probably in Paris.

Bigourdan was neither a  normalien  nor a  polytechnicien.  He dedicated his doctoral work to a  normalien  (1813, agrégé in 1816):  [Servien Abailard]  Armand Lévy (1795-1841)  maître de conférence à l'Ecole Normale  (1831-)  and  professeur de mathématiques élémentaires  (1831-1841) at  Collège Charlemagne.

Bigourdan was awarded his  agrégation  on 1832-09-24  (ranked third in France)  shortly  after  obtaining his doctorate in Paris, on  1832-08-13  (which is quite unusual)  defending the following set of three theses  (spanning 23 pages)  in front of a committee presided by the chemist  Louis-Jacques Thénard (1777-1857).

1.   Equation de la surface capillaire.
2.   Composition intérieure des fluides.
3.   Sur les éléments d'un sphéroïde.

Etienne Bigourdan served as  professeur agrégé  at  Louis-le-Grand  (c. 1836)  and  professeur de physique  in Limoges (-1840) just before his promotion to  mathématiques spéciales  in Rennes  (1840-1842)  and  Rouen  (1842).

He is  correspondant de l'Académie des Sciences  in 1847  (listed as  professeur de mathématiques spéciales à Paris).

In the later part of his academic career, Bigourdan would fall back to less prestigious positions in  mathématiques élémentaires  at  lycée Saint-Louis (-1852)  and, finally, at  lycée impérial Bonaparte  (1852-1865).

Guillaume Bigourdan  (1851-1932)  was an unrelated French astronomer who famously invented a procedure for setting up a telescope  (Bigourdan method).

Et. Bigourdan à P.-F. Dubois  (25 octobre 1840). Letters addressed to Paul-Franç Dubois sous Louis-Philippe.

  Urbain Le Verrier 
Urbain Le Verrier

Urbain Le Verrier   (1811-1877; X1831)
MacTutor   |   Wikipedia   |   Britannica   |   Collège Royal de Caen (1827-1830)

Urbain le Verrier  discovered the planet  Neptune  "at the tip of his pen"  (as Arago said)  on August 31, 1846,  by deducing its position from the recorded perturbations in the orbit of  Uranus.  He was also the founder of French meteorology.

From 1827 to 1830,  Le Verrier  prepared for the  Polytechnique  entrance exam at the Royal College of Caen, when the headmaster was  Jacques-Louis Daniel  (1794-1862, future recteur of Caen and bishop of Coutances).  The professor of special mathematics was  Antoine François Donat Bonnaire (1777-1839)  whose son Charles Antoine Donat Bonnaire  (1799-1886; X1819)  taught physics.

Although Urbain was the most brilliant student of his class in Caen, he failed in the  Polytechnique  entrance competition of 1830.  His father then decided to sell the family home in Saint-Lô to pay for tuition at a fancy preparatory school in Paris  (Institution Mayer)  which allowed Urbain to succeed in 1831.

The  Institution Mayer  had been founded in 1824 by  Mathias Mayer-d'Almbert  (1786-1843; X1805)  and it employed  the mathematician  Charles Choquet, who would later become  Urbain Le Verrier's  father-in-law :
Charles-Adrien Choquet (1798-1880)  had been a mathematical coach at  La Flèche  and he would later obtain a doctorate in astronomy  (1842).  Mayer and Choquet published three editions (1832,1836,1841) of their  Traité élémentaire d'algèbre  which Choquet updated twice  (1845,1849)  after the death of Mayer.  Then, he wrote under his own name two editions of a complement  (1851,1853)  and a consolidated version with a simpler title:  Traité d'algèbre  (1856).  All edited by the dominant French scientific publisher of the era, Mallet-Bachelier  (called Gauthier-Villars after 1864 and acquired by Dunod in 1971).  Charles Choquet came from a family of renowned painters and engravers established in Abbeville, including  his father  (or uncle?)  Pierre, Jean-Baptiste, Isidore Choquet  (1774-1824)  and his grandfather  Pierre-Adrien Choquet  (1743-1813).

All  Mayer  boarders were auditing classes at  Louis-le-Grand,  so that  Urbain Le Verrier  was taught by the legendary  Louis Richard (1795-1849)  professor at  Louis-le-Grand  (from 1822 till his death)  whose students have included the likes of Evariste Galois (1811-1832),  Joseph Serret (1819-1885; X1838) and  Charles Hermite (1822-1901; X1842).

In 1837,  Urbain Le Verrier  married  Lucile Marie Clotilde Choquet,  (the only daughter of his former teacher  Charles Choquet).  They had  3 children.  Their two sons became  polytechniciens  too:  Jean Charles Léon Le Verrier  (1838-1875; X1856)  and  Louis Paul Urbain Le Verrier  (1848-1905; X1867).  So did a grandson of theirs  (son of the latter)  Pierre Victor Joseph Le Verrier  (1882-1964; X1902).  Their daughter  Geneviève Joséphine Lucile Le Verrier  (1853-1931)  was a talented pianist who studied under  César Franck (1822-1890).

Discovery of Neptune   |   Heraldry: Roma

 Evariste Galois 

Evariste Galois   (1811-1832)
MacTutor   |   The Evariste Galois Archive   |   Math93   |   Fictionalization   |   Stamp

At the age of 20,  Evariste Galois  was mortally wounded in a duel  (against  Perscheux d'Herbinvillenot  Ernest Duchâtelet)  over a young lady called  Stéphanie-Félice Poterin du Motel Left for dead, Galois (who had no seconds) was discovered by a local peasant and transported to the  Cochin  hospital in Paris, where he died from peritonitis the next day  (May 31, 1832).

To his brother Alfred, he had whispered:

Ne pleure pas, Alfred.  J'ai besoin de tout mon courage pour mourir à 20 ans.
Please don't cry, Alfred.  I need all my courage to die at twenty.

Held on June 2, the funerals of Galois were attended by more than 2000 people and served as a focal point of  republican  riots which lasted for several days.  His dubious status as a martyred activist could have remained Galois' main claim to fame had it not been for his wish to have his last mathematical papers reviewed by Gauss or Jacobi...  His brother,  Alfred Galois  and his closest friend  Auguste Chevalier  did send out copies of the work, which were apparently ignored by the originally intended recipients.  In 1842, one of these copies reached Joseph Liouville (1809-1882)  who finally published what is now known as  Galois Theory,  in 1846.

The story is poignant enough as it is, but some biographers are perpetuating the  myth  that Galois wrote feverishly all he knew about  Group Theory  on the night before the fateful duel, apologizing again and again for not having the time to do it better...  The leading offender is clearly E.T. Bell (1883-1960) who wrote an emphatic chapter in his popular 1937 collection of biographies entitled  Men of Mathematics.  Actually, there's only one occurrence of such a statement in all the mathematical manuscripts of Galois  (an "author's note" about an incomplete proof).  Otherwise, the myth seems entirely based on the following sentence which appears in the letter known as "Galois' Testament", dated May 29, 1832 and addressed to his friend  Auguste Chevalier.  The passage is about extending  ambiguity theory  (Galois theory)  from rational to  transcendental  functions.

Mais je n'ai pas le temps, et mes idées ne sont pas encore
bien développées sur ce terrain, qui est immense. 

But I am running out of time, and my ideas are not yet
sufficiently developed in this field, which is immense.

Galois' Testament  ends with the following words:

Tu prieras publiquement Jacobi ou Gauss de donner leur avis
non sur la vérité, mais sur l'importance des théorèmes.
Après cela il se trouvera, j'espère, des gens qui trouveront leur profit
à déchiffrer tout ce gâchis.

Je t'embrasse avec effusion.   E. Galois,  le 29 Mai 1832

Until the age of 12, Galois had been schooled entirely by his mother,  Adélaïde-Marie Demante-Galois.  Galois was then enrolled at  Louis-le-Grand  (the most prestigious  lycée  of Paris)  as a boarder in the  quatrième  grade, on 6 October 1823  (or 1 April 1824, according to one Louis-le-Grand record). 

For the first couple of years,  Galois showed no particular interest for mathematics, in the class taught by  Charles Camus (1797-1865).  Born in "Sailly-Zèle"  (Somme)  Charles Louis Constant Camus  had entered  Polytechnique  in 1815 and placed third in the  scientific  Agrégation  for 1821  (which was the first year it took the form of a national competition).

Galois became enthralled with mathematics only in February 1827,  thanks to an exceptional instructor,  Hippolyte Vernier,  who had decided to teach from Legendre's  Elements de Géometrie  (1794).  That textbook was then spearheading the liberation from traditional Euclidean teaching in Europe.  Legend has it that Galois read the textbook in two days.  After that, he neglected all other subjects.

In 1828-1829, Evariste Galois was a  Mathématiques Spéciales  student under Louis Richard (1795-1849)  at  Louis-le-Grand.

Although he never published anything himself, Louis Richard (1795-1849)  was an outstanding teacher of mathematics, in the French  Grandes Ecoles  tradition which is still enduring to this day  (see Lucien Refleu, 1920-2005).  Besides Galois, Louis Richard also taught Urbain Le Verrier (1811-1877; X1831), Joseph Serret (1819-1885; X1838) and, above all, Charles Hermite (1822-1901; X1842) whom Richard saw as most similar to Galois and who would go on to achieve the long, brilliant and prestigious career of which Galois had been deprived by a  stupid  early death.  (Hermite also had a lasting impact by teaching the likes of  Jules Tannery  and  Henri Poincaré.)

In April 1829, on the recommendation of Louis Richard, Galois published his first paper  (Proof of a Theorem on Periodic Continued Fractions)  in the  Annales de Gergonne.  On May 25 and June 1, 1829, he submitted to the Academy his early research on equations of prime degree  (such an equation is solvable by radicals if and only if all its roots are rational functions of any two of them).  He was 17.

Tragedy struck on July 2, 1829  when his father hanged himself in an apartment located close to Louis-le-Grand.  The elder  Nicolas Gabriel Galois (1775-1829)  was an ardent republican who had been elected mayor of Bourg-la-Reine in 1815  (where a street now bears his name).  His nemesis, the new right-wing priest of Bourg-la-Reine, had managed to frame him by forging his signature on malicious epigrams directed at Council members.  The ensuing scandal was more than what Mayor Galois could take.  His suicide sent the young Galois in a tailspin.  The new priest officiated at the burial of the beloved Mayor, which turned into a riot...  (That priest  wasn't  a Jesuit, in spite of what's often reported.)

Evariste was scheduled to take the Polytechnique entrance exam later that month for the second and last time.  Of course, he failed.  Louis Richard then insisted that he should attend Normale.  So, all was not lost...

Evariste Galois befriended fellow republican  Ernest Duchâtelet  (Ernest-Joachim Armynot du Châtelet, born 19 may 1812 to a famous noble family)  an effeminate law student at the time,  he would later become a student at the Ecole des Chartes, a learned journalist, an absinthe alcoholic and a constant companion to one Louis-Achille Boblet  (most notorious for collecting coins rescued from the Seine River).  Duchâtelet had also just lost his father (1829) and his mother had passed away years earlier  (1820).

Normal Subgroups   |   Galois Rings.   |   Galois Fields
"Galois, le mathématicien maudit"  Norbert Verdier  (Belin, 2011).

Antoine  François Joseph  Yvon-Villarceau   (1813-1883)
Serge Mehl (French)   |   Villarceau circles   |   Wikipedia & Wikipédia

Born  Antoine Yvon,  he later transformed his last name into  Yvon Villarceau  (which he spelled without an hyphen).  Villarceau  was the name of a land he once owned and bequeathed to the town of Vendôme.  He became known simply as  Villarceau  (this avoids the confusion brought about by the fact that  Yvon  is a popular first name, but it wasn't his).

Villarceau graduated from Ecole Centrale (1840).  He is best remembered for discovering or rediscovering, in 1848, an amazing elementary fact:  The intersection of a torus with a doubly-tangent plane consists of two intersecting circles  (Villarceau circles).

He was a member of the French  Académie des sciences.

"Théorème sur le tore",  M. Yvon Villarceau
Nouvelles Annales de mathématiques, 7, pp. 345-347  (Paris, 1848)

 Pierre Laurent (1843-1854)

Pierre  Alphonse  Laurent   (1813-1854)
MacTutor   |   Wikipedia & Wikipédia

Pierre Laurent  was married (in Haumont, on 1841-10-18) to  Palmyre Angélique Bernardine Depreux  (b.1821).  They had three children.  Their son,  Pierre Georges Laurent  (b.1843)  also became a  Polytechnicien  (X1861).

Laurent polynomial   |   Doubly infinite Laurent series (1848)

 Congruent ellipses symmetrical 
 with respect to a common tangent.

Auguste Miquel   (1816-1851)
Serge Mehl (French)   |   Jean-Louis Aymé (2012-10-30)   |   Wikipédia

He was born in Albi in 1816.  He graduated from high-school in Toulouse, first as  bachelier ès lettres  (1834)  then  bachelier ès sciences  (1835).

Auguste Miquel then went to Paris to prepare for the  Grandes Ecoles  entrance competition.  He attended  Saint-Louis  and was also coached privately at  Institution Barbet,  where he proved to be extremely brilliant.

Located  3, impasse des Feuillantines  (Paris V)  from 1827 to 1864,  the  Institution Barbet  was one of several competing private preparatory schools  (other examples include  Collège Rollin  and  Institution Mayer).  The founder of this particular institution of higher learning was  Jean-François Barbet  (1799-1880)  who was one of only four students who entered the scientific section of the  Ecole Normale  in 1820.  The other three were:  François Artaud  (possibly the son of  Alexis-François Artaud de Montor, 1772-1849),  the geometer Georges Ritt (1800-1864) author of several textbooks, and Roch Roustan (1801-1870) future  recteur  of  Aix.
The Barbet boarders were auditing the  Mathématiques Spéciales  lectures given at  Saint-Louis,  by either Delisle or Vincent.  Known to his students as  "père Pancu"  (because he'd mispronounce  "perpanculaire" instead of  perpendiculaire)  Augustin Delisle  [Delille]  had been appointed  "agrégé en mathématiques au collège royal de Henri IV" in 1817, before  agrégation  became a formal competition  (1821).  He taught at Saint-Louis until his retirement in 1852  (he died in June 1881).  On the other hand,  Alexandre-Joseph Vincent (1797-1868)  was a former student of Ecole Normale (1816) who had originally been appointed "agrégé en physique à Reims", in 1820.

In 1836, while still a student at  Barbet,  Auguste Miquel proved several clever theorems about intersecting circles.  At that critical stage of his curriculum,  such specialized research may have taken too much of a toll:  Miquel didn't make the cut for  Polytechnique  or  Ecole Normale.  Shortly thereafter, he would start earning a living as a high-school teacher, with the lowly rank of  régent,  without ever becoming an  agrégé  or obtaining a doctorate.

Miquel was a staunch republican.  He published his anti-royalist views in social-democratic journals.  In those days, that didn't do much good for his humble career, which can be summarized as follows  (from scattered nomination records):

  • -1838 :   Régent de mathématiques,  Collège de Nantua.
  • 1838-1840 :   Régent de mathématiques,  Collège de Saint-Dié.
  • -1842 :   Régent de mathématiques élémentaires, Collège de Castres.
  • 1842- :   Régent de mathématiques, Collège de Bagnols.
  • 1842-11-09 :   Granted a one-year sabbatical.
  • -1846 :   Professeur, Collège de Castres.
  • -1849 :   Régent de mathématiques, Collège du Vigan.
  • 1849- :   "... appelé à d'autres fonctions."
NOTE:   In the same period, an unrelated "Miquel" held positions in primary education at Seyne (1840) Barcelonnette (1841) and Toulon (1843-1855).

Miquel called  syntrepent curves  two planar curves which rotate about two fixed points as they roll on each other without slipping.  He coined the word  isotrepent  for a curve syntrepent to itself  (the ellipse is a great example).

Auguste Miquel's first scientific publication  appeared in 1836 on  page 486  of the short-lived monthly journal  Le Géomètre,  founded that same year by the liberal activist  Antoine-Philippe Guillard (1795-1870)  a former student at  Ecole Normale  (1813)  who had been appointed  "agrégé de mathématiques au collège royal de Louis-le-Grand", in 1819.

Miquel's subsequent work was mostly published in  Joseph Liouville's  Journal de mathématiques pures et appliquées  (founded in 1836)  including:

  • "Sur quelques questions relatives à la théorie des courbes",
    Journal de mathématiques pures et appliquéesIII, pp. 202-208  (1838).
  • "Théorèmes de Géometrie", JMPA, III, pp. 485-487  (1838).
  • "Théorèmes sur les intersections des cercles et des sphères",
    Journal de mathématiques pures et appliquéesIII, pp. 517-522  (1838).
  • "Mémoire de Géometrie", JMPA, IX, pp. 20-27  (1844).
  • "Mémoire de Géometrie (deuxième partie)", JMPA, X, pp. 347-350  (1845).
  • "Mémoire de Géometrie (troisième partie)", JMPA, XI, pp. 65-75  (1846).

He also used the  pedagogical counterpart  (1842-1927)  of Liouville's journal:

  • "Problème d'Optique",
    Nouvelles annales de mathématiques, 5, pp. 235-238  (Paris, 1846).

Auguste Miquel died in 1851, at age 35, in obscure circumstances.

Enseigner les mathématiques au XIXème siècle  |  Miquel point  |  Miquel's pentagram  |  Miquel's Theorem (Dutch)

 Victor Puiseux 
 (photographed by Eugene Pirou)

Victor  Alexandre  Puiseux   (1820-1883)
Ph.D 1841   |   MacTutor   |   Academic career (French)   |   Weisstein   |   Wikipedia

Victor Puiseux  was born in Argenteuil  (where a  lycée  and a street now bear his name)  but his family relocated to  Lorraine  when he was three years old.  Victor received his secondary education at the  Collège de Pont-à-Mousson.

Upon graduation from high-school  (1834)  Puiseux was awarded a scholarship to attend  Collège Rollin,  a top-notch Parisian preparatory school where Charles Sturm (1803-1855)  was still  professeur de mathématiques spéciales (1830-1838).  Rollin  students also attended lectures in  lycée Louis-le-Grand.  Puiseux entered  Ecole Normale Supérieure  in 1837 and obtained his  agrégation  in 1840  (ranking first nationally, ahead of his older classmate  Charles Toussaint, 1817-1892).

That stellar performance earned Puiseux a position of  chargé de conférence  at  Ecole Normale  in Paris for one year  (1840-1841).  That gave him enough free time to prepare for a doctorate, which he duly obtained on  1841-08-21,  at the ripe old age of  21,  with two reportedly uninspired theses  (23 pages total)  entitled:

1.  Sur l'invariabilité des grands axes des orbites des planètes.  [Updated in 1878.]
2.  Sur l'intégration des équations du mouvement d'un système de points matériels.

Puiseux was then nominated  (1841)  professeur de mathématiques élémentaires au collège royal de Rennes.  where he was promoted  professeur de mathématiques spéciales  the next year  (1842-11-14)  thus succeeding  Etienne Bigourdan  who went on to a similar position in Rouen.

The job Puiseux thus left in 1842 was given to one  Mr. Thiébault,  coming from  Bourges.  In 1844,  Puiseux  (possibly foregoing an offer of a University position)  would be officially ordered to hold on to his position in Rennes, because his own  suppléant  (Mr. Paignon, agrégé in 1844)  would himself be called upon to teach in  mathématiques élémentaires  for the duration of a leave of absence  (1 year)  then granted to the aforementioned  Thiébault.

Victor Puiseux then became  professor of pure mathematics  at the  University of Besançon  for two years  (1845-1847).   Elected  secretary of the Faculty  in 1847.

The occupation of Victor Puiseux in 1848 is unknown to this writer at this time.

In 1849, Puiseux went back to Paris as a  maître de conférence  in  Ecole Normale,  replacing Jean-Marie Duhamel (1797-1872; X1814).  He would hold this position until 1855.  Simultaneously (in 1853),  he was appointed to the  Collège de France  as  suppléant  of  Jacques Binet  (1786-1856; X1804)  in the chair of astronomy.

In 1856, Victor Puiseux is  chargé de cours  at  the Sorbonne  and soon succeeds  Augustin Cauchy (1789-1857)  as  professor of mathematical astronomy and celestial mechanics.  He held that chair for  26  years  (1857-1883)  until his death.

Puiseux was the doctoral advisor of Camille Jordan (1860).  On  1878-01-18,  his only other doctoral student  (Spiru Haret, 1851-1912)  defended a thesis bearing the exact title Puiseux himself had used for his own doctoral work,  36  years earlier,  namely:  Sur l'invariabilité des grands axes des orbites des planètes.

What Haret established in his doctoral work,  using third-order pertunation methods,  was that the principal axes of planetary orbits undergo secular variations, which would seem to make them unstable in the long run.  That surprising result was an inspiration for the  chaos theory  of  Henri Poincaré.  It was also the motivation for later work (1954) by Kolmogorov  who was almost able claim the absolute stability of the Solar system for deeper reasons.

Simultaneously, Puiseux served as  maître de conférence  from 1862 to 1868 at  Ecole Normale,  where he taught  probabilities  and  differential calculus.  He held a post at the  Bureau des Longitudes  (in the  bureau des calculs  service)  from 1868 to 1872.

He was elected, by a unanimous vote, to the geometry section of the  Académie des sciences  on  1871-07-10.

Victor Puiseux also rose to the administrative rank of  inspecteur général de l'Instruction publique, hors cadre.  As such, in 1880, he was put in charge of inspecting  "all primary schools educating holders of  State scholarships".  This strange parlance was the way all public elementary schools were called, just before the momentous 1881 reforms famously instigated by  Jules Ferry  (prior to which, all families who could afford it were paying full tuition to educate their children, even in the public system).

Puiseux died at the age of 73,  on 9 September 1883,  in  Frontenay,  the village of the family his new daughter-in-law, shortly after her wedding (1883-06-21)  to his eldest son, Pierre.  He had requested that no speech should be made over his dead body.  He had six children but was survived by only two sons,  both of them astronomers:  Pierre Puiseux (1855-1928)  and  André Paul Puiseux (1858-1931).

Puiseux series 1850  (Newton, 1676)   |   Bertrand-Diquet-Puiseux theorem   |   J. Dieudonné on Algebraic Geometry

 Jules Houel 

Jules Hoüel   (1823-1886)
MacTutor   |   Wikipedia

Guillaume Jules Hoüel  was born on April 7, 1823 in the small town of Thaon  (10 km NW of Caen, spelled "Than" before 1843, which is the way the name is still pronounced).  He was educated at the  Lycée Royal de Caen  and at the  Collège Rollin  in Paris, which housed one of the top preparatory schools.

The private  Collège Rollin  took that name in 1830.  It had been founded in 1821 by Joseph Planche and l'abbé Charles Nicolle (1758-1835) as a "new" Collège Sainte-Barbe  and was once called  Sainte-Barbe Nicolle  or  Sainte-Barbe Rollin  to distinguish it from the older  Sainte-Barbe  revived by Victor de Lanneau (1758-1830) in 1798  on  Montagne Sainte-Geneviève  The latter, which lasted until 1999, was built on the same land as the historical  Collège Sainte-Barbe  founded in 1460, which gave it a much stronger claim to the prestigious historical name,  as was legally recognized in 1830.  Sainte-Barbe  (Barbara)  being the patron saint of miners, engineers, architects and mathematicians is also the patron saint of  Polytechnique,  which explains the great symbolic prestige of her name for a French preparatory school.
In 1876, Rollin would move from its original location  (rue Lhomond)  to its current address  (avenue Trudaine).  It lost its private status and was taken over by the municipality,  becoming  Lycée Rollin  in 1919.  The school was renamed in 1944 after the communist  resistance fighter  Jacques Decour (1910-1942)  who had started teaching there in 1937, under his real name of  Daniel Decourdemanche.

Hoüel became  normalien  in 1843  and agrégé in  1847  (7 out of 9 that year).  He first taught in the  lycées  of Bourges, Bordeaux, Pau and Alençon (1851).

On 1855-08-18, he obtained a doctorate for a thesis in celestial mechanics which impressed  Urbain Le Verrier  who offered him to join the  Observatoire de Paris.  Hoüel turned down that offer.  Instead, he spent a couple of years on independent mathematical research at his family home in Thaon.

He was appointed professor of  Mathématiques spéciales at Caen for a just a few weeks  (January-March 1856)  to replace  Charles Toussaint  who became  censeur  of the lycée at that time.  In March, Antoine-Xavier Planes took over.  Toussaint got his old job back in October.

In 1858, Hoüel was appointed to the chair of pure mathematics in Bordeaux, which he held until he retired  (1884).  He had a passion for  non-Euclidean  geometry and a gift for languages:  In 1866, he learned Russian to translate Lobatchevsky and Hungarian to read Bolyai...  In his translation of their work (1870) Houël published a proof of Beltrami (1868) which marks the high point of the subject.

With the younger Gaston Darboux (1842-1917)  Jules Hoüel became founding editor of  Bulletin des sciences mathématiques et astronomiques  in 1870.

Blog à Maths   |   Norbert Verdier   |   François Plantade

 Emile Mathieu 

Emile Léonard Mathieu   (1835-1890; X1854)
MacTutor   |   Wikipedia   |   Mathieu functions   |   Mathieu groups   |   Mathieu transform

Born on 5 May 1835 to Nicolas Mathieu, caissier à la recette générale and his wife Amélie Antoinette Aubertin.  He passed away on 19 October 1890  (at the age of 55)  in Nancy where he had been holding a chair of mathematics since 1873.

He received his doctorate  (Docteur ès Sciences)  in 1859 for a thesis on transitive functions which would lead him to the discovery  (between 1860 and 1873)  of the five  sporadic simple groups  now named after him.

The personal address he gave when he entered Polytechnique (1854) was  12 rue Chevremont  (Metz, Moselle).  Emile Mathieu  had been ranked 168 on the entrance exam and was 152 out of 158 students passing into the second year.  His French military records give of him the following physical description:  Cheveux châtains - Front moyen - Nez moyen - Yeux roux - Bouche large - Menton rond - Visage ovale - Taille 166 - Un signe particulier à la joue droite.

Unrelated inividuals also named  "Emile Mathieu"  include:

Ambitions parisiennes contrariées   |   No known portrait

 Gustav Roch (1839-1866)

Gustav  Adolph  Roch   (1839-1866)
Ph.D. 1862   |   MacTutor   |   Wikipedia   |   Halle (German)

On the advice of his father  (an assistant cook)  Gustav Roch  went to the  Polytechnic Institute  in his hometown of Dresden (Technische Bildungsanstalt)  to train for a career in chemistry.  One teacher there was  Oscar Schlömlich (1823-1901)  who had studied at Berlin under Dirichlet and Steiner.  Schlömlich noticed the mathematical abilities of Roch and persuaded him to switch his major to mathematics and physics.  To accomplish this effectively,  Roch had to take remedial courses at a private institution outside of the  Polytechnic Institute.

In 1859, Roch published his first paper in  Schlömilch's Zeitschrift für Mathematik und Physik  (a journal founded by Schlömilch three years earlier).  In the Spring of 1859, Gustav Roch entered the University of Leipzig.

Riemann-Roch theorem  (Riemann 1857, Roch 1865)

 Edouard Lucas 

Edouard Lucas   (1842-1891)
MacTutor   |   Wikipedia   |   Anne-Marie Décaillot (1998 & 1999)   |   Roland Brasseur (2014)

Edouard Lucas  is the most prominent French number-theorist of the nineteenth century.  As  Number Theory  wasn't fashionable in French Academia at the time, Lucas made a living outside of his chosen specialty.

He was born in Amiens  (where a College and a street now bear his name)  to a family of modest means.  Of his 10 siblings, 2 were stillborn and 2 died young.  Edouard was a brilliant student and would always be supported by scholarships.

After graduating from high-school in Amiens (1859),  Edouard Lucas attended  mathématiques spéciales  for two years at the  lycée impérial de Douai,  first under  Claude David  (1811-1864)  then under  Louis Painvin  (1826-1875).  On his second try, Lucas became a  normalien  in Paris  (1861).

He got his  agrégation  in 1864, outranked only by  Gaston Darboux  (1842-1917).  Because he was not yet 25, his official nomination as  agrégé  was delayed.

Lucas was an  associate astronomer  at the Paris Observatory from 1864 to 1869, in the midst of a long period of bitter tensions (1854-1870) between the scientific staff and the director Urbain le Verrier (1811-1877; X1831) the discoverer of Neptune (1846-08-31).  Starting in 1867, Lucas would escape from  Le Verrier's  constant mobbing  by studying mathematical problems in his hometown of Amiens.  He became acquainted with the mathematics pertaining to the industrial weaving of fabrics  (using  Jacquard punchcards)  through the work of another native of Amiens:  Edouard Gand  (1815-1891)  who had founded the  Société industrielle d'Amiens  in 1861.  This would provide the topic of Lucas' first publication (1867).

Lucas was sacked by Le Verrier in the Summer of 1869 and appointed to teach high-school seniors in Tours, with a decrease in pay  (1869-09-08).  His refusal of the position left him with only a low allocation and he joined the army as a junior officer.  He served as a decorated artillery officer in the  Franco-Prussian War (1870-1871)  and rose to the rank of captain.

On 1872-04-10,  he was nominated professor of  mathématiques spéciales  in the small town of  Moulins, where he stayed until he was offered more desirable positions in Paris, alternating between  Lycée Charlemagne  (1876-1879, 1890-1891)  and  lycée Saint-Louis  (1879-1890).  He was granted an extended leave of absence from Saint-Louis for two school years  (1882 to 1884)  after the death of his wife of  9  years  (Marthe Boyron, 1852-1882, mother of his two children).  During that time, he prepared an edition of the works of  Fermat.

His last transfer from Saint-Louis to Charlemagne  (1890-08-20)  was actually a switch of equivalent positions between himself and  Gaston Gohierre de Longchamps  (1842-1906).  Several students of Saint-Louis had threatened to leave the school if they were assigned to the class of Lucas, because they thought that his style would not prepare them adequately for the competition they were facing.  Apparently, Lucas did not face the same  (unfounded)  rejection at Charlemagne, where he ended up spending the last year of his life.

Lucas died at the age of 49  (3 October 1891)  from a severe infection following a freak accident:  A waiter had wounded his cheek with a broken plate at a banquet of the  Association française pour l'avancement des sciences  (AFAS).  Edouard Lucas is buried in  Montmartre Cemetery.

In 1876, Lucas proved the primality of a 39-digit number  (the  12th  Mersenne prime)  which would remain the largest known prime for 75 years  (until 1951):

2127 - 1   =   170141183460469231731687303715884105727

To do so, over the course of 19 years  (he had started to work on the problem at age 15)  Lucas eventually devised a  specialized  primality test for Mersenne numbers  (i.e., numbers which come just before a power of two).  That test was streamlined in 1930 by  Derrick H. Lehmer (1905-1991)  as part of his own doctoral dissertation at Brown University.  The  Lucas-Lehmer test  remains, to this day, the most efficient way to prove the primality of  some  large numbers.

Towers of Hanoi (1883)  |  Umbral calculus  |  Théorie des nombres 528 pages (Gauthier-Villars, 1891)

 Jules Tannery (1848-1910) 
 Photo by A. Gerschel & Sons (c. 1866)

Jules Tannery   (1848-1910)
MacTutor   |   Wikipedia   |   Dico Spé   |   Career

Like his older brother Paul Tannery (1843-1904),  Jules Tannery  was an alumnus of the "Taupe Laplace"  (Lycée Malherbe de Caen) where he taught briefly (1871-1872) early in his career.  His star student at the time was Léon Lecornu (1854-1940) who later became a member of the  Académie des sciences.  Tannery earned his doctorate in 1874 at the  Ecole Normale Supérieure  (ENS)  under  Charles Hermite (1822-1901; X1842)  [the man who had proved the transcendentality of  e  just one year earlier, in 1873].

Jules Tannery  was first appointed at ENS-Ulm in 1881 and also took up lecturing duties at ENS-Sèvres in 1882, shortly after its creation  (that counterpart of ENS-Ulm for girls had been created in 1881 and fused with ENS-Ulm in 1985).  Tannery supervised four doctoral students, including  Jacques Hadamard  (1865-1963, who proved the Prime Number Theorem)  and Jules Drach (1871-1949).

 Tannery's pear 
with typical geodesic

Other students of Tannery's at ENS included the likes of Paul Painlevé  (twice a Prime Minister of France, in 1917 and 1925)  and  Émile Borel (1871-1956).  Jules Tannery was elected to the French  Académie des sciences  in 1907.

Tannery devised the teardrop-shaped surface of revolution pictured at left, dubbed  Tannery's pear,  as a single lobe of the two-lobe algebraic surface  (degree 4)  of cartesian equation:

8 a2 (x2 + y2 )  =  (a2 - z2 ) z2

Parametrically, for  both  lobes:
      x   =   (a / Ö32)  sin u  cos v
      y   =   (a / Ö32)  sin u  sin v
      z   =     a  sin u/2

Every  geodesic curve  (like the bold line shown at left)  is an  algebraic  closed curve  that goes around the axis  twice  and crosses itself once!

If need be, the  entire  surface described by the above unrestricted equations can be called  Tannery's hourglass  (it consists of two distinct congruent  Tannery pears  sharing the same axis and the same  cone-point ).  The cone's half-angle is:

Arctg  1/Ö8   =   19.47122...°

Jules Tannery is also remembered for  Tannery's Limiting Theorem  which states that the limit of an infinite sum is the sum of the limits, under certain conditions...

Mathematical Genealogy   |   Teaching Geometry   |   Tannery's Limiting Theorem

 Eugène Cosserat 

François Cosserat   (1852-1914; X1870)

Lucien Cosserat   (1856-1897; X1875)

Eugène  Maurice Pierre  Cosserat  
(1866-1931; ENS 1883)   MacTutor   |   Wikipedia

Lucien Constant Cosserat  contributed to the joint work of his two brothers.  However, due to his early demise, he couldn't co-sign the masterpiece on  micropolar elasticity  published by François and Eugène in 1909.

Genealogy :

The father of the three brothers was François-Constant Cosserat, a well-off entrepreneur based in Amiens, France.  He was granted a British patent  (number 1798)  for improvements in industrial smoke-burning furnaces on July 18, 1864.

Mathematical Genealogy   |   Correlator
"Théorie des corps déformables"  by  Eugène & François Cosserat  (Hermann, 1909). 230 pages.

 Paul Petit 

Paul  Emile  Petit   (1862-1936)
Officier de la Légion d'Honneur   |   Founder of the Mines de Nancy school

Paul Petit  was born on 29 March 1862 in Lucy, Meurthe.

He entered the  Ecole Normale Supérieure  (ENS, Ulm)  in 1883  (placing last; 20/20).  Before graduation,  he was appointed  professeur de physique  in a newly-created position at  Collège de Barbezieux  (1886-02-13)  future  Lycée Elie Vinet.  Petit duly graduated from ENS in 1886 with an  Agrégation  in physics  (again, taking the very last slot; 9/9).

In 1886, he became  sous-directeur  in the  Laboratoire des Hautes-Etudes  created by Berthelot.  In March 1889, Petit obtained a doctorate in chemistry.

Thereafter, he spent his entire career in Nancy, where he was first appointed  chargé de cours  in chemistry on 1889-10-31.  In 1893, Petit founded the  Ecole de Brasserie de l'Université de Nancy, of which he was the first administrator.  In 1894,  he was appointed  Professeur de Chimie Agricole.  He later rose to the rank of  Doyen de la Faculté des Sciences de Nancy.

On 28 March 1919,  Paul Petit was instrumental in the creation of the  Institut Métallurgique et Minier de Nancy,  a major engineering school which everybody would soon call  Les Mines de Nancy.  The official name changed several times.  Since 1985,  it is:  Ecole Nationale Supérieure des Mines de Nancy.  Paul Petit was its first academic director in 1919  (when it was part of the University of Nancy).

Ecole des Mines de Nancy (1919-2009)

 Henri Pade 

Henri  Eugène  Padé   (1863-1953)
MacTutor   |   Wikipedia   |   "Asymptotology" by Igor V. Andrianov & Leonid I. Manevitch

Henri Padé  was born on 1863-12-17 in  Abbeville  to a family hailing from the nearby rural village of Cahon  (250 inhabitants; modern French postal code 80132).  His father,  Jean-Baptiste Domice Padé,  was a  rouennier  (see below)  born in Cahon on 1821-02-15,  the son of a shepherd born in 1790 and the grandson of a weaver born in 1765.  Henri's mother,  Joséphine Pétronille Eléonore Thiébault  was born in Cahon on 1831-09-27.  She was the daughter of a weaver born in 1794.  Jean-Baptiste and herself were married in Cahon on 1859-02-25.

Rouenneries   are cotton fabrics in which threads were dyed in various shades of red before weaving.  Such threads were first spun in 1787,  on state-owned spinning machines operating in  Rouen  (hence the name).  Weaving was mostly done in the  Pays de Caux  around Yvetoot.  That was the fashion for over 60 years, from the  First French Empire onward.  In 1863,  about 60,000 looms were in operation in the  Pays de Caux  and another 20,000 were located in nearby Picardy,  where Cahon is.
People who worked the fields in summertime would work the looms in the Winter.  A loom was attended by one weaver and one assistant  (who was often a woman or a child).  This occupation was more highly regarded than agriculture and those who did both called themselves weavers  (tisserands).  On Henri's birth certificate,  Jean-Baptiste Padé said he was  marchand de rouenneries,  implying he would mostly trade or sell the merchandise,  rather than weave it himself  (unlike a  tisserand, employed by a  fabricant).  Shortly after Henri's birth,  the shortage of cotton brought about by the  American Civil War (1861-1865)  precipitated the downfall of this rural activity,  which was subsequenly mechanized on an industrial scale,  in  Amiens  and elsewhere.

Henri Padé  completed his secondary education in Lille at the age of 17  (his baccalaureate was officially awarded on 1881-09-30).  He then underwent two years of preparatory school at  Lycée Saint-Louis.

Padé entered the prestigious  Ecole Normale Supérieure  in 1883,  tenth of a list of 20,  given below in order of merit.  The first 11 were nominated on 1883-08-07  in a list of 20.  Of those, 9 chose Polytechnique and were replaced by a list of 9 published on 1883-10-19.  Only the next-to-last on that second list (Pierre Labarbe) chose Polytechnique and he was replaced by Paul Petit on 1883-10-27.  Unexplicably, the 1884 summary of the results below showed only 19 names  (Franc was ommitted but his misspelled name is in the current records of the ENS).

  1. Jules Riemann (1863-1941).  Professor at Louis-le-Grand.  Cor's co-author.
  2. Paul [André Marie] Janet (1863-1937).  Agrégé in Physics (1/9) in 1886.
  3. André [Grégoire] Duboin.  First prize in chemistry CG. Louis-le-Grand.
  4. Félix [Guillaume Joseph] Bonnel.  On a scholarship from Lyons (1881).
  5. Eugène Cosserat (1866-1931).  The youngest of the  Cosserat Brothers.
  6. [Théodule] Edmond Colléatte (1864-fl.1933).  Agrégé in Physics (4) 1893.
  7. Paul [Léon, Félix] Franc.  Prix d'honneur en maths spé (Nancy, 1883).
  8. Maurice Lelieuvre (1864-1949).  Successor of  Cor  at  La Taupe Laplace.
  9. Narcisse Cor (1863-1949)  who got a coveted scholarship to Göttingen.
  10. Henri Padé (1863-1953).  Studied  Padé approximants  from 1891 to 1907.
  11. Paul Painlevé (1863-1933).  Mathematician & statesman  (prime minister).
  12. [Julien] Octave Rouen
  13. Emile [Henri, Jean-Baptiste] Chrétien (1861-1955).  Professeur de Lycée.
  14. Charles Roos
  15. [Pierre] Raymond Le Vavasseur (1862-1930).  Group theory.
  16. [Pierre] André Puzin (1861-)Agrégé in Mathematics in 1887 (12/13).
  17. Lucien Poincaré (1862-1920).  Brother of Raymond,  cousin of Henri.
  18. Louis Régis (1866-)Agrégé in Mathematics in 1887 (4/13).
  19. [Jules, Théaul] Albert Quiquet (1862-1934).  Leading actuary & author.
  20. Paul [Emile] Petit (1862-1936).  Founded Mines de Nancy school in 1919.

The star of that class, Jules Riemann, was ranked first overall upon admission and first in mathematics upon graduation (see below).  He doesn't seem to be directly related to  Bernhard Riemann (1826-1866).  In physics, top honors went to Paul Janet,  son of the French philosopher  Paul [Alexandre René] Janet (1823-1899).

At least three of the above  (Cor, Painlevé and Padé)  would go to Göttigen after graduation,  to study under Klein and Schwarz.  Apparently, Padé had to take a longer route to do so  (see below). 

Henri Padé was awarded two  licence  degrees in August 1885  (Mathematics on the 15th,  Physics on the 20th).  For ENS students, this was mostly a formality which served as insurance against the very real possibility of failing the  agrégation  competition later  (back in those days, there were only 13 open slots per year in mathematics and 9 in physics).

In 1886, six  " élèves sortants de l'ENS "  got their  Agrégation de Mathématiques.  Namely:  Jules Riemann (1) Eugène Cosserat (2) Narcisse Cor (5) Henri Padé (6) Maurice Lelieuvre (7) and Paul Painlevé (9/13).  Two made it in physics:  Paul Janet (1/9) and Paul Petit (9/9).
That wasn't the end of it, since you could compete any time after graduation.  Among those who entered ENS in 1883,  two made it in mathematics on their second attempt in 1887 (in a competition dominated by Vessiot and Hadamard)  namely:  Louis Régis (4) and André Puzin (12).  Likewise,  Lucien Poincaré was successful in the physics contest of 1887  (6).
Two of their classmates had to wait a bit longer:  Raymond Le Vavasseur got his  agrégation  in 1889 (ranked 3rd, in Mathematics) and Colléatte was finally successful in 1893 (ranked 4th, in Physics).  All told,  13 of the 20 students who entered ENS in 1883 ended up  agrégés  (9 in Mathematics, 4 in Physics).

At first,  Padé was appointed  professor of mathematics  at the  lycée de Limoges  (which became  lycée Gay-Lussac  on 1889-02-09).  Henri Padé's nomination, dated 1886-09-04, was said to be temporary as was the custom for junior staff.  He was indeed immediately reassigned to Carcassonne instead  (1886-10-21, still temporarily, of course).  The  lycée de Carcassonne  had been created in 1853 as an upgrade to the old collège communal  (it took the name of  Lycée Paul Sabatier  in 1960, when it moved from its original location at  89, rue de Verdun).

Padé's next appointment was at  Montpellier  (1887-10-29)  in the  Grand Lycée  (of Medieval origin)  which became the  Lycée Joffre  when it moved in 1947.

At that time,  Henri Padé published his first scientific paper, which dealt with the irrationality of  e  and  p  (1888).

In 1889,  he took a sabbatical from Montpellier to study in Germany.  He first spent one semester at Leipzig,  where he took the course of  Adolph Mayer (1839-1908)  on the differential equations of mechanics.  (He registered on 1889-10-18 and passed his final exam on 1890-03-28.)  Padé then transferred to  Göttingen where he stayed for the entire year 1890-1891  (he was granted an unpaid leave of absence on 1890-12-03, as a  former  professor at Montpellier).  On 1891-05-05,  Padé obtained a degree in mathematics from Göttingen,  having attended lectures by Felix Klein (1849-1925)  and Hermann Schwarz (1843-1921).  At that time,  he translated into French Felix Klein's celebrated  Erlangen Program (1872)  for the  Annales de l'Ecole Normale Supérieure (1891).

Back to France,  Padé undertook doctoral work under Charles Hermite (1822-1901)  while resuming his teaching career with an appointment at the  Lycée de Poitiers  (1891-09-19)  at a senior rank  (2-ème classe)  contrasting with his previous nominations (6-ème classe).  A few months later  (1891-12-11)  he was appointed to the  Lycée de Lyon  to teach a preparatory class for  Saint-Cyr.

On Friday 1892-04-08 at 14:00,  Henri Padé  defended his doctoral thesis on the theory of what we now call  Padé approximantsSur la représentation approchée d'une fonction par des fractions rationelles.  Besides Hermite (thesis supervisor) the jury consisted of Emile Picard (1856-1941)  and Paul Appell (1855-1930).  Padé passed  avec toutes boules blanches  (i.e., by unanimous vote).  His lesser thesis was entitled  Formation des groupes fuchsiens.  Fonctions modulaires.  Padé officially received his doctorate on 1892-06-21.

Also in 1892,  he published a small educational book,  prefaced by  Jules Tannery,  entitled:  Premières leçons d'algèbre élémentaire, nombres positifs et négatifs, opérations sur les polynomes  (Gauthier-Villars & fils, Paris).

In 1893, he left his position in Lyons and was appointed (1893-09-02) to a newly-created position near his hometown,  teaching high-school seniors "A" at the  Lycée  of Lille  (which took its current name of  Lycée Faidherbe that very year).

In January 1897,  Padé became  Maître de conférences  at the nearby University of Lille,  succeeding  Emile Borel (1871-1956)  who had been appointed to ENS in Paris.  Padé taught rational nechanics at IDN from 1897 to 1901,  putting to good use what he had learned from Adolph Mayer in Leipzig, 7 years earlier.

In 1901,  Padé left Lille for Poitiers,  as  chargé de cours.  In June 1902,  he was promoted  Professor of Rational and Applied Mechanics  at the  University of Poitiers,  suceeding Antoine Henri Durrande (1831-1904; ENS 1851).  In November 1903,  Henri Padé accepted an appointment as  Professor of Mechanics  at the University of Bordeaux  (as re-founded on 10 July 1896)  where he would become  Doyen de la Faculté des Sciences  on 1906-12-07.

On 1906-12-17,  Padé received the  Grand Prix  of the French Academy of Sciences by winning a competition on "better convergence criteria" for algebraic continued fractions.  His submission consisted of two sealed covers  (plis cachetés  filed in February and June 1903).  This marked the peak of his research career.

Padé ended his career as a university professor on 1908-11-17, at age 44, to become the youngest  Rector  in France  (there were 13 rectors at the time)  successively heading the  Académies  of Besançon (November 1908)  Dijon (1917) and Aix-Marseille (1923) where he retired in 1934, at the age of 70.

Padé became a Knight of the Legion of Honor on 1910-05-06  (decorated by Appell)  and was promoted Officer of the Legion on Honor on 1927-03-09.

Henri Padé passed away in Aix-en-Provence at the age of 89, on 1953-07-09.  He was survived by his wife of 60 years,  Hélène Caudron,  whom he had married in Abbeville on 1893-08-12  (she was born on 1876-01-15, died on 1955-12-15 and is burried next to her husband).  Both Henri and Hélène Padé were good musicians.  He was fond of Schumann and Schubert.  She played a grand piano.  They had three daughters.  The eldest married before 1922.  The youngest, Odette, was the second wife of Georges Bonfils and the mother of Claude Bonfils.

 Hélène & Henri Padé
Hélène & Henri Padé,  at Beaucourt on 6 June 1922.

Between 1888 and 1907,  Henri Padé wrote 42 scientific articles, without any co-authors.  29 of his papers are about continued fractions or Padé approximants.

A Brief History of Padé Approximants :

In 1730,  James Stirling (1692-1770)  and  Daniel Bernoulli (1700-1782)  independently introduced Padé approximants.  Around the same time,  Euler (1707-1783)  gave Padé-type approximations to the sums of some series.

In 1740,  according to Claude Brezinsky  (Birth and early developments of Padé approximants)  one George Anderson  stumbled upon three different rational approximations to the logarithm function.  Anderson was apparently a resident of  Twickenham  who is only known through the eight mathematical letters he sent to  William Jones (1675-1749)  between 1736 and 1740  (at which time he said he was going to the University of Leyden,  the oldest university in the Netherlands).

In 1758,  Johann Heinrich Lambert (1728-1777)  found some Padé approximants by direct computations of their coefficients.

In 1776,  Lagrange (1736-1813)  obtained such approximations from the convergents of continued fractions.

In 1837,  Kummer (1810-1893)  used approximants as convergence accelerators.

In 1845,  Jacobi (1804-1851)  expressed Padé approximants using  determinants.

In 1861,  Padé approximants appeared in the doctoral thesis of  Hermann Hankel (1839-1873).

In 1870,  the doctoral thesis of Frobenius (1849-1917)  established some relations between Padé approximants.  Padé was surely unaware of this in 1892.

In 1873,  Charles Hermite  (Padé's future thesis advisor)  proved  e  to be transcendental by using simultaneous  Padé approximants  of several series.

The methods introduced by Padé in his 97-page thesis  (1892)  were used for  divergent series  in the book which  Emile Borel (1871-1956)  published in 1901.

Padé approximants  were given their modern name by  E.B. Van Vleck (1863-1943)  who also coined the locution  Padé table  in a 1903 paper.  At a meeting of the AMS in Boston  (1903)  Van Vleck issued the following clarification:

The existence of approximants was, of course, well-known before Padé, but no systematic examination of them had been made except by Frobenius, who determined the important relations which normally exist between them.  Padé goes further, and arranges the approximants, expressed each in its lowest terms, into a table.

In 1948, the subject was resurrected for good by Hubert Stanley Wall (1902-1971) who had earned his doctorate in 1927 from the University of Wisconsin-Madison, with a thesis on that topic, under the aforementioned  E.B. Van Vleck.

In 1987,  a monograph of  Adhemar Bultheel (c.1948-)  extended the scope of Padé approximants from one-sided formal power series to two-sided Laurent series.

Mathematical Genealogy   |   Padé tables   |   Continued fractions   |   Ellipse perimeter

 Ernest Vessiot 

Ernest  Paulin Joseph  Vessiot   (1865-1952)
MacTutor   |   Dico Spé   |   L'œuvre scientifique de M. Ernest Vessiot by Elie Cartan (1947)

In the 1884 entrance exam to the  Ecole Normale Supérieure, Vessiot was second only to  Jacques Hadamard  (1865-1963) who was subsequently a classmate of his.  In the  agrégation  contest  of 1887,  he finished first and Hadamard second.

After his brilliant graduation, Vessiot held several teaching positions, starting at Lyons in 1887, then Lille (1892) Toulouse, Lyons again and Paris (1910).

Ernest Vessiot  obtained his doctorate in 1892, under C. Emile Picard (1856-1941)  with a dissertation about the action of continuous groups of transformations  (Lie groups)  on the independent solutions of a differential equation.  In that domain, he would later extend results of Jules Drach (1902) and Elie Cartan (1907).

In 1914, he succeeded  François Cosserat  (1852-1914; X1870)  as president of the  Société Mathématique de France.  Vessiot would hold the post of director of the  Ecole Normale Supérieure  until his retirement in 1935.  He was elected to the  Académie des Sciences  in 1943.

Picard-Vessiot theory   |   Mathematical Genealogy   |   Correlator

 Jules Drach 

Jules  Joseph  Drach   (1871-1949)
MacTutor   |   Wikipedia & Wikipédia   |   Work of Jules Drach

Jules Drach  did his doctoral work at  Ecole Normale Supérieure  under the supervision of  Jules Tannery  (just like  Jacques Hadamard  earlier).

Drach was  chargé de cours  at the University of Poitiers when Henri Padé left for Bordeaux and he took over Padé's duties.  In 1904,  he was officially appointed as the successor of Padé in the chair of  Mécanique rationnelle et appliquée.

Mathematical Genealogy   |   Rues de Ludres

 Andre Gerardin 

André Gérardin   (1879-1953)
Christian Boyer (2005)

Born in Nancy.  Died in Nancy.  Once described as  "the most active mathematical descendant of  Edouard Lucas in France".  He is among the most quoted authors in the monumental  History of the Theory of Numbers  (1919)  by  L.E. Dickson (1874-1954).

Gérardin created and/or edited four periodical journals about Number Theory:

  • Sphinx-Œdip  (1906-1932...)  monthly.
  • Lettre Mathématique Circulante  (1943-1944).  No extant copies.
  • Intermédiaire des Recherches Mathématiques (1944)  with Paul Belgodère.
  • Diophante  (Diophantus)  four times a year, from 1948 to 1952.

AFAS   |   Sur quelques nouvelles machines algébriques

Paul Poulet   (1887-1946)
Poulet numbers  |  Super-Poulet numbers  |  ChronoMath (French)  |  Wikipedia (French)

Paul Poulet was an autodidact Belgian mathematician best remembered for charting the pseudoprimes to base 2 which he tabulated up to 50 million in 1926 and up to 100 million in 1938.  Those are now commonly called  Poulet numbers  in his honor  (they're also known as  Fermatians  or  Sarrus numbers ).

In 1918, Paul Poulet discovered the first aliquot cycle  (where each number is the sum of the proper divisors of its predecessor)  namely:

( 12496, 14288, 15472, 14536, 14264 )

In 1925, Poulet published  43  new multiperfect numbers, including his discovery of the first two known 8-perfect numbers.

"Sur les nombres multiparfaits"   by Paul Poulet,
49th conference of the Association française pour l'avancement des sciences  (Grenoble, 1925)
"Tables des nombres composés inférieurs à 50 000 000  répondant au théorème de Fermat pour le module 2"
by Paul Poulet, 50th conference of the Association française pour l'avancement des sciences  (Lyon, 1926)
"Tables des nombres composés vérifiant le théorème de Fermat pour le module 2, jusqu'à 100 000 000"
by Paul Poulet,  Sphinx (Brussels), 8, pp. 42-45 (1938).

 Yves Glenisson 
 Yves Glenisson 
 (November 1962)  
Yves Glénisson  (1962)

Yves-Edouard Glénisson   (1929-2011)
Doris Glénisson  |  Formules de Glénisson  |  Genealogy  |  Wikipédia

Yves Glénisson  was a Belgian mathematician and a trained engineer who was born in Louvain (Belgium) on May 3, 1929.  He was the uncle of the writer Fabienne "Amélie" Nothomb (1966-).  He inherited the title of Roman Count which had been granted in 1902 to his great-grandfather Edouard-Antoine Glénisson (1837-1904) by pope Leo XIII along with the above arms  (inspired from the  Kinschot arms).  Yves Glénisson passed away a few weeks after his eighty-second birthday, on a Sunday morning, May 29, 2011.

 Yves Glenisson 
Yves Glénisson never bore his Belgian family arms:  De sable, à la croix pattée d'or cantonnée de douze abeilles du même, posées en pal.

Yves Glénisson is best remembered for a new way to compute the roots of a polynomial, which he published with Léon Derwidué,  in 1959.

Yves Glénisson  &  Léon Derwidué,
Une nouvelle méthode de calcul des zéros des polynômes
Acad. Roy. Belg. Bull. Cl. Sci. (5) 45 (1959) pp. 197-204.

Thanks to  Countess Doris Glénisson  (eldest daughter of Yves)  for her private communications and the permission to reproduce the above portrait of her father.

McNamee   |   Householder & Stewart, 1971   |   Glénisson & Derwidué, 1960 (pdf, 2485 kB)

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