Pierre Vernier (1584-1638)
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,
calipers and other precision measuring instruments.
Originally, he described a quadrant allowing
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
Improvements were attempted by
Jacob Curtius (1554-1594)
and by the Bavarian Jesuit
(né Schlussel, 1538-1612)
who is best remembered as the astronomer who engineered the modern
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):
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.
de M. Sturm et de ses applications numériques" (Nantes & Paris, 1836)
After his retirement in 1838, Etienne Midy published
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 (1785-1838; X1801)
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
Jacques Thénard (1777-1857) a famous teacher who had invented
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
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
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 (1794-1872; X1812)
Christian Nitschelm |
Jacques Babinet was born on 1794-03-05 in
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,
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
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
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
(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)
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
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).
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,
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
According to a
possibly a hoax with some
of truth, Hippolyte fathered a mysteriously plagiarized poet called Hugo Vernier
(1836-1864) born to Sarah Judith Singer on September 3, 1836 in
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
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 !
of the focus-directrix characterization of conics, using Dandelin spheres
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
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
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)
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):
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.
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
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
Bigourdan was awarded his agrégation on 1832-09-24 (ranked third in France)
shortly after obtaining his doctorate in Paris, on
(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
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).
Bigourdan à P.-F. Dubois (25 octobre 1840). Letters addressed to Paul-Franç Dubois sous Louis-Philippe.
Urbain Le Verrier
Urbain Le Verrier (1811-1877; X1831)
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
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
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 :
(1798-1880) had been a mathematical coach
at La Flèche
and he would later obtain a
doctorate in astronomy
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,
(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
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
Evariste Galois (1811-1832)
The Evariste Galois Archive
At the age of 20, Evariste Galois
was mortally wounded in a duel (against
over a young lady called
Stéphanie-Félice Poterin du Motel.
Left for dead, Galois (who had no
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
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
sur ce terrain, qui est immense.
But I am running out of time, and my ideas are not yet
in this field, which is immense.
Galois' Testament ends with the following words:
Tu prieras publiquement Jacobi ou
Gauss de donner leur avis|
sur la vérité, mais sur l'importance des
Après cela il se trouvera, j'espère, des gens qui trouveront leur profit
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,
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).
He took his first mathematics class in February 1827
and quickly became enthralled with the subject.
He had an exceptional instructor,
Hippolyte Vernier, who
taught from Legendre's
Elements de Géometrie (1794) the textbook which was then spearheading the liberation
from traditional Euclidean teaching, all over Europe.
In 1828-1829, Evariste Galois was a
Mathématiques Spéciales student
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),
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
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
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
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).
"Galois, le mathématicien maudit"
Norbert Verdier (Belin, 2011).
Antoine François Joseph Yvon-Villarceau (1813-1883)
Serge Mehl (French)
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
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).
"Théorème sur le tore", M. Yvon Villarceau
Nouvelles Annales de mathématiques, 7, pp. 345-347 (Paris, 1848)
Auguste Miquel (1816-1851)
Serge Mehl (French)
Jean-Louis Aymé (2012-10-30)
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
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
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
Artaud de Montor, 1772-1849),
the geometer Georges Ritt (1800-1864) author of several textbooks, and
Roch Roustan (1801-1870) future recteur of
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,
(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
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
- 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
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
de mathématiques pures et appliquées (founded in 1836) including:
"Sur quelques questions relatives à la théorie des courbes",
Journal de mathématiques pures et appliquées,
III, pp. 202-208 (1838).
"Théorèmes de Géometrie",
JMPA, III, pp. 485-487 (1838).
sur les intersections des cercles et des sphères",
Journal de mathématiques pures et appliquées,
III, 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
counterpart (1842-1927) of Liouville's journal:
Nouvelles annales de mathématiques, 5, pp. 235-238 (Paris, 1846).
Auguste Miquel died in 1851, at age 35, in obscure circumstances.
mathématiques au XIXème siècle
Miquel's Theorem (Dutch)
Victor Alexandre Puiseux (1820-1883)
Academic career (French)
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
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
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
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
(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
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
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
J. Dieudonné on
Jules Hoüel (1823-1886)
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.
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
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.
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
(7 out of 9 that year).
He first taught in the lycées of
Bourges, Bordeaux, Pau and Alençon (1851).
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
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
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
Emile Léonard Mathieu (1835-1890; X1854)
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
Edouard Lucas (1842-1891)
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
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
by studying mathematical problems in his hometown of Amiens.
He became acquainted with the mathematics pertaining to
the industrial weaving of fabrics (using
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
(1876-1879, 1890-1891) and
(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
Edouard Lucas is buried in Montmartre Cemetery.
In 1876, Lucas proved the primality of a 39-digit number
Mersenne prime) which would remain
the largest known prime for 75 years (until 1951):
2127 - 1 =
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
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)
Théorie des nombres 528 pages (Gauthier-Villars, 1891)
Jules Tannery (1848-1910)
Like his older brother
Tannery (1843-1904), Jules Tannery was an alumnus of the
(Lycée Malherbe de Caen) where he taught briefly (1871-1872) early in his career.
His star student at the time was
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).
Other students of Tannery's at ENS included the likes of
Painlevé (twice a Prime Minister of France, in 1917 and 1925)
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:
(a / Ö32) sin u cos v
(a / Ö32) sin u sin v
a sin u/2
Every geodesic curve (like the bold line shown at left)
is an algebraic
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
Tannery's Limiting Theorem
François Cosserat (1852-1914; X1870)
Lucien Cosserat (1856-1897; X1875)
Eugène Cosserat (1866-1931; ENS 1883)
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.
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.
"Théorie des corps déformables" by Eugène & François Cosserat
(Hermann, 1909). 230 pages.
Ernest Vessiot (1865-1952)
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.
Vessiot held several teaching positions, starting at Lyon in 1887,
then Lille (1892) Toulouse, Lyon again and Paris (1910).
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.
Ernest Vessiot obtained his doctorate in 1892, under
C. Emile Picard
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).
Jules Drach (1871-1949)
Work of Jules Drach
Like Jacques Hadamard earlier,
Jules Drach did his doctoral work at
Ecole Normale Supérieure under the supervision of
Rues de Ludres
André Gérardin (1879-1953)
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
- Diophante (Diophantus)
four times a year, from 1948 to 1952.
quelques nouvelles machines algébriques
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
(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
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 Glénisson (1962)|
Yves-Edouard Glénisson (1929-2011)
Formules de Glénisson
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"
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
(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 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.
Householder & Stewart, 1971
& Derwidué, 1960 (pdf, 2485 kB)
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