Jules Tannery (24 March 1848 – 11 December 1910) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard. Tannery's theorem on interchange of limits and series is named after him. He was a brother of the mathematician and historian of science Paul Tannery. Under Hermite, he received a doctorate in 1874 for his thesis ''Propriétés des intégrales des équations différentielles linéaires à coefficients variables.'' Tannery was an advocate for

mathematics education In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out Scholarly method, scholarly research into the transfer of mathematical know ...

, particular as a means to train children in logical consequence through

synthetic geometry Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulates ...

and

mathematical proof A mathematical proof is a deductive reasoning, deductive Argument-deduction-proof distinctions, argument for a Proposition, mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use othe ...

s. Tannery discovered a surface of the fourth order of which all the

geodesic In geometry, a geodesic () is a curve representing in some sense the locally shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a conn ...

lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think." He notably influenced

Pierre Duhem Pierre Maurice Marie Duhem (; 9 June 1861 – 14 September 1916) was a French theoretical physicist who made significant contributions to thermodynamics, hydrodynamics, and the theory of Elasticity (physics), elasticity. Duhem was also a prolif ...

, Paul Painlevé, Jules Drach, and

Émile Borel Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French people, French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability. Biograp ...

to take up science. His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking. Tannery was "an original thinker, a successful teacher, and a writer endowed with an unusually clear, brilliant and attractive style." G. B. Mathews (1910
Jules Tannery

Nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

85:175 (#2145)

Works

* 1894
Leçons sur l'Arithmétique théorique et pratique
Armand Colin & Cie, via Internet Archive * ''Rôle du nombre dans les sciences'' * 1893: J. Tannery and J. Mol
Eléments de la théorie des fonctions elliptiques. Tome I, Introduction. Calcul différentiel. Ire partie
(Paris : Gauthier-Villars et fils) * 1893: J. Tannery and J. Molk
Eléments de la théorie des fonctions elliptiques. Tome II, Calcul différentiel. IIe partie
(Paris : Gauthier-Villars et fils) * 1893: J. Tannery and J. Molk
Eléments de la théorie des fonctions elliptiques. Tome III, Calcul intégral. Ire partie, Théorèmes généraux. Inversion
(Paris : Gauthier-Villars et fils) * 1893: J. Tannery and J. Molk
Eléments de la théorie des fonctions elliptiques. Tome IV, Calcul intégral. IIe partie, Applications
(Paris : Gauthier-Villars et fils) * 1901
Notice sur les travaux scientifique de M. Jules Tannery
Gauthier-Villars via Internet Archive * 1904
Introduction à la théorie des fonctions d'une variable, volume 1
Librairie Scientifique A. Hermann * 1910
Introduction á la théorie des fonctions d'une variable, volume 2
Librairie Scientifique A. Hermann * 1906
Leçons d'algèbra et d'analyse, volume 1
via Internet Archive * 1906
Leçons d'algèbra et d'analyse, volume 2
via Internet Archive * 1910
Correspondence entre Lejeun Dirichlet et Liouville
via

Internet Archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ...

* 1924
Science et Philosophie
with Introduction by

, Librairie Felix Alcan via Internet Archive

References

* George Sarton (1947) "Paul, Jules, and Marie Tannery (with a note on Grégoire Wyrouboff)",

Isis Isis was a major goddess in ancient Egyptian religion whose worship spread throughout the Greco-Roman world. Isis was first mentioned in the Old Kingdom () as one of the main characters of the Osiris myth, in which she resurrects her sla ...

38 (1/2): 33–51.

External links

* * {{DEFAULTSORT:Tannery, Jules 19th-century French mathematicians Members of the French Academy of Sciences Academic staff of the University of Paris 1848 births 1910 deaths