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**Paul Tannery** (20 December 1843 – 27 November 1904) was a French mathematician and historian of mathematics. He was the older brother of mathematician Jules Tannery, to whose *Notions Mathématiques* he contributed an historical chapter. Though Tannery's career was in the tobacco industry, he devoted his evenings and his life to the study of mathematicians and mathematical development.

**France**, officially the **French Republic**, is a country whose territory consists of metropolitan France in Western Europe and several overseas regions and territories. The metropolitan area of France extends from the Mediterranean Sea to the English Channel and the North Sea, and from the Rhine to the Atlantic Ocean. It is bordered by Belgium, Luxembourg and Germany to the northeast, Switzerland and Italy to the east, and Andorra and Spain to the south. The overseas territories include French Guiana in South America and several islands in the Atlantic, Pacific and Indian oceans. The country's 18 integral regions span a combined area of 643,801 square kilometres (248,573 sq mi) and a total population of 67.3 million. France, a sovereign state, is a unitary semi-presidential republic with its capital in Paris, the country's largest city and main cultural and commercial centre. Other major urban areas include Lyon, Marseille, Toulouse, Bordeaux, Lille and Nice.

**Mathematics** includes the study of such topics as quantity, structure, space, and change.

**Jules Tannery** was a French mathematician, brother of the mathematician and historian of science Paul Tannery, 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.

Tannery was born in Mantes-la-Jolie on 20 December 1843, to a deeply Catholic family. He attended private school in Mantes, followed by the Lycées in Le Mans and Caen. He then entered the École Polytechnique, on whose entrance exam he excelled. His curriculum included mathematics, the sciences, and the classics, all of which would be represented in his future academic work. Tannery's life of public service began as he then entered the École d'Applications des Tabacs as an apprentice engineer.

**Mantes-la-Jolie** is a commune based in the Yvelines department in the Île-de-France region in north-central France. It is located to the west of Paris, 48.4 km (30.1 mi) from the centre of the capital. Mantes-la-Jolie is a subprefecture of the department.

**Caen**, is a commune in northwestern France. It is the prefecture of the Calvados department. The city proper has 108,365 inhabitants, while its urban area has 420,000, making Caen the largest city in former Lower Normandy. It is also the third largest municipality in all of Normandy after Le Havre and Rouen and the third largest city proper in Normandy, after Rouen and Le Havre. The metropolitan area of Caen, in turn, is the second largest in Normandy after that of Rouen, the 21st largest in France.

**École polytechnique** is a French public institution of higher education and research in Palaiseau, a suburb southwest of Paris. It is one of the most prestigious and selective French scientific and engineering schools, called *grandes écoles* in French. It is known for its *ingénieur polytechnicien* scientific degree program which is equivalent to both a bachelor and master of science. Its entrance exam, the X-ENS exam, is renowned for its selectivity with a little over 500 admitted students out of the 53 848 students enrolled in the preparatory programs for the French scientific and engineering schools entrance exams.

As an assistant engineer, Tannery spent two years in the state tobacco factory at Lille. In 1867, he moved to Paris; three years later, he served as an artillery captain in the Franco-Prussian War. Biographies of Tannery describe him as an ardent patriot and claim that he never fully accepted the humiliating Treaty of Frankfurt.

**Lille** is a city at the northern tip of France, in French Flanders. On the Deûle River, near France's border with Belgium, it is the capital of the Hauts-de-France region, the prefecture of the Nord department, and the main city of the European Metropolis of Lille.

**Paris** is the capital and most populous city of France, with an area of 105 square kilometres and an official estimated population of 2,140,526 residents as of 1 January 2019. Since the 17th century, Paris has been one of Europe's major centres of finance, diplomacy, commerce, fashion, science, and the arts.

The **Franco-Prussian War** or **Franco-German War**, often referred to in France as the **War of 1870**, was a conflict between the Second French Empire and later the Third French Republic, and the German states of the North German Confederation led by the Kingdom of Prussia. Lasting from 19 July 1870 to 28 January 1871, the conflict was caused by Prussian ambitions to extend German unification and French fears of the shift in the European balance of power that would result if the Prussians succeeded. Some historians argue that the Prussian chancellor Otto von Bismarck deliberately provoked the French into declaring war on Prussia in order to draw the independent southern German states—Baden, Württemberg, Bavaria and Hesse-Darmstadt—into an alliance with the North German Confederation dominated by Prussia, while others contend that Bismarck did not plan anything and merely exploited the circumstances as they unfolded. None, however, dispute the fact that Bismarck must have recognized the potential for new German alliances, given the situation as a whole.

After his graduation from the École Polytechnique, Tannery had become interested in Auguste Comte and his positivist philosophy. After the war, his interest in mathematics continued, and Comte's ideas would influence his approach to the study of the history of science. Tannery moved several times with his career in the tobacco industry: to Périgord in 1872, to Bordeaux in 1874, to Le Havre in 1877, and to Paris in 1883. Bordeaux had something of an intellectual atmosphere, and though Tannery moved to Le Havre (near his parents, who lived at Caen) at his own request, he would also directly request the move to Paris, where his research and academic pursuits would be able to flourish.

**Isidore Marie Auguste François Xavier Comte** was a French philosopher and writer who formulated the doctrine of positivism. He is sometimes regarded as the first philosopher of science in the modern sense of the term.

**Positivism** is a philosophical theory stating that certain ("positive") knowledge is based on natural phenomena and their properties and relations. Thus, information derived from sensory experience, interpreted through reason and logic, forms the exclusive source of all certain knowledge. Positivism holds that valid knowledge is found only in this *a posteriori* knowledge.

**Bordeaux** is a port city on the Garonne in the Gironde department in Southwestern France.

It was in Paris that Tannery took on his first two major editorial works. In 1883, he began an edition of Diophantus's manuscripts, and in 1885, he and Charles Henry began an edition of one of Fermat's works. This work was made possible by access to the Bibliothèque Nationale, and so Tannery had to reduce his efforts in 1886 when he was transferred to Tonneins. Even without access to the Bibliothèque, Tannery remained hard at work, however, as he published two books composed of articles he had been writing for the * Revue philosophique de la France et de l'étranger * and for the *Bulletin de sciences mathematiques*.

**Diophantus of Alexandria** was an Alexandrian Hellenistic mathematician, who was the author of a series of books called *Arithmetica*, many of which are now lost. Sometimes called "the father of algebra", his texts deal with solving algebraic equations. While reading Claude Gaspard Bachet de Méziriac's edition of Diophantus' *Arithmetica,* Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted in the margin without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of Diophantine equations and of Diophantine approximations remain important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as *adaequalitas* in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought.

**Charles Henry** (1859–1926) was a French librarian and editor. He was born at Bollwiller, Haut-Rhin, and was educated in Paris, where in 1881 he became assistant and afterward librarian in the Sorbonne. As a specialist in the history of mathematics, he was sent to Italy to seek some manuscripts of that nature which the government wished to publish. He edited several works upon kindred subjects, as well as memoirs, letters, and other volumes, and wrote critiques upon the musical theories of Rameau and Wronski. He is also credited with the invention of several ingenious devices and instruments used in psychophysiological laboratories. He published C. Huet's correspondence under the title *Un érudit, homme du monde, homme d'église, homme de cour* (1880), and he issued also *Problèmes de géométrie pratique* (1884) and *Lettres inédites de Mlle. de Lespinasse à Condorcet et à D'Alembert* (1887).

**Pierre de Fermat** was a French lawyer at the *Parlement* of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' *Arithmetica*.

In 1888, Tannery moved back to Bordeaux, where he studied Greek astronomy and directed the tobacco factory. Two years later, he was back in Paris; he would remain near Paris until his death. Despite a heavy professional workload, he continued to be productive in his work in the history of science. His editions of Diophantus and Fermat were published, along with over 250 articles. From 1890 forward, Tannery's other major work focused on a new edition of Descartes's works and correspondence, on which he collaborated with Charles Adam, an historian of modern philosophy.

**René Descartes** was a French philosopher, mathematician, and scientist. A native of the Kingdom of France, he spent about 20 years (1629–1649) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces. He is generally considered one of the most notable intellectual figures of the Dutch Golden Age.

Scandal arose in 1903 when the Collège de France began a search for a new professor of the history of science. Tannery was considered something of a shoo-in; he even began writing his inaugural lecture. Instead, the position went to Grégoire Wyrouboff, who concentrated on modern mathematicians instead of Tannery's classical and seventeenth-century idols. Wyrouboff was also a freethinker, an asset to the secularist Third Republic, while Tannery was Catholic.

Tannery died soon thereafter, on 27 November 1904, in Pantin, just outside Paris. His wife, Marie, would survive until 1945, and she published several of his works posthumously, helping to ensure that his legacy would live on.

He was an Invited Speaker of the ICM in 1904 in Heidelberg.^{ [1] }

Baron **Augustin-Louis Cauchy** was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors. He almost singlehandedly founded complex analysis and the study of permutation groups in abstract algebra.

**Gaspard-Gustave de Coriolis** was a French mathematician, mechanical engineer and scientist. He is best known for his work on the supplementary forces that are detected in a rotating frame of reference, leading to the Coriolis effect. He was the first to apply the term *travail* for the transfer of energy by a force acting through a distance.

**Gabriel Lamé** was a French mathematician who contributed to the theory of partial differential equations by the use of curvilinear coordinates, and the mathematical theory of elasticity.

**Jacques Salomon Hadamard** ForMemRS was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.

**Laurent-Moïse Schwartz** was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 1950 for his work on the theory of distributions. For several years he taught at the École polytechnique.

**Jacques Charles François Sturm** ForMemRS was a French mathematician.

**Charles-Ange Laisant**, French politician and mathematician, was born at Indre, near Nantes on 1 November 1841, and was educated at the École Polytechnique as a military engineer.

**Henri Claudius Rosarius Dulac** was a French mathematician.

**Grigory Nikolayevich Vyrubov**, or **Grégoire Wyrouboff** was a Russian Positivist philosopher and historian of science.

**Charles Hermite** FRS FRSE MIAS was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.

**Frédéric Hélein** is a French mathematician. He is university professor at Paris Diderot University.

**Abel Étienne Louis Transon** was a French mathematician, utopian socialist and journalist.

**Marie Georges Humbert** was a French mathematician who worked on Kummer surfaces and the Appell–Humbert theorem and introduced Humbert surfaces. His son was the mathematician Pierre Humbert. He won the Poncelet Prize of the Académie des Sciences in 1891.

**Charles-François- Maximilien Marie** (1819–1891) was a French mathematician, historian of mathematics. He was the author of

**Jules Joseph Drach** was a French mathematician.

**Émile Victor Jamet** was a French mathematician.

**Paul Jean Joseph Barbarin** was a French mathematician, specializing in geometry.

- ↑ Tannery, P. (1905). "
*Pour l'histoire du problème inverse des tangentes*".*Verhandlungen des dritten Mathematiker-Kongresses in Heidelberg von 8. bis 13. August 1904*. Leipzig: B. G. Teubner. pp. 502–514.

- Bryan, G.H. (March 1905). "Obituary Notice: M. Paul Tannery".
*The Mathematical Gazette*. The Mathematical Association.**3**(50): 168. - O'Connor, John J.; Robertson, Edmund F., "Paul Tannery",
*MacTutor History of Mathematics archive*, University of St Andrews . - Sarton, George (November 1947). "Paul, Jules, and Marie Tannery (with a note on Grégoire Wyrouboff)".
*Isis*. University of Chicago Press.**38**(1/2): 33–51. doi:10.1086/348033. - "Tannery, Paul".
*Dictionary of Scientific Biography*. Scribner. 1970. pp. 251–257.

- O'Connor, J J; E F Robertson. "How do we know about Greek mathematicians?" . Retrieved 2009-03-19.
- "Paul Tannery".
*Osiris*. Saint Catherines Press.**4**: 633–689. 1938. doi:10.1086/368485. (French) - Sarton, George; Pierre Boutroux (1938). "L'OEuvre de Paul Tannery".
*Osiris*. Saint Catherines Press.**4**: 690–705. doi:10.1086/368486. (French) - Sarton, George (November 1947). "Paul, Jules, and Marie Tannery (with a note on Grégoire Wyrouboff)".
*Isis*. University of Chicago Press.**38**(1/2): 33–51. doi:10.1086/348033. - "Tannery, Paul".
*Dictionary of Scientific Biography*. Scribner. 1970. pp. 251–257.

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