Paul Tannery's parents were Delphin Tannery, who was an engineer working for the French railways, and Opportune Perrier. Delphin and Opportune Tannery had three children, the eldest being a daughter while the second oldest was Paul and Jules Tannery was the youngest. Delphin Tannery's job with the railways involved him moving around the country depending on where railways were being constructed. The family moved from Mantes to Redon in Ille-et-Vilaine in the Brittany region of northwestern France. He later worked at Mondeville close to Caen.
Paul was brought up in a deeply Christian family. His parents Delphin and Opportune Tannery, who were Roman Catholics, gave him his early education, then he attended schools in several towns as his parents moved because of his father's job. First he attended school a private school in Mantes, then the Lycée in Le Mans finally completing his secondary education at the Lycée at Caen. Although he was enrolled for a science course at Caen, his interests included classics and philosophy.
His parents who were very keen to see their sons achieve great things with their education so they were delighted when, after completing his secondary education in 1860, Tannery sat the entrance examinations in science for the École Polytechnique. Having attained one of the highest possible grades in both examination he entered the school, taking a wide range of courses in science, mathematics, technology and classical subjects such as Hebrew. He graduated from the École Polytechnique in 1863 and entered the École d'Application des Tabacs. He would spend the rest of his working life involved with the tobacco industry.
It was in this period after he graduated the Tannery became interested in the positivist philosophy of Comte. Auguste Comte, the French philosopher known as the founder of sociology and of positivism, published his philosophy in a work entitled Cours de philosophie positive Ⓣ in six volumes between 1830 and 1842. It presented a philosophy designed to produce a system of government making full use of technology in a way appropriate to modern industrial society. Tannery was much influenced by Comte's philosophy and it would influence his work throughout his life.
Tannery worked from 1865 to 1867 in the state tobacco factory at Lille before moving to Paris to an administrative post in the administration of the state tobacco industry. The Franco-Prussian War began on 19 July 1870. Tannery, a staunch French patriot, served in the French army as an artillery captain. The war went badly for France and on 19 September 1870 the Germans began a siege of Paris. Tannery was present during the siege, and was dismayed when Paris surrendered on 28 January 1871. The Treaty of Frankfurt, signed on 10 May 1871 was an humiliation for France, with Germany annexing Alsace and half of Lorraine. Tannery refused to acknowledge the terms of this treaty.
The war having ended, Tannery returned to his administrative post but he became very interested in mathematics being particularly influenced by his brother Jules Tannery who by this time was teaching mathematics. Sent to Périgord to help with the construction of buildings, Tannery became ill. This in many ways worked in his favour since he used the time during which he was recovering to study more deeply, in particular learning ancient languages.
Sent to Bordeaux in 1874, again to help with construction work, Tannery found there friends and university facilities which allowed him to spend all his free time working on the history of mathematics in ancient cultures. He had all the necessary skills to make a major contribution to this field and indeed his first publication, occurred around this time. Taton writes in  that he became:-
... a fairly regular contributor to about fifteen French and foreign periodicals. He published hundreds of memoirs, articles, notes, and reviews while pursuing a brilliant career in the state tobacco administration. Although many other historians of science have been obliged to conduct their research concurrently with their professional activities, none of them seems to have produced a body of work comparable to Tannery's in scope and importance.In 1877 Tannery made the rather strange move of requesting a move to Le Havre. This was a strange move since he was immediately deprived of the academic environment of Bordeaux. However, several trips abroad saw his became friends with other notable historians of science such as Heiberg, Zeuthen and Moritz Cantor. He carried on a correspondence with the mathematicians he had met after his return. For example the paper  describes three letters he exchanged with Zeuthen dealing with questions in the Greek theory of conic sections and the significance of certain constructions by means of "neusis."
Tannery married Marie-Alexandrine Prisset in 1881. She was 13 years younger than he was and, had relatively little education but, after Tannery's death, she would undertake the difficult task of preparing a complete publication of his works with remarkable skill.
By 1883 Tannery was finding the academic isolation of Le Havre too much to bear and he applied for a transfer to Paris. This was granted and, although he did not remain there for very long, it proved a period in which his work on the history of Greek geometry flourished. From 1886 until 1888 Tannery was in Tonneins and, deprived of library and other resources, he was unable to carry out any serious work on the history of mathematics except editorial work. In January 1888 he returned to Bordeaux as director of the tobacco factory and was able to slot into the intellectual life he had lived there earlier.
From 1890 until 1893 he was back at the headquarters of the administration of the state tobacco industry in Paris, and then in 1893 he made his final move to be director of a tobacco factory at Pantin near Paris. A rather strange, and sad, episode occurred near the end of his life. The chair of history of science at the Collège de France became vacant in 1903. Tannery was named as the first choice to fill the post by the two consultative bodies. So certain was Tannery that his appointment after that was merely a formality, that he started work on writing his inaugural lecture.. The minister of education chose not to follow the recommendations of the consultative bodies, however, and appointed a philosopher with little experience in the history of science. It seems that the government did not want a Roman Catholic for the post and also preferred the course proposed by the other candidate on contemporary science rather than Tannery's proposed course on the history of science. It did not escape the notice of Tannery, his friends, and his international colleagues that a course on the history of science seemed appropriate for a professor of the history of science. All their protests were in vain and, as Taton writes in :-
... there is no doubt that the "scandal of 1903" did great damage to the development of the history of science in France.He died of cancer of the pancreas at the age of sixty while still at the height of his intellectual powers.
His main contributions were to the history of Greek mathematics and to the philosophy of mathematics. He published a history of Greek science in 1887, a history of Greek geometry in the same year, and a history of ancient astronomy in 1893.
Tannery did work of great importance as an editor of famous mathematics texts. He edited the work of Fermat in three volumes (jointly with C Henry) between 1891 and 1896. In addition he edited the work of Diophantus in two volumes (1893-95). He was an editor of the twelve volume complete works of Descartes Oeuvres de Descartes (1897-1913).
Tannery became so skilled in using Greek numerals in his historical work that he believed that they had certain advantages over our present system.
Taton, himself a famous historian of mathematics, sums up Tannery's work in :-
Perhaps its most notable characteristic is an unwavering concern for rigour and precision. the detailed studies that constituted the bulk of his output were, in Tannery's view, only a necessary stage in the elaboration on much broader syntheses that would ultimately lead to a comprehensive history of science that he himself could openly initiate.
Article by: J J O'Connor and E F Robertson