**Joseph Gergonne** was a French mathematician who published an influential journal and made contributions to duality theory in projective geometry.

- However, he died when Joseph was twelve years old.
- Joseph was educated at the Collège de Nancy which was a religious establishment.
- Gergonne gave his support becoming a captain in the National Guard.
- The Assembly called for 100,000 military volunteers and Gergonne joined the French army being assembled to defend Paris against the Prussians.
- On 20 September 1792 Kellermann led the French forces at Valmy with Gergonne in his army.
- Gergonne returned to the French army, this time as secretary to the general staff of the Moselle army.
- Gergonne spent a month at the Châlons artillery school in 1794 and after this he was commissioned as a lieutenant.
- Gergonne was attached to these forces which entered Spain and laid siege to the town of Figueras capturing it.
- At this stage Gergonne was sent with his regiment to Nimes in southern France.
- In that city the École Centrale had been set up shortly before and Gergonne was appointed to the chair of transcendental mathematics.
- Gergonne, however, settled down at this point.
- Finding problems getting his mathematics papers published, Gergonne established his own mathematics journal, the first part appearing in 1810.
- The Journal was officially called the Annales de mathématiques pures et appliquées Ⓣ(Annals of Pure and Applied Mathematics) but became known as Annales de Gergonne .
- Gergonne's mathematical interests were in geometry so it is not surprising that it was this topic which figured most prominently in his journal.
- Many famous mathematicians published in the twenty-one volumes of the Annales de Gergonne which appeared during a period of twenty-two years.
- In addition to Gergonne himself (who published around 200 articles), Poncelet, Servois, Bobillier, Steiner, Plücker, Chasles, Brianchon, Dupin, Lamé, Galois and many others had papers appear in the Journal.
- In 1813 Gergonne wrote a prize winning essay for the Bordeaux Academy Methods of synthesis and analysis in mathematics.
- The essay tells us a lot about Gergonne's mathematical ideas.
- Perhaps surprisingly, since Gergonne was himself a geometer, he suggests that algebra is a more important topic than geometry.
- We will examine Gergonne's contributions to geometry later in this article, but for the moment it is worth noting that he did publish on other topics.
- Gergonne looked at how to estimate the values of the response function, and of its derivatives, at a point when there are random errors in the observed values.
- Gergonne was appointed to the chair of astronomy at the University of Montpellier in 1816.
- It was in 1830 that Gergonne became rector of the University of Montpellier.
- Gergonne retired in 1844 at the age of 73.
- Gergonne provided an elegant solution to the Problem of Apollonius in 1816.
- Gergonne introduced the word polar and the principle of duality in projective geometry was one of his main contributions.
- Gergonne's first contributions to duality appear in a series of papers beginning in 1810.
- We have already illustrated Gergonne's interest in the philosophy of mathematics with a description of his unpublished essay on the topic in 1813.

Born 19 June 1771, Nancy, France. Died 4 May 1859, Montpellier, France.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive