**Joseph Fourier** studied the mathematical theory of heat conduction. He established the partial differential equation governing heat diffusion and solved it by using infinite series of trigonometric functions.

- There Joseph studied Latin and French and showed great promise.
- In 1787 Fourier decided to train for the priesthood and entered the Benedictine abbey of St Benoit-sur-Loire.
- Fourier was unsure if he was making the right decision in training for the priesthood.
- Fourier did not take his religious vows.
- Up until this time there had been a conflict inside Fourier about whether he should follow a religious life or one of mathematical research.
- Certainly Fourier was unhappy about the Terror which resulted from the French Revolution and he attempted to resign from the committee.
- However this proved impossible and Fourier was now firmly entangled with the Revolution and unable to withdraw.
- Fourier defended members of one faction while in Orléans.
- It seems that Fourier ...
- This incident was to have serious consequences but after it Fourier returned to Auxerre and continued to work on the revolutionary committee and continued to teach at the College.
- Later in 1794 Fourier was nominated to study at the École Normale in Paris.
- The school opened in January 1795 and Fourier was certainly the most able of the pupils whose abilities ranged widely.
- Fourier began teaching at the Collège de France and, having excellent relations with Lagrange, Laplace and Monge, began further mathematical research.
- By 1 September 1795 Fourier was back teaching at the École Polytechnique.
- In 1798 Fourier joined Napoleon's army in its invasion of Egypt as scientific adviser.
- While in Cairo Fourier helped found the Cairo Institute and was one of the twelve members of the mathematics division, the others included Monge, Malus and Napoleon himself.
- Fourier was elected secretary to the Institute, a position he continued to hold during the entire French occupation of Egypt.
- Fourier was also put in charge of collating the scientific and literary discoveries made during the time in Egypt.
- Fourier returned to France in 1801 with the remains of the expeditionary force and resumed his post as Professor of Analysis at the École Polytechnique.
- Fourier was not happy at the prospect of leaving the academic world and Paris but could not refuse Napoleon's request.
- It was during his time in Grenoble that Fourier did his important mathematical work on the theory of heat.
- The first objection, made by Lagrange and Laplace in 1808, was to Fourier's expansions of functions as trigonometrical series, what we now call Fourier series.
- Further clarification by Fourier still failed to convince them.
- The second objection was made by Biot against Fourier's derivation of the equations of transfer of heat.
- Fourier had not made reference to Biot's 1804 paper on this topic but Biot's paper is certainly incorrect.
- Fourier submitted his 1807 memoir together with additional work on the cooling of infinite solids and terrestrial and radiant heat.
- Only one other entry was received and the committee set up to decide on the award of the prize, Lagrange, Laplace, Malus, Haüy and Legendre, awarded Fourier the prize.
- With this rather mixed report there was no move in Paris to publish Fourier's work.
- Fourier managed to avoid this difficult confrontation by sending word that it would be dangerous for Napoleon.
- When he learnt of Napoleon's escape from Elba and that he was marching towards Grenoble with an army, Fourier was extremely worried.
- However as Napoleon marched into the town by one gate Fourier left in haste by another.
- Napoleon was angry with Fourier who he had hoped would welcome his return.
- Fourier was able to talk his way into favour with both sides and Napoleon made him Prefect of the Rhône.
- However Fourier soon resigned on receiving orders, possibly from Carnot, that the was to remove all administrators with royalist sympathies.
- However Napoleon was defeated on 1 July and Fourier did not receive any money.
- Fourier was elected to the Académie des Sciences in 1817.
- In 1822 Delambre, who was the Secretary to the mathematical section of the Académie des Sciences, died and Fourier together with Biot and Arago applied for the post.
- After Arago withdrew the election gave Fourier an easy win.
- Shortly after Fourier became Secretary, the Académie published his prize winning essay Théorie analytique de la chaleur in 1822.
- During Fourier's eight last years in Paris he resumed his mathematical researches and published a number of papers, some in pure mathematics while some were on applied mathematical topics.
- Biot claimed priority over Fourier, a claim which Fourier had little difficulty showing to be false.
- Poisson, however, attacked both Fourier's mathematical techniques and also claimed to have an alternative theory.
- Fourier wrote Historical Précis Ⓣ(Historical summary) as a reply to these claims but, although the work was shown to various mathematicians, it was never published.
- Fourier's work provided the impetus for later work on trigonometric series and the theory of functions of a real variable.

Born 21 March 1768, Auxerre, Bourgogne, France. Died 16 May 1830, Paris, France.

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Algebra, Analysis, Bourbaki, Group Theory, Topology

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