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Person: Fourier, Jean Baptiste Joseph

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.

Mathematical Profile (Excerpt):

• 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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Tags relevant for this person:

Algebra, Analysis, Bourbaki, Group Theory, Topology

Thank you to the contributors under CC BY-SA 4.0!

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@J-J-O'Connor

@E-F-Robertson

References

Adapted from other CC BY-SA 4.0 Sources:

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