Jean Baptiste Joseph Fourier

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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.  Laplace, and later  Poisson, had similar objections.

The Institute set as a prize competition subject the propagation of heat in solid bodies for the 1811 mathematics prize. 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. The report was not however completely favourable and states:-

... the manner in which the author arrives at these equations is not exempt of difficulties and that his analysis to integrate them still leaves something to be desired on the score of generality and even rigour.

With this rather mixed report there was no move in Paris to publish Fourier's work.

When Napoleon was defeated and on his way to exile in Elba, his route should have been through Grenoble. 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. He tried to persuade the people of Grenoble to oppose Napoleon and give their allegiance to the King. However as Napoleon marched into the town Fourier left in haste.

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. He could not have completely fallen out with Napoleon and  Carnot, however, for on 10 June 1815, Napoleon awarded him a pension of 6000 francs, payable from 1 July. However Napoleon was defeated on 1 July and Fourier did not receive any money. He returned to Paris.

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 Academy published his prize winning essay Théorie analytique de la chaleur in 1822. This was not a piece of political manoeuvring by Fourier however since  Delambre had arranged for the printing before he died.

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. His life was not without problems however since his theory of heat still provoked controversy.  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 as a reply to these claims but, although the work was shown to various mathematicians, it was never published.

Fourier's views on the claims of  Biot and  Poisson are given in the following, see:-

Having contested the various results [ Biot and  Poisson] now recognise that they are exact but they protest that they have invented another method of expounding them and that this method is excellent and the true one. If they had illuminated this branch of physics by important and general views and had greatly perfected the analysis of  partial differential equations, if they had established a principal element of the theory of heat by fine experiments ... they would have the right to judge my work and to correct it. I would submit with much pleasure .. But one does not extend the bounds of science by presenting, in a form said to be different, results which one has not found oneself and, above all, by forestalling the true author in publication.

Fourier's work provided the impetus for later work on trigonometric series and the theory of functions of a real variable.

J J O'Connor and E F Robertson

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