[drooglyman]

For what it's worth, I just spent ~10 minutes looking for a solid source on this and couldn't find confirmation.

The closest I found was a bio[1], which includes the following:

> 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.

So it's not entirely wrong, but I think that all-star team was not his defense committee.

[1] https://mathshistory.st-andrews.ac.uk/Biographies/Fourier

[Someone]

https://link.springer.com/chapter/10.1007/978-0-387-98098-0_... states the same, and mentions what I couldn’t find earlier: that they criticized Fourier for his lack of rigour (I remember that as something along the lines of “but if that’s correct, this also is and that can’t be true, can it?”, (with “this” being Gibb’s phenomenon (https://en.wikipedia.org/wiki/Gibbs_phenomenon)), but chances are high that isn’t happen, either.

Edit: https://www.comsol.com/blogs/happy-birthday-joseph-fourier/ has more info. If he did a thesis defense (did he?), I guess there’s a decent chance Laplace and Lagrange (his supervisor, according to https://www.genealogy.math.ndsu.nodak.edu/id.php?id=17981) were there.

Legendre seems doubtful. Weirdly, Legendre doesn’t seem to exist in the Mathematics Genealogy Project.

Edit 2: https://www.gutenberg.org/files/16775/16775-h/16775-h.htm#PA... (by https://en.wikipedia.org/wiki/François_Arago, who was only 18 years younger than Fourier) is the best I can find on this. It says:

“The first memoir of Fourier on the theory of heat dates from the year 1807. The Academy, to which it was communicated, being desirous of inducing the author to extend and improve his researches, made the question of the propagation of heat the subject of the great mathematical prize which was to be awarded in the beginning of the year 1812. Fourier did, in effect, compete, and his memoir was crowned. But, alas! as Fontenelle said: "In the country even of demonstrations, there are to be found causes of dissension." Some restrictions mingled with the favourable judgment. The illustrious commissioners of the prize, Laplace, Lagrange, and Legendre, while acknowledging the novelty and importance of the subject, while declaring that the real differential equations of the propagation of heat were finally found, asserted that they perceived difficulties in the way in which the author arrived at them. They added, that his processes of integration left something to be desired, even on the score of rigour. They did not, however, support their opinion by any arguments.”