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Besides the famous cartoon, of course, there seems to be no portrait of Legendre. Legendre is well regarded nowadays and he was also quite influential at his time, for example, Jacobi and Abel praised him. Furthermore, he came from a wealthy family. So it is surprising to me that there is no actual portrait of him.

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    $\begingroup$ Thomas Carlyle, Reminiscences, London: Macmillan 1887, p. 163: "Old Legendre, the Mathematician (whose Geometry I had translated in Edinburgh) was the only man of real note with whom I exchanged a few words. A tall, bony, gray, old man; who received me with dignity and kindness; ... asked about my stay here, and finding I was just about to go, answered “Diantre !” with an obliging air of regret: his rugged, sagacious, sad and stoical old face is still dimly present with me." $\endgroup$
    – njuffa
    Mar 10 at 6:31

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Because (Adrien-Marie) Legendre, the mathematician, wanted it this way, see Duren, Changing Faces: The Mistaken Portrait of Legendre, who quotes Poisson:

"We know from testimony of Poisson that Legendre did not welcome personal attention, but wanted his work to speak for itself. Speaking at Legendre’s funeral, Poisson said:"Our colleague often expressed the desire that in speaking of him it would be only a question of his works, which are in fact his whole life. I will comply strictly with his wish in this tribute that I come to pay..." In view of these remarks, it seems likely that Legendre actively discouraged the making of portraits."

This is in contrast to the absence of Hooke's portraits, where the cause is more mysterious, see Henderson on Hooke, Newton, and the ‘missing’ portrait. In the absence of Adrien-Marie's real portraits, a portrait of a French revolutionary Louis Legendre was substituted for his as early as 1900, and reproduced even by some historians, like Eves and Struik. The error was only discovered by two University of Strasbourg students in 2005.

"Once the traditional portrait was known to be false, a feverish search began for a true portrait of Adrien-Marie Legendre. Miraculously, an authentic portrait was discovered during the year 2008 in the library of the Institut de France in Paris, among a rare collection of seventy-three caricatures of members of the Institute. One of the watercolor sketches (depicted on the cover of this issue of the Notices) shows the heads of Legendre and Fourier, with bodies lightly sketched in pencil. Their names “Legendre” and “Fourier” are written below the sketch. Fourier is easily recognized from existing portraits, but Legendre takes on a totally new appearance. This is the only image of Adrien-Marie Legendre known to exist.

[...] The album of caricatures has a mysterious history. It is the work of Julien-Léopold Boilly (1796–1874). His father Louis-Léopold Boilly (1761–1845) was a more famous artist, a member of the Académie des Beaux-Arts best known for his oil portraits. The younger Boilly was commissioned to do a series of engravings of members of the Institute, but the work was never finished; the partial collection (also in the library of the Institut de France) includes a formal portrait of Fourier but apparently none of Legendre... The collection also contains a caricature of Laplace, but no other mathematicians are represented.

The entire album can be viewed on the website of the Réunion des musées nationales (Click on “recherche”, then type in “Boilly” for searching and click repeatedly on “suivante”). The two Boilly artists appear to be confused, since the website attributes the album of caricatures to the father Louis-Léopold. In the juxtaposition of Legendre and Fourier, the artist seems to be commenting on a contrast of personalities: Fourier fat and jolly, Legendre lean and acerbic. However, the historical record sometimes portrays Legendre in quite a different light. A case in point is the kind reception he gave to Abel and Jacobi."

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    $\begingroup$ Le Moniteur Universel, Sunday, January 20, 1833, p. 162: Institut de France. Académie Royale des Sciences. Discourse prononcé aux funérailles de M. Legendre, par M. Poisson, président du bureau des longitudes. Messieurs ... Notre confrère a souvent exprimé le desir qu’en parlant de lui il ne fût question que des ses travaux, qui sont, en effet, toute sa vie. Je me conformerai religieusement à sa volonté, dans cet hommage que je viens rendre, au nom de l’Académie des sciences (1) et au bureau des longitudes, au géomètre illustre.. $\endgroup$
    – njuffa
    Mar 10 at 8:42
  • $\begingroup$ I was unable to find the Boilly portrait at the given Réunion des musées nationales link. Can anyone else find it there? Once found, clicking through to the page of the specific portrait should offer a permalink permalien (like this) to share it by. $\endgroup$ Mar 11 at 9:53

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