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I have watched a video about Napoleon's theorem — maybe it was contributed by Napoleon, maybe not. I also know that Laplace himself said Napoleon was good at mathematics. However, did Napoleon make any contributions to mathematics other than his theorem?

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    $\begingroup$ This Wikipedia article traces the history of "Napoleon's Theorem." Judge by yourself, but my reading is that Napoleon's contribution to this theorem was about the same as Cardinal Mazarin's contribution to the pastry named after him, see here. As for Laplace's citation: There is a huge difference between "being good at math" (say, at the level required for an artillery officer) and capable of making an original contribution to it. $\endgroup$
    – Moishe Kohan
    Jan 3, 2022 at 16:23

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First of all, a very interesting document (in french) here by Nicole DHOMBRES gives abundant information about the scientific level of Napoleon.

Now, as a complement to the last sentence of the answer by Alexandre Eremenko, here is a testimony of the way mathematics had left their imprint on Napoleon. Here are two excerpts from the very interesting memoirs of baron de Comeau (in "Le tacticien de Napoléon : Mémoires de guerre du Baron de Comeau" available as a Google book).

These excerpts are from chapter XXXVIII. The reference to Bezout is explained by the fact that the two books entitled "Cours de mathématiques à l'usage du corps de l'artillerie" by Bezout, clearly written, were reference books in Brienne, the Artillery School that Napoleon attended. A revised version of the second of these books can be found here.

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My own translation of these texts (I have added quotes when Napoleon is speaking).

"It is comparable to our blackboard where we were maneuvering algebra. You have made a large use of this algebra in all your campaigns. I remember you were good at that and had a fair understanding that minus times minus make plus. I haven't been bad at applying this principle: minus Germany, minus Austria, minus Prussia, minus Italy, accept that (showing himself), I am a large plus.

"Malborough is going to war" (18th century french song sang by Napoleon). He stopped close to me. "I would have liked to avoid this war. Alexander [tsar Alexander I] doesn't know any longer where he is going, where we draw him. Bezout has taught you, like me, that mass times speed gives the kinetic energy, the momentum. I have enough for the mass. The speed will be there, before his sun goes down. Days last a long time in Russia when it is sunny. I will fight two, three battles. If he considers stopping."

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  • $\begingroup$ WOW never knew he actually said that! $\endgroup$
    – user15948
    Jan 5, 2022 at 21:17
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The main contribution of Napoleon to math was his strong support of the new education system established by the revolutionary government some time before he came to power. For example, he re-established Ecole Normale Superieure which was previously closed by the Consulate. This became one of the top institutions of mathematics education and research. He also established the Scuola Normale Superiore in Pisa.

Napoleon was presumably "good in math", as a graduate of Ecole Militaire, but did not make any original contribution.

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  • $\begingroup$ This Web site says that he could have proved the Napoleon theorem, but it is not an important contribution to math and the originality is questionable, uh.edu/engines/epi2550.htm $\endgroup$
    – markvs
    Jan 5, 2022 at 2:52
  • $\begingroup$ Thanks for the information! $\endgroup$
    – user15948
    Jan 5, 2022 at 21:19
  • $\begingroup$ Napoleon's contribution to mathematics is of the same status as Elena Ceaușescu 's contribution to chemistry. $\endgroup$
    – fdb
    Jan 10, 2022 at 15:28
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    $\begingroup$ I am not aware of Elena Ceaușescu 's contribution to chemistry but Zoia Ceaușescu was a mathematician, and had 22 published papers in specialized journals, unlike Napoleon. $\endgroup$
    – Alexandre Eremenko
    Jan 10, 2022 at 23:01
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Ok, here is another tale, not sure how much of it I believe, taken from Chapter 3 of the book

The chapter begins with:

In December of 1797 there took place in Paris a brilliant gathering of prominent writers and scholars, with the immortal Lagrange and Laplace among them. A most conspicuous member of the company was the young and victorious General Napoleon Bonaparte, who ... had occasion to entertain Lagrange and Laplace with a kind of solution of some elementary problems of elementary geometry that was completely unfamiliar to either of the two world famous mathematicians. Legend has it that after having listened to the young man for a considerable while, Laplace, somewhat peeved, remarked, "General, we expected everything of you, except lessons in geometry." N. A. Court

This quote, appears to be due to Nathan Altshiller Court, from Oklahoma University. I have no idea how reliable N. A. Court is as a storyteller. But he kept his source of the story secret. The quote is taken from

The editorial note following Court's paper says:

There is reason to believe that the idea of undertaking geometric constructions with compasses alone was suggested to Mascheroni by the earlier work of Giambattista Benedetti (1530-1590)....

Martin then continues:

Napoleon proposed to the French mathematicians the problem of dividing a circle into four congruent arcs by using the compass alone. Although not original with Napoleon, the problem has become known as Napoleon's Problem. During his campaign in northern Italy, Napoleon had encountered the poet and geometer Lorenzo Mascheroni (1750-1800). Mascheroni was a professor at the University of Pavia, where Christopher Columbus had once been a student. Mascheroni's most famous mathematical work is his "Geometria del Compasso," published in 1797. This work, which began with an ode of some literary merit that was dedicated to Napoleon, showed that all the ruler and compass constructions can be accomplished with the euclidean compass alone.

Well, in fact, Mascheroni was not the first to prove that theorem (ostensibly, solving "Napoleon's Problem" as a special case). Mascheroni's theorem had been (unknown to Mascheroni) proved in 1672 by a little known Danish mathematician Georg Mohr (as discussed in the same paper by N.A.Court).

So, if we were to believe N.A.Court, Napoleon's contribution in this case was to propose "Napoleon's Problem" to a group of French mathematicians, a problem which was solved 30 years earlier.

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    $\begingroup$ I'm just getting mind-blown by these answers. Thanks! $\endgroup$
    – user15948
    Jan 6, 2022 at 2:09
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in the sense that chess is a mathematical game, there's the napoleon opening.

https://en.wikipedia.org/wiki/Napoleon_Opening

Edit: user15948 says it's not such a good opening. I'm not saying it is. It's just an opening that is named after the guy.

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Napoleon points

In geometry, Napoleon points are a pair of special points associated with a plane triangle. It is generally believed that the existence of these points was discovered by Napoleon Bonaparte, the Emperor of the French from 1804 to 1815, but many have questioned this belief.1 The Napoleon points are triangle centers and they are listed as the points X(17) and X(18) in Clark Kimberling's Encyclopedia of Triangle Centers.

The name "Napoleon points" has also been applied to a different pair of triangle centers, better known as the isodynamic points.[2]

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