Many reputable sources (I can give as many as you want) describe Da Vinci as a mathematician, but they never mention a single theorem, result, or lemma that he proved. There's the golden ratio spiral, but that's ad hoc nonsense and certainly not what all the writers were thinking of. He used perspective in drawings, but that was already used and hardly counts anyways. Thus I'm wondering whether anyone here happens to know if he actually proved anything. I suspect not, but I'd be arguing against dozens of writers, journalists, and historians and it's impossible to prove a negative.
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10$\begingroup$ This would probably be more appropriate at hsm.stackexchange.com $\endgroup$– Neil StricklandCommented Oct 18, 2022 at 19:17
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4$\begingroup$ Fermat never really proved very much in the way of theorem, result, or lemma either, as far as we’re aware (key word: proof). What constituted a “proof”, “mathematician” or even “mathematics” in the 1400s is vastly different from in the 2000s. $\endgroup$– Carl-Fredrik Nyberg BroddaCommented Oct 18, 2022 at 19:44
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6$\begingroup$ I think the term "mathematician" is used more generally than you suppose. A math enthusiast that spends an enormous amount of time learning, using, and appreciating pre-existing mathematics is still a mathematician in most peoples' eyes. Mandelbrot did not prove much (as far as I know) but he's still called a mathematician. In that regard, I think Da Vinci qualifies. $\endgroup$– Ryan BudneyCommented Oct 18, 2022 at 19:52
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5$\begingroup$ I suppose I am saying "mathematician" and "mathematics researcher" are not exactly synonymous. $\endgroup$– Ryan BudneyCommented Oct 18, 2022 at 19:55
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3$\begingroup$ The fact that $C_n$ and $D_n$ are the only finite subgroups of $O(2)$ is often attributed to da Vinci. $\endgroup$– Dustin G. MixonCommented Oct 18, 2022 at 22:59
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I follow up on Dustin Mixon's comment.
Hermann Weyl, in his 1952 book Symmetry (page 66), argues that Leonardo classified the only possible central symmetries in two dimensions, now referred to as the cyclic group $C_n$ and the dihedral group $D_n$.
Leonardo da Vinci engaged in systematically determining the possible symmetries of a central building and how to attach chapels and niches without destroying the symmetry of the nucleus. In abstract modern terminology, his result is essentially our table of the possible finite groups of rotations (proper and improper) in two dimensions.
For a further discussion, see The Octagon in Leonardo’s Drawings, by Mark Reynolds.
To call this Leonardo's theorem is a stretch, since Leonardo did not actually formulate this classification as a theorem, at best it is implicit in his drawings.
