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.

## 1 Answer

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.

8more comments