Eh. There's two kinds of mathematical beauty (maybe more, I'm making this up): concepts and proofs. The other day I saw a proof of the minimax principle (abou

Eh. There's two kinds of mathematical beauty (maybe more, I'm making this up): concepts and proofs. The other day I saw a proof of the minimax principle (about eigenvalues maximizing the Rayleigh coefficient) that used a variational problem over eigenfunctions. This is fairly "ugly" mathematics conceptwise, and there are simpler standard proofs, but this one made the top of my head pop out like that emoji. It explains why Rayleigh coefficients have that name, and links practical statistics/ML concerns (low-rank matrix approximation) to light and refraction.