I am planning to write a little note detailing several proofs of Lagrange's theorem that every natural number can be written as the sum of four perfect squares. I know of three different proofs so far:
- a completely elementary proof by descent.
- a proof via Minkowski's theorem and lattices.
- Jacobi's proof via modular forms.
Can anybody think of any more nice, relatively elementary proofs of this result? Thanks in advance.