All levels – Miscellaneous results

The miscellaneous results include theorems that are not part of the curriculum but I want to include.

"Recommended level for proof" means you should be familiar with all material up until that level, not just that level. The levels are all designed to be done sequentially, with these as extras.

Bertrand's postulate Fermat's theorem on sums of two squares Irrationality of π Basel problem (sum of reciprocals of squares) Fundamental theorem of symmetric polynomials Abel's theorem for power series Cramer Wold Theorem Multivariate Central Limit Theorem Non-existance of a quintic formula with roots and basic operations