Four Squares

"Any positive integer can be written as the sum of four square numbers", says Lagrange's four-square theorem. After years of intermittently trying to figure out why, a recent peek reveals why the why was so non-obvious. The simplest classical proof involves:

• a clever-deep algebraic formula to reduce the challenge to prime numbers
• a pigeonhole principle to reduce it to multiples of primes
• an infinite descent to reduce that multiple to 1

Q.E.D. — and how non-obvious, in retrospect!

(cf [1], [2], [3], [4], ...) - ^z - 2019-08-12