Visual proof of Fermat's two-square theorem: https://www.youtube.com/watch?v=DjI1NICfjOk

The theorem (https://en.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares) states that a prime number can be represented as the sum of two squares of integers iff it is congruent to 1 mod 4. In 1990, Don Zagier published a "one-line proof" involving a tricky algebraically-defined involution among triples of numbers. The linked Mathologer video explains how to see the same involution more intuitively, as a dissection of polyominoes.