Pythagorean theorem
One of the oldest theorems, always fresh :)
I’ve been interested lately in the Pythagorean theorem, and the myriad of ways one can prove it.
An excellent resource is the website Cut The Knot.
Another great source is John C. Sparks’ The Pythagorean Theorem: Crown Jewel of Mathematics.
I used my tablet to write down my own version of some of the nicest proofs, see below.