Cycles in human history?
Maximizing the probability of getting a medal in diving.
The most mathematical flag, from Numberphile. (The pictures you’ll want to see are here.)
John D. Barrow asks: How fast can Usain Bolt run? PDF, one-hour lecture on more general topics including this.
The optimal angle of release in shot put, by Alexander Lenz and Florian Rappl: paper at the arxiv, Technology Review blog (It’s not 45 degrees.)
Cosmos: A Three-Movement Choral Suite, by Kenley Kristofferson. (Yeah, I know, it’s not math. Deal with it.)