It has been [noted](https://mathoverflow.net/a/369677/8628) already that [Noam Elkies](https://en.wikipedia.org/wiki/Noam_Elkies) is an accomplished composer.

What I find at least as extraordinary about him is that he can hum-whistle some of Bach's [two-part inventions](https://en.wikipedia.org/wiki/Inventions_and_Sinfonias_(Bach)). (Anecdotal "evidence", will remove this answer if it is false.)