>They had a language requirement for a math PhD. To get a PhD you had to either be fluent in one of French, German, or Russian, or you had to have a sufficient reading ability in two of those to read the current and historical math literature in those languages.

This a thing of the past, from a time when people in the USSR still published things of note in Russian (the same for the other countries/languages your mentioned). Today everyone publishes in English and I don't of a single math department that still has that as a requirement.

I also don't know of any other such extracurricular requirements for any program (can't even imagine what it would be - community service???)