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The biographical sketch of Rabbi Moshe Feinstein that appears in Igrot Moshe volume 8 describes the following (my translation):

The Communist takeover meant the schools taught against religion. Some of the older Jewish students would argue back, citing teachings of their rabbi [Moshe Feinstein]. One infuriated teacher (herself Jewish) finally replied, "What does that rabbi of yours know, if he can't solve this calculus problem?!"

Eventually the problem was brought to Rabbi Feinstein; who requested a calculus textbook, read it, and then solved it.

Have any details about this story (other than the ones printed there) survived to this day?

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    Well, the original you paraphrased does imply it's differential calculus.
    – msh210 ♦
    Commented Jun 13, 2011 at 19:01
  • 2
    I suggest you ask him: daattorah.blogspot.com
    – simchashatorah
    Commented Jun 14, 2011 at 3:04
  • Perhaps this should be asked on Math.SE ;)
    – AviD
    Commented Jun 14, 2011 at 7:10
  • the same story has one version with dozen of Gedolim, rav Aharon Kotler, Chafets Chayim. etc.
    – kouty
    Commented Jan 3, 2017 at 12:52
  • @Kouty the story is printed by Rabbi Feinstein's family, which gives it some decent heft. R' Aharon Kotler very nearly got on a train to leave yeshiva and study mathematics in Moscow, and his sister spent the rest of her life regretting that he didn't do so; I thus find it unlikely that he would solve a Communist's challenge to solve a calculus problem. The Chofetz Chaim? He was rosh yeshiva, not town rabbi, when the communists ruled Radin. So I'd find it unlikely.
    – Shalom
    Commented Jan 4, 2017 at 0:43

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There is a very slightly different account here, which places the story in the context of religious persecution and Rav Moshe's ostensible motivations for leaving Russia.

But something tells me by "details about this story" you mean "specific contents of the calculus problem", in which case this is no help. . .

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