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Are there any apparently easy problems or conjectures in basic real analysis (that is, calculus) that are still open? By apparently easy, I mean: so much so, that, if it was for the statement alone, they could be part of a calculus book for undergraduates?

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  • $\begingroup$ Asked before (but only one answer) $\endgroup$
    – Winther
    Jan 7, 2015 at 21:28
  • $\begingroup$ @Winther Thank you, but my question is more specific than that. $\endgroup$ Jan 7, 2015 at 22:48
  • $\begingroup$ I do not know how low-level you're looking for, but I remember learning about the Invariant subspace problem and thinking it was very simple to understand. en.wikipedia.org/wiki/Invariant_subspace_problem $\endgroup$ Jan 7, 2015 at 23:12

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Look for questions marked as open-problem or open-problem-list on mathoverflow. I guess you will find some open problems there.

Here a list of some open questions i have found there:

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