Innocent looking open problems in real analysis 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?

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:


*

*Convergence of a series and this question

*Gourevitch's conjecture

*Cover of the unit square by rectangles

*...

