For the beginning of the list, see here.
- Collatz conjecture, or the problem.
- The invariant subspace problem. (The link requires a BSU account to download the paper.)
- The sum-product problem.
- Is there a polynomial such that ?
- The Bombieri-Lang conjecture and the closely related question by Friedman/Ziegler of whether there is a polynomial that maps injectively into .
- The inscribed square problem.
- Are the values of the function at the odd positive integers irrational?
- Schanuel’s conjecture.
- David Gale’s subset take-away problem.
- The Jacobian conjecture.
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