Open problem
Foundations and logic
A question that has not been settled: no accepted proof, no disproof, and for questions that are not yes-or-no, no known solution.
What is usually left out
Open is not the same as unsettled-in-principle. The continuum hypothesis is not open in this sense — it is proved independent of ZFC, which is itself a definitive answer about what those axioms can decide. A problem can also stop being open without anyone finding the answer, if it is shown that no answer exists.