An open problem is a problem that can be formally stated and for which a solution is known to exist but which has not yet been solved. It is common in graduate schools to point out open problems to students. However, Fermat's last theorem and the Four color theorem are two notable open problems that have been closed or solved by faculty members, as they would have more expertise and resources than students.
Important open problems exist in many fields, such as in the field of theoretical computer science, computer scheduling, and real-time computing.

Kirby's Problem List in Low-Dimensional Topology - Problems list in PostScript format.
Open Problems in Topology - Collection includes problems in set theory, continua, algabraic structures, analysis, and dynamics. Page includes glossary of terms. Links are in PDF.
The Boise Problem Book - Problems in combinatorial set theory and topology, collected by Marion Scheepers.
Thrackle.org - John Conway's Thrackle Conjecture: a compilation of what is known about the question.
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