In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major unresolved challenge is to determine if the problem admits a polynomial time algorithm, that is, whether the problem lies in the complexity class P.
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“Our political problem now is “Can we, as a nation, continue together permanentlyforever—half slave, and half free?” The problem is too mighty for me. May God, in his mercy, superintend the solution.”
—Abraham Lincoln (1809–1865)