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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“What happened at Hiroshima was not only that a scientific breakthrough ... had occurred and that a great part of the population of a city had been burned to death, but that the problem of the relation of the triumphs of modern science to the human purposes of man had been explicitly defined.”
—Archibald MacLeish (1892–1982)