Editing Conjecture (section)

===P versus NP problem===
{{main|P versus NP problem}}
The [[P versus NP problem]] is a major [[List of unsolved problems in computer science|unsolved problem in computer science]]. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer; it is widely conjectured that the answer is no. It was essentially first mentioned in a 1956 letter written by [[Kurt Gödel]] to [[John von Neumann]].  Gödel asked whether a certain NP-complete problem could be solved in quadratic or linear time.<ref>Juris Hartmanis 1989, [http://ecommons.library.cornell.edu/bitstream/1813/6910/1/89-994.pdf Gödel, von Neumann, and the P = NP problem], Bulletin of the
European Association for Theoretical Computer Science, vol. 38, pp. 101–107</ref> The precise statement of the P=NP problem was introduced in 1971 by [[Stephen Cook]] in his seminal paper "The complexity of theorem proving procedures"<ref>{{Cite book|last=Cook|first=Stephen|author-link=Stephen Cook|year=1971|chapter=The complexity of theorem proving procedures|chapter-url=http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=805047|title=Proceedings of the Third Annual ACM Symposium on Theory of Computing|pages=151–158|doi=10.1145/800157.805047|isbn=9781450374644|s2cid=7573663}}</ref> and is considered by many to be the most important open problem in the field.<ref>[[Lance Fortnow]], [https://wayback.archive-it.org/all/20110224135332/http://www.cs.uchicago.edu/~fortnow/papers/pnp-cacm.pdf ''The status of the '''P''' versus '''NP''' problem''], Communications of the ACM 52 (2009), no.&nbsp;9, pp.&nbsp;78–86. {{doi|10.1145/1562164.1562186}}</ref> It is one of the seven [[Millennium Prize Problems]] selected by the [[Clay Mathematics Institute]] to carry a US$1,000,000 prize for the first correct solution.