P versus NP problem
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- If P = NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in "creative leaps," no fundamental gap between solving a problem and recognizing the solution once it's found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss; everyone who could recognize a good investment strategy would be Warren Buffett.
- Scott Aaronson. Reasons to believe., point 9.
- The P versus NP problem was first mentioned in a 1956 letter from Kurt Gödel to John von Neumann, two of the greatest mathematical minds of the twentieth century.
- Lance Fortnow (2013). The Golden Ticket: P, NP, and the Search for the Impossible. Princeton University Press. p. 6. ISBN 0-691-15649-2.
- Hodge conjecture
- Riemann hypothesis
- Poincaré conjecture (solved)
- Birch and Swinnerton-Dyer conjecture