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# famous open questions in mathematics

Despite the fact that at least a generation of mathematicians has tried to solve these problems, they still remain open:

1. 2. 3. Poincaré conjecture

4. 5. Birch and Swinnerton-Dyer conjecture

6. P vs NP problem

7. Hodge conjecture

8. 9. 10. Schanuel’s conjecture

11. 12. 13. Existence of an odd perfect number

14. 15. 16. Lehmer’s conjecture

Open problems 3 to 8, together with the quest for a mathematical foundation explaining the mass gap property in Yang-Mills theory, constitute a collection of problems known as the Millennium Problems. Please see http://www.claymath.org/millennium/ for more detail.

Related:

TwoGeneratorProperty, MillenniumProblems

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## Mathematics Subject Classification

00A20*no label found*

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