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. 1.
2. 2.
3. 3.

Poincaré conjecture

4. 4.
5. 5.
6. 6.

P vs NP problem

7. 7.
8. 8.

Solution to the Navier-Stokes equations

9. 9.
10. 10.

Schanuel’s conjecture

11. 11.
12. 12.

Irrationality of Euler’s constant $\gamma$

13. 13.

Existence of an odd perfect number

14. 14.

Koethe conjecture

15. 15.
16. 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/http://www.claymath.org/millennium/ for more detail.

Note: A mathematical foundation for the partial solution of the the mass gap property in Yang-Mills theory has been published by G. Cleaver and K. Tanaka (2000): “Ratio of Quark Masses in Duality Theories.”, http://arxiv.org/abs/hep-th/0002089v1on line, and can be accessed as a http://arxiv.org/PS_cache/hep-th/pdf/0002/0002089v1.pdfPDF file .

Title famous open questions in mathematics FamousOpenQuestionsInMathematics 2013-03-22 14:42:52 2013-03-22 14:42:52 rspuzio (6075) rspuzio (6075) 15 rspuzio (6075) Example msc 00A20 TwoGeneratorProperty MillenniumProblems