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.

6.
P vs NP problem
 7.

8.
Solution to the NavierStokes equations
 9.

10.
Schanuel’s conjecture
 11.

12.
Irrationality of Euler’s constant $\gamma $

13.
Existence of an odd perfect number

14.
Koethe conjecture
 15.

16.
Lehmer’s conjecture
Open problems 3 to 8, together with the quest for a mathematical foundation^{} explaining the mass gap property in YangMills 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 YangMills theory has been published by G. Cleaver and K. Tanaka (2000): “Ratio of Quark Masses in Duality Theories.”, http://arxiv.org/abs/hepth/0002089v1on line, and can be accessed as a http://arxiv.org/PS_cache/hepth/pdf/0002/0002089v1.pdfPDF file .
Title  famous open questions in mathematics 

Canonical name  FamousOpenQuestionsInMathematics 
Date of creation  20130322 14:42:52 
Last modified on  20130322 14:42:52 
Owner  rspuzio (6075) 
Last modified by  rspuzio (6075) 
Numerical id  15 
Author  rspuzio (6075) 
Entry type  Example 
Classification  msc 00A20 
Related topic  TwoGeneratorProperty 
Related topic  MillenniumProblems 