13. Lehmers Mahler measure problem and Lehmers totient problem on the existence of composite numbers such that , where is the totient function.
14. Determining if the Euler-Mascheroni constant is irrational.
15. Deriving an analytic form for the square site percolation threshold.
16. Determining if any odd perfect numbers exist.
The Clay Mathematics Institute of Cambridge, Massachusetts has named seven Millennium Prize Problems, selected by focusing on important classic questions in mathematics that have resisted solution over the years. A $7 million prize fund has been established for the solution to these problems, with $1 million allocated to each. The problems consist of the Riemann hypothesis, Poincar conjecture, Hodge conjecture, Swinnerton-Dyer Conjecture, solution of the Navier-Stokes equations, formulation of Yang-Mills theory, and determination of whether NP-problems are actually P-problems.
In 1900, David Hilbert proposed a list of 23 outstanding problems in mathematics , a number of which have now been solved, but some of which remain open. In 1912, Landau proposed four simply stated problems, now known as Landaus problems, which continue to defy attack even today. One hundred years after Hilbert, Smale proposed a list of 18 outstanding problems.
K. S. Brown, D. Eppstein, S. Finch, and C. Kimberling maintain webpages of unsolved problems in mathematics. Classic texts on unsolved problems in various areas of mathematics are Croft et al. , in geometry, and Guy , in number theory.
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