Unsolved problems in mathematics - Definition and Overview

This article describes some currently unsolved problems in mathematics.

The seven Millennium Prize Problems set by the Clay Mathematics Institute are:

• P versus NP
• The Hodge Conjecture
• The Poincaré Conjecture
• The Riemann Hypothesis
• Yang-Mills Existence and Mass Gap
• Navier-Stokes Existence and Smoothness
• The Birch and Swinnerton-Dyer Conjecture

Other still-unsolved problems:

• Twin prime conjecture
• Number of Magic squares
• Gilbreath's conjecture
• Goldbach's conjecture
• Hilbert's sixteenth problem
• Generalized star height problem
• Collatz conjecture
• Schanuel's conjecture
• infinitely many Mersenne primes (Lenstra-Pomerance-Wagstaff conjecture)
• infinitely many regular primes
• infinitely many Cullen primes
• infinitely many palindromic primes in base 10
• about e^−½ of all prime numbers are regular
• infinitely many even perfect numbers
• existence of odd perfect numbers
• existence of quasiperfect numbers

See also those problems listed as conjectures (list of conjectures).

Problems solved recently:

• Kepler's conjecture 1998
• Fermat's last theorem 1994
• Four color theorem 1977

See also: Hilbert's 23 problems, Timeline of mathematics

Quotes

"Problems worthy of attack prove their worth by fighting back." — Piet Hein (1905–1996)

External links

• Winkelmann, Jörg, "Some Mathematical Problems (http://www.math.unibas.ch/~winkel/problem.html)". Feb 3, 2004.