Unsolved problems in mathematics
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:
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". Feb 3, 2004.
Categories: Conjectures | Unsolved problems in mathematics