Unsolved problems in mathematics
From Free net encyclopedia
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
- Goldbach's weak conjecture
- Perfect cuboid
- Hilbert's sixteenth problem
- Generalized star height problem
- Collatz conjecture
- Schanuel's conjecture
- abc conjecture
- infinitely many Mersenne primes (Lenstra-Pomerance-Wagstaff conjecture); equivalently, infinitely many even perfect numbers
- infinitely many regular primes
- infinitely many Cullen primes
- infinitely many palindromic primes in base 10
- all Fermat number is composite for n>4.
- there are infinitely/finitely many Fermat number that are prime/composite number.
- Lehmer's conjecture
- about e−½ of all prime numbers are regular
- existence of odd perfect numbers
- existence of quasiperfect numbers
- modeling black hole mergers
- Is γ (the Euler-Mascheroni constant) irrational?
- What is the lowest Riesel number?
See also those problems listed as conjectures (list of conjectures).
Problems solved recently:
- Catalan's conjecture 2002
- Kato's conjecture 2001
- Taniyama-Shimura conjecture 1999
- Kepler conjecture 1998
- Fermat's last theorem 1994
- Bieberbach conjecture 1985
- Four color theorem 1977
See also: Hilbert's 23 problems, Timeline of mathematics
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Quotes
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External links
- Winkelmann, Jörg, "Some Mathematical Problems". Mar 9, 2006.
- List of links to unsolved problems in mathematics, prizes and research.
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Books discussing unsolved problems
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- Template:Cite bookde:Ungelöste Probleme der Mathematik
es:Problemas no resueltos de las matemáticas fi:Luettelo ratkaisemattomista matemaattisista ongelmista he:בעיה פתוחה במתמטיקה it:Problemi irrisolti in matematica ko:수학의 미해결 문제 pt:Problemas em aberto da Matemática sv:Olösta matematiska problem