Wednesday, October 5, 2011

List of Unsolved Problems in Mathematics

This article lists some unsolved problems in mathematics. See individual articles for details and sources.


[edit] Millennium Prize Problems

Of the seven Millennium Prize Problems set by the Clay Mathematics Institute, six have yet to be solved:
The seventh problem, the Poincaré conjecture, has been solved. The smooth four-dimensional Poincaré conjecture is still unsolved. That is, can a four-dimensional topological sphere have two or more inequivalent smooth structures?

[edit] Other still-unsolved problems

[edit] Additive number theory

[edit] Number theory: prime numbers

[edit] General number theory

[edit] Algebraic number theory

[edit] Discrete geometry

[edit] Ramsey theory

[edit] General algebra

[edit] Combinatorics

[edit] Graph theory

[edit] Analysis

[edit] Dynamics

  • Fürstenberg conjecture – Is every invariant and ergodic measure for the \times 2,\times 3 action on the circle either Lebesgue or atomic?
  • Margulis conjecture — Measure classification for diagonalizable actions in higher-rank groups

[edit] Partial differential equations

[edit] Group theory

[edit] Set theory

[edit] Other

[edit] Problems solved recently

[edit] See also

[edit] References

  1. ^ Green, Ben (2004), "The Cameron-Erdős conjecture", The Bulletin of the London Mathematical Society 36 (6): 769–778, arXiv:math.NT/0304058doi:10.1112/S0024609304003650MR2083752.

[edit] Books discussing unsolved problems

  • Fan Chung; Ron Graham (1999). Erdos on Graphs: His Legacy of Unsolved Problems. AK Peters. ISBN 1-56881-111-X.
  • Hallard T. Croft; Kenneth J. Falconer; Richard K. Guy (1994). Unsolved Problems in Geometry. Springer. ISBN 0-387-97506-3.
  • Richard K. Guy (2004). Unsolved Problems in Number Theory. Springer. ISBN 0-387-20860-7.
  • Victor Klee; Stan Wagon (1996). Old and New Unsolved Problems in Plane Geometry and Number Theory. The Mathematical Association of America. ISBN 0-88385-315-9.
  • Marcus Du Sautoy (2003). The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics. Harper Collins. ISBN 0060935588.
  • John Derbyshire (2003). Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Joseph Henry Press. ISBN 0309085497.
  • Keith Devlin (2006). The Millennium Problems - The Seven Greatest Unsolved* Mathematical Puzzles Of Our Time. Barnes & Noble. ISBN 0-7607-8659-8.
  • Vincent D. Blondel, Alexandre Megrestski (2004). Unsolved problems in mathematical systems and control theory. Princeton University Press. ISBN 0-691-11748-9.

[edit] Books discussing recently solved problems

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