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List of unsolved problems in mathematics



[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]Graph theory



  • 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]Problems solved recently

[edit]See also



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