What are the unsolved math problems

Unsolved problems in mathematics

In principle, you can have any number unsolved math problems describe, because the subject area of ​​mathematics is unlimited. Nevertheless, important unsolved problems have emerged several times in the history of mathematics, which have been and are recognized as important within science and which have been and are tried to solve with particular zeal.

Millennium Problems

Main article: Millennium Problems

Most recently, in 2000, the Clay Institute in Cambridge, Massachusetts, presented the seven (from its point of view) most important unsolved problems in mathematics and offered prize money of one million dollars each for a published solution. So far, one of the so-called Millennium Problems has been solved when Grigori Perelman was able to verify the Poincaré conjecture by proving the more general geometry of 3-manifolds in 2002.

Hilbert problems

Main article: Hilbert problems

David Hilbert, who on August 8, 1900 at the International Congress of Mathematicians in Paris, formulated 23 previously unsolved problems in mathematics, obviously served as a model for the Clay Institute. 13 of these problems have so far been comprehensively resolved. There are still no satisfactory results for three of them. The most prominent unsolved problem is still the Riemann Hypothesis, which is also included in the Clay list.

Other known unsolved issues and questions

Solutions to famous problems

"Unsolved" problems of geometry

For many centuries there were also some famous unsolved problems (constructions) in geometry, a branch of mathematics. These are also called the "Classical Problems of Ancient Mathematics". It was not until 1882 (proof of the impossibility of squaring the circle) that the "unsolved" geometric problems could be recognized as "impossible to solve" problems.


  • Pierre Basieux: The top seven math guesswork. rororo, 2004, ISBN 3-499-61932-6
  • Simon Singh: Fermat's last sentence, dtv, 2000, ISBN 3-423-33052-X
  • Elliott Pearl: Open Problems in Topology, Elsevier, 2007, ISBN 0-444-52208-5
  • George G. Szpiro: The Poincaré adventure: A mathematical world puzzle is solved, Piper, 2010, ISBN 978-3-492-25725-1

Web links