Thurston's 24 questions

Thurston's 24 questions are a set of mathematical problems in differential geometry posed by American mathematician William Thurston in his influential 1982 paper Three-dimensional manifolds, Kleinian groups and hyperbolic geometry published in the Bulletin of the American Mathematical Society. These questions significantly influenced the development of geometric topology and related fields over the following decades.

The questions appeared following Thurston's announcement of the geometrization conjecture, which proposed that all compact 3-manifolds could be decomposed into geometric pieces. This conjecture, later proven by Grigori Perelman in 2003, represented a complete classification of 3-manifolds and included the famous Poincaré conjecture as a special case.

By 2012, 22 of Thurston's 24 questions had been resolved.

Thurston's 24 questions are:

• Geometrization conjecture
• Hilbert's problems
• Taniyama's problems
• List of unsolved problems in mathematics
• Poincaré conjecture
• Smale's problems