| Revision as of 18:01, 27 December 2024 editGregariousMadness (talk | contribs)Extended confirmed users1,409 edits ←Created page with '{{short description|Set of 24 mathematics problems posed by William P. Thurston}} '''Thurston's 24 questions''' are a set of mathematical problems 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''.<ref name="Thur...'Tag: Disambiguation links added | Revision as of 18:05, 27 December 2024 edit undoGregariousMadness (talk | contribs)Extended confirmed users1,409 editsNo edit summaryNext edit → | ||
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| {{short description|Set of 24 mathematics problems posed by William P. Thurston}} | {{short description|Set of 24 mathematics problems posed by William P. Thurston}} | ||
| '''Thurston's 24 questions''' are a set of ] posed by ] ] ] in his influential 1982 paper ''Three-dimensional manifolds, ] and ]'' published in the '']''.<ref name="Thurston">{{citation|last=Thurston|first=William P.|title=Three-dimensional manifolds, Kleinian groups and hyperbolic geometry|year=1982|journal=]|pages=357-379}}</ref> These questions significantly influenced the development of ] and related fields over the following decades. By 2012, 22 of Thurston's 24 questions had been resolved. | '''Thurston's 24 questions''' are a set of ] posed by ] ] ] in his influential 1982 paper ''Three-dimensional manifolds, ] and ]'' published in the '']''.<ref name="Thurston-1982">{{citation|last=Thurston|first=William P.|title=Three-dimensional manifolds, Kleinian groups and hyperbolic geometry|year=1982|journal=]|pages=357-379}}</ref> These questions significantly influenced the development of ] and related fields over the following decades. By 2012, 22 of Thurston's 24 questions had been resolved.<ref name="Thurston-2014">{{citation|last=Thurston|first=William P.|title=Three-dimensional manifolds, Kleinian groups and hyperbolic geometry|year=2014|journal=Jahresbericht der Deutschen Mathematiker|pages=3-20|year=2014|volume=116}}</ref> | ||
| == History == | == History == | ||
| The questions appeared following Thurston's announcement of the ], which proposed that all ] ] could be decomposed into geometric pieces.<ref name="Thurston"/> This conjecture, later proven by ] in 2003, represented a complete classification of 3-manifolds and included the famous ] as a special case. | The questions appeared following Thurston's announcement of the ], which proposed that all ] ] could be decomposed into geometric pieces.<ref name="Thurston-1982"/> This conjecture, later proven by ] in 2003, represented a complete classification of 3-manifolds and included the famous ] as a special case.<ref name="Thurston-2014"/> | ||
| == References == | == References == | ||
Revision as of 18:05, 27 December 2024
Set of 24 mathematics problems posed by William P. ThurstonThurston's 24 questions are a set of mathematical problems 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. By 2012, 22 of Thurston's 24 questions had been resolved.
History
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.
References
- ^ Thurston, William P. (1982), "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry", Bulletin of the American Mathematical Society: 357–379
- ^ Thurston, William P. (2014), "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry", Jahresbericht der Deutschen Mathematiker, 116: 3–20
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