斯梅尔问题

斯梅尔问题（英語：Smale's problems）是美国数学家斯蒂芬·斯梅尔于1998年提出的18个当时未解决的数学问题。时任国际数学联盟副主席、俄国数学家弗拉基米尔·阿诺尔德当时参照20世纪初希尔伯特的23个问题而向世界上的主要数学家征集面向21世纪的数学问题，斯梅尔便是在此背景下提出了斯梅尔问题，作为对阿诺尔德的答复。 千禧年大奖难题 Smale, Steve. Mathematical Problems for the Next Century. Mathematical Intelligencer. 1998, 20 (2): 7–15doi=10.1007/bf03025291.  Smale, Steve. Mathematical problems for the next century. Arnold, V. I.; Atiyah, M.; Lax, P.; Mazur, B. (编). Mathematics: frontiers and perspectives. American Mathematical Society. 1999: 271–294. ISBN 0821820702.  Perelman, Grigori. The entropy formula for the Ricci flow and its geometric applications. 2002. arXiv:math.DG/0211159  |class=被忽略 (帮助).  Perelman, Grigori. Ricci flow with surgery on three-manifolds. 2003. arXiv:math.DG/0303109  |class=被忽略 (帮助).  Perelman, Grigori. Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. 2003. arXiv:math.DG/0307245  |class=被忽略 (帮助).  Shub, Michael; Smale, Steve. On the intractability of Hilbert’s Nullstellensatz and an algebraic version of "NP≠P?". Duke Math. J. 1995, 81: 47–54. Zbl 0882.03040. doi:10.1215/S0012-7094-95-08105-8.  Bürgisser, Peter. Completeness and reduction in algebraic complexity theory. Algorithms and Computation in Mathematics 7. Berlin: Springer-Verlag. 2000: 141. ISBN 3-540-66752-0. Zbl 0948.68082.  Albouy, A.; Kaloshin, V. Finiteness of central configurations of five bodies in the plane. Annals of Mathematics. 2012, 176: 535–588. doi:10.4007/annals.2012.176.1.10.  Asaoka, M.; Irie, K. A C∞ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. Geometric and Functional Analysis. 2016, 26: 1245–1254. doi:10.1007/s00039-016-0386-3.  Kozlovski, O.; Shen, W.; van Strien, S. Density of hyperbolicity in dimension one. Annals of Mathematics. 2007, 166: 145–182. doi:10.4007/annals.2007.166.145.  Bonatti, C.; Crovisier, S.; Wilkinson, A. The C1-generic diffeomorphism has trivial centralizer. Publications Mathématiques de l'IHÉS. 2009, 109: 185–244. arXiv:0804.1416 . doi:10.1007/s10240-009-0021-z.  Tucker, Warwick. A Rigorous ODE Solver and Smale's 14th Problem (PDF). Foundations of Computational Mathematics. 2002, 2 (1): 53–117. doi:10.1007/s002080010018.  Beltrán, Carlos; Pardo, Luis Miguel. On Smale's 17th Problem: A Probabilistic Positive answer (PDF). Foundations of Computational Mathematics. 2008, 8 (1): 1–43 [2018-09-30]. doi:10.1007/s10208-005-0211-0. （原始内容存档 (PDF)于2020-06-07）.  Beltrán, Carlos; Pardo, Luis Miguel. Smale's 17th Problem: Average Polynomial Time to compute affine and projective solutions (PDF). Journal of the American Mathematical Society. 2009, 22: 363–385 [2018-09-30]. Bibcode:2009JAMS...22..363B. doi:10.1090/s0894-0347-08-00630-9. （原始内容存档 (PDF)于2020-06-07）.  Cucker, Felipe; Bürgisser, Peter. On a problem posed by Steve Smale. Annals of Mathematics. 2011, 174 (3): 1785–1836. doi:10.4007/annals.2011.174.3.8.  Lairez, Pierre. A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time. Foundations of Computational Mathematics. 2016,. to appear.  Shub, Michael; Smale, Stephen. Complexity of Bézout's theorem. I. Geometric aspects. J. Amer. Math. Soc. 1993, 6 (2): 459–501. doi:10.2307/2152805. . http://recursed.blogspot.jp/2006/02/tucson-day-3-interview-with-steve.html （页面存档备份，存于互联网档案馆） Friday, February 03, 2006 Tucson - Day 3 - Interview with Steve Smale