Otevřené problémy v matematice

Termín otevřené problémy vyjadřuje dosud nevyřešené problémy, včetně těch neřešitelných. Již od renesance se v každém století objevuje řešení více matematických problémů než v předchozím století, ale mnoho matematických problémů, velkých i menších, stále zůstává nevyřešeno. Tyto nevyřešené problémy se vyskytují ve více oborech, včetně fyziky, informatiky, algebry, analýzy, kombinatoriky, algebraické, diskrétní a euklidovské geometrie, teorie grafů, čísel, množin, dynamických systémů, parciálních diferenciálních rovnic a dalších. Některé problémy mohou patřit do více než jedné disciplíny matematiky a mohou být studovány pomocí technik z různých oblastí. Za řešení dlouhodobého problému se často udělují ceny a značná pozornost se věnuje seznamům nevyřešených problémů, jako je seznam problémů s cenou tisíciletí.

Seznamy nevyřešených problémů v matematice

V průběhu času se v matematice objevilo více seznamů nevyřešených problémů.

Seznam Počet problemů Počet nevyřešených
nebo částečně vyřešených		 Autor seznamu Rok vytvoření
Hilbertovy problémy[1] 23 15 David Hilbert 1900
Landauovy problémy[2] 4 4 Edmund Landau 1912
Taniyamaovy problémy[3] 36 - Jutaka Tanijama 1955
Thurstonových 24 otázek[4][5] 24 - William Thurston 1982
Smaleovy problémy 18 14 Stephen Smale 1998
Problémy tisíciletí (Millennium Prize problémy) 7 6[6] Clayův matematický ústav 2000
Simonovy problémy 15 <12[7][8] Barry Simon 2000
Nevyřešené problémy v matematice pro 21. století[9] 22 - Jair Minoro Abe, Šotaro Tanaka 2001
Matematická výzva DARPA[10][11] 23 - DARPA 2007

Nevyřešené problémy

Odkazy

Reference

V tomto článku byl použit překlad textu z článku List of unsolved problems in mathematics na anglické Wikipedii.

  1. ↑ THIELE, Rüdiger. Mathematics and the historian's craft. The Kenneth O. May Lectures. Redakce Van Brummelen Glen. [s.l.]: [s.n.], 2005. (CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC; sv. 21). ISBN 978-0-387-25284-1. Kapitola On Hilbert and his twenty-four problems, s. 243–295. 
  2. ↑ GUY, Richard. Unsolved Problems in Number Theory. 2nd. vyd. [s.l.]: Springer, 1994. Dostupné v archivu pořízeném z originálu dne 2019-03-23. ISBN 978-1-4899-3585-4. S. vii. .
  3. ↑ SHIMURA, G. Yutaka Taniyama and his time. Bulletin of the London Mathematical Society. 1989, s. 186–196. Dostupné v archivu pořízeném z originálu dne 2016-01-25. DOI 10.1112/blms/21.2.186. 
  4. ↑ Archived copy [online]. [cit. 2016-01-22]. Dostupné v archivu pořízeném z originálu dne 2016-02-08. 
  5. ↑ THREE DIMENSIONAL MANIFOLDS, KLEINIAN GROUPS AND HYPERBOLIC GEOMETRY [online]. [cit. 2016-02-09]. Dostupné v archivu pořízeném z originálu dne 2016-04-10. 
  6. ↑ Millennium Problems [online]. [cit. 2015-01-20]. Dostupné v archivu pořízeném z originálu dne 2017-06-06. 
  7. ↑ Fields Medal awarded to Artur Avila [online]. 2014-08-13 [cit. 2018-07-07]. Dostupné v archivu pořízeném z originálu dne 2018-07-10. 
  8. ↑ BELLOS, Alex. Fields Medals 2014: the maths of Avila, Bhargava, Hairer and Mirzakhani explained [online]. 2014-08-13 [cit. 2018-07-07]. Dostupné v archivu pořízeném z originálu dne 2016-10-21. 
  9. ↑ ABE, Jair Minoro; TANAKA, Shotaro. Unsolved Problems on Mathematics for the 21st Century. [s.l.]: IOS Press, 2001. Dostupné online. ISBN 978-9051994902. 
  10. ↑ DARPA invests in math [online]. CNN, 2008-10-14 [cit. 2013-01-14]. Dostupné v archivu pořízeném z originálu dne 2009-03-04. 
  11. ↑ Broad Agency Announcement (BAA 07-68) for Defense Sciences Office (DSO) [online]. DARPA, 2007-09-10 [cit. 2013-06-25]. Dostupné v archivu pořízeném z originálu dne 2012-10-01. 

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