Problemata Hilbertiana
Multi tool use
Tertium problema de tetrahedris tractat
Problemata Hilbertiana sunt viginti tria problemata mathematica quae enuntiavit David Hilbert in Congressu Internationali Mathematicorum, Lutetiae, anno 1900. Paene omnia saeculo vigesimo soluta sunt, praeter octavum, de hypothesi Riemanniana, et partes octavi decimi.
Problemata |
Hypothesis de continuo
- Utrum axiomata arithmeticae inter se congruant, utrum completa sint
- Utrum tetrahedra, quae eandem basin et eandem altitudinem habent, etiam eandem volumen habeant
- De geometriis non-Euclideanis dictis (hoc problema haud intellegitur)
- De catervis Lie
Axiomata mathematica physicae
- Utrum numerus ab sit transcendentalis, si a est numerus algebraicus et b numerus algebraicus irrationalis
- Hypothesis Riemanniana
- De reciprocitate in corporis nescioquibus
- De aequationibus Diophantinis
- De formis quadraticis
- Extensio theorematis Kronecker
- De "nomographia," hoc est, quales functiones per parametris simplicior scribi possunt
- Qualia systemata invariantium sunt finita
- De calculo Schubert
- De topologia flexuum algebraicorum
- Quales functiones per summas quantitatum quadraticorum scribi possunt
- De tegulis; utrum forma sit quae spatium impleat
- Utrum solutiones in calculo variationum sint semper analyticae
- De quantitatibus in liminibus
- Coniectura Riemann et Hilbert de aequationibus differentialibus
- De functionibus automorphicis
- De calculo variationum
Bibliographia |
- Jeremy J. Gray. The Hilbert Challenge. Oxonii: Oxford University Press, 2000. ISBN 0-19-850651-1
- David Hilbert. "Mathematische Probleme. Vortrag, gehalten auf dem internationalen Mathematike-Congress zu Paris, 1900." Archiv für Mathematik und Physik I, 44-63 et 213-237. Versio anglica, Mary Winston Newson, Bulletin of the American Mathematical Society 8 (1902), 437-479.
- Benjamin Yandell. The Honors Class: Hilbert's Problems and their Solvers. Natick: A.K. Peters, 2002. ISBN 1568811411
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