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...cluding the bases of the latter), and regarded this as the greatest of his mathematical achievements. ...e [[Archimedes Palimpsest]] has provided new insights into how he obtained mathematical results.<ref>{{cite web | title = Archimedes - The Palimpsest|author=| publ ...

...description had in turn been generalized to higher-dimensional spaces in a mathematical formalism introduced by [[Bernhard Riemann]] in the 1850s. With the help of ...gravity: they are how matter tells spacetime how to curve. In the theory's mathematical formulation, all these quantities are but aspects of a more general physica ...

...department at the [[University of Göttingen]], a world-renowned center of mathematical research. The philosophical faculty objected, however, and she spent four y ...her's theorem]]'', has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics".<ref name="hillle ...

...>{{cite book| author = [[Isaac Newton|Newton I]]| year = 1974| title = The Mathematical Papers of Isaac Newton, Volume VI: 1684–1691| editor = DT Whiteside| publis ...uthors.<ref name="alt_reconstructions">[[Robert Simson|Simson R]] (1734) ''Mathematical Collection'', volume VII, p. 117.<br>{{cite book| author = Zeuthen HG| year ...

...p and its operation. This allows one to handle entities of very different mathematical origins in a flexible way, while retaining essential structural aspects of ...and firmly established around 1870. Modern [[group theory]]—a very active mathematical discipline—studies groups in their own right.{{cref|a}} To explore groups, ...

...n domain]]s. The Euclidean algorithm has been generalized further to other mathematical structures, such as [[knot (mathematics)|knots]] and [[multivariate polynom ...nteger factorization]] algorithms. Finally, it is a basic tool for proving theorems in modern [[number theory]], such as [[Lagrange's four-square theorem]] and ...

...</ref><ref>{{cite book|title=Nets, Puzzles, and Postmen: An Exploration of Mathematical Connections|author=Peter M. Higgins|year=2007|publisher=Oxford University P ...tician) | title = Euler: The Master of Us All| year = 1999| publisher =The Mathematical Association of America | pages = 17}}</ref> He is also renowned for his wor ...

...g—that it encountered [[Controversy over Cantor's theory|resistance]] from mathematical contemporaries such as [[Leopold Kronecker]] and [[Henri Poincaré]]<ref>Dau ...ngen|University of Göttingen]], then and later a very important center for mathematical research. In 1867, Berlin granted him the [[Doctor of Philosophy|PhD]] for ...

In this context, "[[almost surely]]" is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey; rath [[Category:Mathematical theorems]] ...

...mathematical proof|Proofs]] have been formulated with varying degrees of [[mathematical rigour]], taking into account preferred development of the real numbers, ba ...generally unrelated to 0.999…, but they are of considerable interest in [[mathematical analysis]]. ...

...w class of preferred motions, too, defines a geometry of space and time—in mathematical terms, it is the [[geodesic]] motion associated with a specific [[connectio ...time's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a [[conformal structure]].<ref>E.g. {{Harvnb|Ehlers|197 ...

These mathematical techniques, combined with material supplied by Captain [[Gustave Bertrand]] ...t cryptanalysts of all time".<ref>Kahn, 1996, p. 974</ref> Rejewski used a mathematical theorem that one mathematics professor has since described as "the theorem ...

...''F'''_rnd is uncorrelated with the position '''r'''). Using the mathematical identities ...hin | first = AI | authorlink = Aleksandr Khinchin | year = 1949 | title = Mathematical Foundations of Statistical Mechanics ([[George Gamow|G. Gamow]], translator ...