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Gomory's theorem (mathematical logic) Goodstein's theorem (mathematical logic) Gordon–Newell theorem (queueing theory) Gottesman–Knill theorem (quantum computation) Gradient theorem (vector calculus) Graph structure theorem (graph theory) Grauert–Riemenschneider vanishing theorem (algebraic geometry) Great orthogonality theorem (group theory)
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The first question sets up an elementary combinatorics question; but the second suggests both a solution (using generating functions) and a generalisation. The third gives another combinatorics question which can be solved by means of generating functions. Indeed, questions 1-26 follow generating function through further examples.
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]
Alemannisch; العربية; বাংলা; Беларуская (тарашкевіца) Català; Чӑвашла; Čeština; Deutsch; Ελληνικά; Español
Cayley's theorem; Clique problem (to do) Compactness theorem (very compact proof) Erdős–Ko–Rado theorem; Euler's formula; Euler's four-square identity; Euler's theorem; Five color theorem; Five lemma; Fundamental theorem of arithmetic; Gauss–Markov theorem (brief pointer to proof) Gödel's incompleteness theorem. Gödel's first ...
Cartan's theorems A and B; Cayley–Bacharach theorem; Chasles–Cayley–Brill formula; Chasles' theorem (geometry) Chevalley–Iwahori–Nagata theorem; Chevalley's structure theorem; Chow's lemma; Chow's moving lemma; Clifford's theorem on special divisors
Of the cleanly formulated Hilbert problems, numbers 3, 7, 10, 14, 17, 18, 19, and 20 have resolutions that are accepted by consensus of the mathematical community. Problems 1, 2, 5, 6, [g] 9, 11, 12, 15, 21, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems.
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