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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 ...
The proofs of the Kronecker–Weber theorem by Kronecker (1853) and Weber (1886) both had gaps. The first complete proof was given by Hilbert in 1896. In 1879, Alfred Kempe published a purported proof of the four color theorem, whose validity as a proof was accepted for eleven years before it was refuted by Percy Heawood.
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures; List of data structures; List of derivatives and integrals in alternative calculi; List of equations; List of fundamental theorems; List of hypotheses; List of inequalities; Lists of ...
Zeros. Polynomials. Determinants. Number Theory. Geometry. The volumes are highly regarded for the quality of their problems and their method of organisation, not by topic but by method of solution, with a focus on cultivating the student's problem-solving skills. Each volume the contains problems at the beginning and (brief) solutions at the end.
Proofs from THE BOOK contains 32 sections (45 in the sixth edition), each devoted to one theorem but often containing multiple proofs and related results. It spans a broad range of mathematical fields: number theory, geometry, analysis, combinatorics and graph theory.
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