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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 ...
In 1808 Legendre published an attempt at a proof of Dirichlet's theorem, but as Dupré pointed out in 1859 one of the lemmas used by Legendre is false. Dirichlet gave a complete proof in 1837. 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.
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 ...
In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority of the cases ...
Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the n th triangular number. In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.
Old axiom II.4 is renamed as Theorem 5 and moved. Old axiom II.5 (Pasch's Axiom) is renumbered as II.4. V.2, the Axiom of Line Completeness, replaced: Axiom of completeness. To a system of points, straight lines, and planes, it is impossible to add other elements in such a manner that the system thus generalized shall form a new geometry ...