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It is to be regretted that this first comprehensive and thorough-going presentation of a mathematical logic and the derivation of mathematics from it [is] so greatly lacking in formal precision in the foundations (contained in 1– 21 of Principia [i.e., sections 1– 5 (propositional logic), 8–14 (predicate logic with identity/equality), 20 ...
The diagram accompanies Book II, Proposition 5. [1] A mathematical proof is a ... in terms of other concepts already known. Mathematical proof was ...
Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges
Pages which contain only proofs (of claims made in other articles) should be placed in the subcategory Category:Article proofs. Pages which contain theorems and their proofs should be placed in the subcategory Category:Articles containing proofs. Articles related to automatic theorem proving should be placed in Category:Automated theorem proving.
Many mathematicians then attempted to construct elementary proofs of the theorem, without success. G. H. Hardy expressed strong reservations; he considered that the essential "depth" of the result ruled out elementary proofs: No elementary proof of the prime number theorem is known, and one may ask whether it is reasonable to expect one.
List of mathematical functions; List of mathematical identities; List of mathematical proofs; List of misnamed theorems; List of scientific laws; List of theories; Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields.