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The 59 pages that link to Mathematical proof, each with the reason it gives.
Euclid's ElementsRelated: Euclid's propositions demonstrate how definitions and postulates support deductive conclusions.
EuclidRelated: Euclid’s propositions made proof the organizing method of a comprehensive mathematical text.
Deductive reasoningRelated: Proofs use deductive steps to establish theorems from axioms and prior results.
Classical logicRelated: Classical logic supplies standard rules for formal mathematical deduction.
Pierre de FermatRelated: Fermat often recorded claims without proofs, leaving later mathematicians to reconstruct or establish them.
Ancient Greek mathematicsRelated: Greek mathematicians made proof central to establishing geometric results.
Formal systemRelated: A proof records a system's rule-governed route from assumptions to a theorem.
Greek mathematicsRelated: Proof distinguishes the Greek theoretical tradition from merely recording numerical procedures.
Surjective functionRelated: A surjectivity proof must show an appropriate input exists for every codomain element.
Goldbach's conjectureRelated: Only a proof covering every eligible even integer would settle the conjecture.
MathematicsRelated: Proof distinguishes mathematical justification from conjecture or empirical support.
Doubling the cubeRelated: The impossibility claim depends on a proof, not on the failure of historical attempts.
Imre LakatosRelated: Lakatos treated proof as a revisable process involving conjectures, counterexamples, and repaired arguments.
Modus tollensRelated: Proofs use the rule to infer that a hypothesis is false when it would entail a false result.
George PólyaRelated: Pólya distinguished finding a plausible result from proving that it must be true.
LogicRelated: Proofs demonstrate validity by chaining licensed inferences.
DemonstrationRelated: It is a modern, rigorously specified practice closely aligned with demonstration.
Nicolas BourbakiRelated: The group’s texts make explicit proof the standard for every major claim.
Philosophy of mathematicsRelated: Proof is the principal standard for establishing mathematical results.
Axiomatic systemRelated: A proof is the formal derivation that establishes a theorem from the system.
Deductive systemRelated: A proof records the rule-governed steps that constitute a derivation.
Liu HuiRelated: His commentary often explains why procedures in The Nine Chapters produce correct results.
Pure mathematicsRelated: Proof distinguishes established results from conjectures across pure mathematics.
Mathematical conjectureRelated: A proof turns a conjecture into an established theorem.
Mathematical puzzleRelated: A rigorous solution explains why a puzzle answer works, not just what it is.
Theoretical computer scienceRelated: Proofs establish correctness, impossibility, and complexity claims.
Automated reasoningRelated: Automated theorem provers seek formal derivations that meet this standard.
Mathematical problemRelated: Proof is the required output when a problem asks for a theorem to be established.
History of mathematical notationRelated: Notation affects how proofs are compressed, read, and checked.
MathematicianRelated: Proof distinguishes established mathematical results from conjectures.
Anne's theoremRelated: A theorem’s proof or subject matter can help identify it when its name is uncertain.
Axiom (mathematics and logic)Related: A proof makes explicit how axioms support a derived statement.
Erdős–Mordell inequalityRelated: Many distinct proof techniques have been developed for the inequality.
If and only ifRelated: Proving an iff requires separate arguments for each direction.
Mathematical conceptsRelated: Proof distinguishes established mathematical claims from conjectures or calculations.
PandrosionRelated: Pappus’s objections raise questions about whether Pandrosion supplied a complete proof or construction.
Peg solitaireRelated: Proof can establish impossibility without relying on exhaustive search.