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The 59 pages that link to Mathematical proof, each with the reason it gives.

• Mathematical inductionNarrower topic: Induction is one method within the broader practice of mathematical proof.

• 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.

• EvidenceCompared with: Evidence contributes to proof, but the two differ in whether a conclusion is established.

• Classical logicRelated: Classical logic supplies standard rules for formal mathematical deduction.

• InferenceCompared with: Proof aims at demonstrative establishment, while inference also includes uncertain, evidence-based conclusions.

• CounterexampleCompared with: A counterexample refutes a universal statement but does not prove an alternative theorem.

• History of mathematicsNarrower topic: Changing standards of proof help explain differences among mathematical traditions.

• 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.

• Constructive proofNarrower topic: Constructive proof is one way of establishing a mathematical statement.

• Surjective functionRelated: A surjectivity proof must show an appropriate input exists for every codomain element.

• TheoremNarrower topic: A theorem is established by a proof that derives its conclusion from accepted premises.

• Chinese mathematicsNarrower topic: Chinese texts often foregrounded executable procedures rather than extended deductive proofs.

• 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.

• Recreational mathematicsCompared with: Some recreational challenges prize a surprising answer, while proof establishes why it must be correct.

• George PólyaRelated: Pólya distinguished finding a plausible result from proving that it must be true.

• Bernard BolzanoNarrower topic: Bolzano treated proof as a source of mathematical knowledge, not merely a record of discovery.

• 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.

• William ThurstonNarrower topic: His essay challenged narrow measures of proof by distinguishing verification from understanding.

• 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.

• Grigori PerelmanNarrower topic: Perelman’s papers required detailed verification before the proof became accepted mathematics.

• Liu HuiRelated: His commentary often explains why procedures in The Nine Chapters produce correct results.

• Millennium Prize ProblemsNarrower topic: A prize requires a proof, not numerical evidence or a plausible conjecture.

• 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.

• Formal scienceBroader topic: It exemplifies how formal science justifies claims without experimental measurement.

• Russell CroweBroader topic: Crowe appeared in this early Australian film alongside Hugo Weaving.

• 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.

• Butterfly theoremNarrower topic: Its history includes many distinct proofs of the same midpoint claim.

• Equation solvingCompared with: Solving finds satisfying values; proving establishes a general claim about them.

• Finsler–Hadwiger theoremNarrower topic: Different proof styles expose the same geometric necessity in the theorem.

• History of mathematical notationRelated: Notation affects how proofs are compressed, read, and checked.

• MathematicianRelated: Proof distinguishes established mathematical results from conjectures.

• Pitot theoremNarrower topic: The theorem follows from a short proof using equal tangent segments.

• Poincaré–Birkhoff theoremNarrower topic: The theorem’s history includes a celebrated proof whose original formulation required later clarification.