mathematical proof
Formal logical argument
A mathematical proof is a rigorous logical argument demonstrating that a statement must be true, proceeding from accepted axioms and previously established results through steps that follow necessarily from one another.
Unlike evidence in science or law, a valid proof establishes its conclusion with certainty—once proven, a theorem remains true forever.
The proof proceeds by contradiction.
- axiomSelf-evident starting principle
- first principlesBasic truths underlying reasoning
- number theoryPure math studying integers
- deductionConclusion from premises
- algebraMath using symbols
theorem · logic · QED · validity · lemma · inference · corollary · geometry · reductio ad absurdum · proposition · if and only if · quantifiers · set theory · Fermat's Last Theorem · truth table · calculus · computer science · topology
- logic termsif, then, valid, premises, and
- logicpremise, premises, conclusion, conclusions, inference
- theorytheory, hypothesis, theorem, axiom, postulate
- pure reasonpure reason, a priori, synthetic a priori, self-evident truth, first principles
mathematical proofconjecture
Guess from limited facts
speculation · guess · intuition · hypothesis · hunch
mathematical proofhand-waving
Vague gesturing as explanation
gut feeling · inductive reasoning · anecdotal evidence · educated guess · empirical evidence
mathematical proofdisproof
Evidence showing falsehood
refutation · counterexample · falsification · open problem · contradiction
mathematical, mathematics, mathematically, mathematician, mathematicians, proof, proofs, disprove, disproves