theorem
Logically established conclusion
A theorem is a statement in mathematics or logic that has been proven true through rigorous demonstration from accepted axioms and previously established theorems.
Unlike a hypothesis or conjecture, a theorem carries the weight of proof: The Pythagorean theorem relates the sides of a right triangle.
In casual use, theorem sometimes refers to any general principle or rule that seems reliably true, though mathematicians reserve the term for formally proven propositions.
Base form, or helper theorem
- corollaryLogical natural consequence
- conjectureGuess from limited facts
- postulateAssumed starting point
- axiomSelf-evident starting principle
hypothesis · deduction · induction · inference · contradiction · validity · soundness · rigor
French number theorist
- BayesProbability theorem eponym
- binomialExpression with two terms
- fundamentalForming the base
- calculusMathematical analysis system
algebra · topology · incompleteness · existence · uniqueness · convergence · fixed-point · prime number
Self-evident starting principle
- propositionStatement expressing a judgment
- corollaryLogical natural consequence
- lemmaBase form, or helper theorem
- conjectureGuess from limited facts
postulate · statement · law · principle · rule · thesis · assumption · premise
Accordance with reality
- certaintyTotal absence of doubt
- knowledgeUnderstood facts and skills
- a prioriIndependent of experience
- necessityIndispensable requirement
universality · reason · rationality · abstraction · validity · analytic · synthetic · Spinoza
lemma
Base form, or helper theorem
- corollaryLogical natural consequence
- conjectureGuess from limited facts
- postulateAssumed starting point
axiom · hypothesis · deduction · induction · inference · contradiction · validity · soundness · rigor · formalism
Fermat
French number theorist
- BayesProbability theorem eponym
- binomialExpression with two terms
- fundamentalForming the base
calculus · algebra · topology · incompleteness · existence · uniqueness · convergence · fixed-point · prime number
axiom
Self-evident starting principle
- propositionStatement expressing a judgment
- corollaryLogical natural consequence
- lemmaBase form, or helper theorem
conjecture · postulate · statement · law · principle · rule · thesis · assumption · premise · assertion
truth
Accordance with reality
- certaintyTotal absence of doubt
- knowledgeUnderstood facts and skills
- a prioriIndependent of experience
necessity · universality · reason · rationality · abstraction · validity · analytic · synthetic · Spinoza · Wittgenstein
Pythagorean
Of ancient Greek mathematics
- EuclideanFlat-space geometry type
- congruenceState of agreement
- triangleThree-sided plane figure
parallel · angle · polygon · circle · vertex · perimeter · bisector · tangent · secant · plane
- philosophy termstruth, reason, knowledge, wisdom, logic
- geometric proofsaxiom, postulate, lemma, corollary, QED
- Proof Theoryproof, axiom, lemma, corollary, logical proof
- proofsproof by contradiction, contrapositive, contradiction, lemma, corollary
- mathematicsalgebra, arithmetic, calculus, geometry, number
- cognitionthinking, reasoning, thought, cognition, remembering
theoremconjecture
Guess from limited facts
postulate · assumption · hypothesis · axiom · premise
theoremfallacy
Error in reasoning
contradiction · counterexample · paradox · refutation · disproof
- in theoryHypothetically, not actually
- conspiracy theoriesUnproven secret plot beliefs
- conspiracy theoryAttributed to hidden plotters
- conspiracy theoristOne who suspects cover-ups
- big bang theoryUniverse origin hypothesis
- theory of evolutionBiological change over generations
theory, theories, theoretical, theorize, theorist, theoretically, theorizing, theorists, theorized