theorems
Math's established truths
Theorems are propositions that have been proven true through logical reasoning from accepted premises.
The term belongs primarily to mathematics and formal logic, where a theorem follows necessarily from axioms and previously established results: the Pythagorean theorem, Gödel's incompleteness theorems.
Outside technical contexts, theorem sometimes appears loosely for any principle or rule that seems demonstrably true.
Demonstration of truth
- lemmaBase form, or helper theorem
- corollaryLogical natural consequence
- axiomSelf-evident starting principle
- postulateAssumed starting point
proposition · conjecture · hypothesis · derivation · demonstration · formula · equation · statement
proof
Demonstration of truth
- lemmaBase form, or helper theorem
- corollaryLogical natural consequence
- axiomSelf-evident starting principle
postulate · proposition · conjecture · hypothesis · derivation · demonstration · formula · equation · statement · generalization
Pythagorean
Of ancient Greek mathematics
- mathaddition, subtraction, multiplication, division, algebra
- math skillsarithmetic, addition, subtraction, multiplication, division
- mathematicsalgebra, arithmetic, calculus, geometry, number
- math conceptsangle, numbers, algebra, circle, equations
- ancient mathalgebra, arithmetic, geometry, fractions, addition
- Greek mathematicsEuclid, Archimedes, Pythagoras, geometry, axiom
theoremsconjectures
Unverified assumptions or theories
hypotheses · postulates · speculations · guesses · suppositions
theoremsfallacies
Invalid logical arguments
contradictions · paradoxes · falsehoods · absurdities · refutations
theoremsaxioms
Accepted starting principles
postulates · premises · first principles · assumptions · definitions
- theoretical physicistsScientists exploring nature through mathematics
- Pythagorean theoremRelates right triangle sides
- theoretical physicsNature explained through equations
- Fermat's Last TheoremNo integer cubes sum to cubes
- Pythagoras' theoremRight triangle side relationship
- Cantor's theoremPowersets always strictly larger