ThmDex – An index of mathematical definitions, results, and conjectures.
Glossary of mathematical words
Word Explanation
ansatz 'an educated guess'
axiom a mathematical statement which is accepted as true without a proof in order to start somewhere and derive a theory
characterization theorem a result which says that two mathematical statements are equivalent
closed-form expression often used in the context of real or complex calculus to describe a mathematical expression which consists only of real or complex arithmetic and such that any functions present in the expression are only the elementary functions
conjecture a result which has not yet been proven but which is strongly suspected to be true
corollary a result which follows effortlessly from another result
exercise a light challenge which requires only the application of routine operations already known to the student (compare to 'problem')
factorization a multiplicative-type algebraic operation (e.g. integer multiplication, binary set intersection, ...) repeatedly applied (compare to 'partition')
gedankenexperiment 'a thought experiment'
hypothesis a word deriving from latin, being a synonym for 'assumption'
lemma a supporting result, something used to reach a theorem or a proposition
parameter in the context of a collection of mathematical object, a parameter refers to an element of the index set
partition an additive-type algebraic operation (e.g. integer addition, binary set union, ...) repeatedly applied (compare to 'factorization')
penultimate step the expression or statement from which the final theorem (or proof) follows with a single step of deduction
portmanteau theorem
postulate an archaic near-synonym for 'axiom'
proposition a result of secondary interest
problem a substantial challenge which requires perhaps even the invention of new methods not yet known to the student (compare to 'exercise')
representation theorem
subdefinition a synonym for a special case or a particular case of a definition
subresult a synomym for special case or particular case of a result
theorem a result of primary interest
well-defined often used in the context to a function or a mapping recently introduced or defined, meaning that the mapping satisfies the actual definition of a map, being a right-unique and left-total binary relation