| 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 |
