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 |