Today it is considered an egregious faux pas to speak or write in the crude antedated terms of our grandfathers. To assist the isolated student and the less sophisticated teacher, we have prepared the following list of currently fashionable mathematical terms in academia. We pass this list on to the general public as a matter of charity and in the hope that it will lead to more refined elucidation from young scholars.

What’s Out? |
What’s In? |

thinking | hypothesizing |

proof by contradiction indirect proof |
reductio ad absurdum |

mistake | non sequitur |

starting place | handle |

with corresponding changes | mutatis mutandis |

counterexample | pathological exception |

consequently | ipso facto |

swallowing results | digesting proofs |

therefore | ergo |

has an easy-to-understand but hard-to-find solution | obvious |

has two easy-to-understand but hard-to-find solutions |
trivial |

truth | tautology |

empty | vacuous |

drill problems | plug-n-chug work |

criteria | rubric |

example | substantive instantiation |

similar structure | homomorphic |

very similar structure |
isomorphic |

same area | isometric |

arithmetic | number theory |

count | enumerate |

one | unity |

generally | globally |

specifically | locally |

constant | invariant |

bonus result | corollary |

distance | metric measure |

several | a plurality |

function | operator |

argument | operand |

fourth power quartic |
biquadratic |

random | stochastic |

unique condition | singularity |

uniqueness | unicity |

tends to zero | vanishes |

tip-top point | apex |

half-closed | half-open |

concave | non-convex |

rectangular prism | parallelopiped |

perpendicular (adj.) | orthogonal |

perpendicular (n.) | normal |

Euclid | Descartes |

Fermat | Wiles |

path | trajectory |

shift | rectilinear translation |

similar | homologous |

very similar |
congruent |

change direction | perturb |

join | concatenate |

approximate to two or more decimal places | accurate |

high school geometry plane geometry |
geometry of the Euclidean plane under the Pythagorean metric |

clever scheme | algortihm |

brace, { | squiggle |

decimal | denary |

alphabetical order | lexicographical order |

Michael Stueden, November 7, 1994.