Glossary of mathematical jargon

The field of mathematics has a vast vocabulary of specialist technical terms. It also has a small amount of jargon: commonly used phrases which are part of the culture of mathematics, and distinguish the insider from the neophyte. These terms often appear in lectures and even in print as informal shorthand for more rigorous arguments or more precise ideas.

Mathematical jargon includes:

• (generalized) abstract nonsense
• almost all
• arbitrary
• back-of-the-envelope
• clearly
• handwaving
• if and only if (iff)
• in general — In mathematics, in general is used to mean "in all cases". (Contrast this with the usual meaning of in general: "in most cases".) Examples:
  • In expository writing, an author will often first give an example of a construction and then write "and in general the construction proceeds as follows".
  • In asserting a fact, one might say something like "a triangle has π internal radians; a quadrilateral has 2π; and, in general, an n-gon has (n-2)π."
  • In proving a statement, one might first prove a special case and continue with "and the proof in general is".
• left-hand side, right-hand side (LHS, RHS)
• necessary and sufficient
• pathological, well-behaved
• Q.E.D.
• required to prove (RTP), wish to show (WTS)
• rigor (rigour)
• sharp
• sufficiently large, suitably small, arbitrarily large, arbitrarily small
• trivial
• upstairs, downstairs — In a fiber bundle, the total space is often said to be "upstairs", with the base space "downstairs".
• up to, modulo, mod out by
• without (any) loss (of generality) (WLOG, WOLOG, WALOG), we may assume (WMA)