"A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street."
--David Hilbert
"I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces."
--Paul R. Halmos
"A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so."
-- John von Neumann
"Chebyshev said it, and I say it again. There is always a prime between n and 2n."
--Paul Erdős
"The first sign of senility is that a man forgets his theorems, the second sign is that he forgets to zip up, the third sign is that he forgets to zip down."
--Stanislaw Ulam
Montreal Weather
Research
"Graph theory, like lattice theory, is the whipping boy of mathematicians in need of concealing their feelings of insecurity."