From the infamous MathOverlow thread
I went to visit him while he was lying ill at the hospital. I had come in taxi cab number 14 and remarked that it was a rather dull number. “No” he replied, “it is a very interesting number. It’s the smallest number expressible as the product of 7 and 2 in two different ways.”
A British mathematician was giving a talk in Grothendieck’s seminar in Paris. He started “Let X be a variety…”. This caused some talking among the students sitting in the back, who were asking each other “What’s a variety?”. J.-P. Serre, sitting in the front row, turns around a bit annoyed and says “Integral scheme of finite type over a field”.
What’s an anagram of Banach-Tarski? Banach-Tarski Banach-Tarski.
Q: Why is it important to study Verma modules of Lie algebras?
A: The most widely used modules of Lie algebras and Lie groups are finite-dimensional irreducible representations, the Weyl modules. Of course, you should learn them first when you study representation theory. But they are only the tip of the iceberg.
An introverted mathematician is one who looks at his shoes when he talks to you. An extroverted mathematician is one who looks at your shoes when he talks to you.
Source: Steven Krantz’s A Primer of Mathematical Writing (pp.169)
Q: When did Bourbaki stop writing books?
A: When they realized that Serge Lang was a single person
How we do it…
Aerodynamicists do it in drag.
Algebraists do it by symbolic manipulation.
Algebraists do it in a ring, in fields, in groups.
Analysts do it continuously and smoothly.
Applied mathematicians do it by computer simulation.
Banach spacers do it completely.
Bayesians do it with improper priors.
Catastrophe theorists do it falling off part of a sheet.
Combinatorists do it as many ways as they can.
Complex analysts do it between the sheets
Computer scientists do it depth-first.
Cosmologists do it in the first three minutes.
Decision theorists do it optimally.
Functional analysts do it with compact support.
Galois theorists do it in a field.
Game theorists do it by dominance or saddle points.
Geometers do it with involutions.
Geometers do it symmetrically.
Graph theorists do it in four colors.
Hilbert spacers do it orthogonally.
Large cardinals do it inaccessibly.
Linear programmers do it with nearest neighbors.
Logicians do it by choice, consistently and completely.
Logicians do it incompletely or inconsistently.
(Logicians do it) or [not (logicians do it)].
Number theorists do it perfectly and rationally.
Mathematical physicists understand the theory of how to do it, but have difficulty obtaining practical results.
Pure mathematicians do it rigorously.
Quantum physicists can either know how fast they do it, or where they do it, but not both.
Real analysts do it almost everywhere
Ring theorists do it non-commutatively.
Set theorists do it with cardinals.
Statisticians probably do it.
Topologists do it openly, in multiply connected domains
Variationists do it locally and globally.
Cantor did it diagonally.
Fermat tried to do it in the margin, but couldn’t fit it in.
Galois did it the night before.
Mðbius always does it on the same side.
Markov does it in chains.
Newton did it standing on the shoulders of giants.
Turing did it but couldn’t decide if he’d finished.