(Pretentious) Quotes I like

A value is, a computation does.

Paul Blain Levy, “Call-By-Push-Value: A Functional/Imperative Synthesis”

“What can you prove with exterior algebra that you cannot prove without it?” Whenever you hear this question raised about some new piece of mathematics, be assured that you are likely to be in the presence of something important. In my time, I have heard it repeated for random variables, Laurent Schwartz’ theory of distributions, ideles and Grothendieck’s schemes, to mention only a few. A proper retort might be: “You are right. There is nothing in yesterday’s mathematics that could not also be proved without it. Exterior algebra is not meant to prove old facts, it is meant to disclose a new world. Disclosing new worlds is as worthwhile a mathematical enterprise as proving old conjectures.

Gian-carlo Rota, Indiscrete Thoughts p. 48, 1997 (Originally seen here)

We have had to fight against the myth of the mainstream which says, for example, that there are cycles during which at one time everybody is working on general concepts, and at another time anybody of consequence is doing only particular examples, whereas in fact serious mathematicians have always been doing both. One should not get drunk on the idea that everything is general. Category theorists should get back to the original goal: applying general results to particularities and to making connections between different areas of mathematics.

F. William Lawvere, An Interview with F. William Lawvere, Bulletin of the International Center for Mathematics, June 2008, (link)