"I do not need these concepts for what I want to do."
G.-C. Rota writes in "Indiscrete thoughts", Edited by F. Palonti, Birkhauser, (1997). p.48:
“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.”
30 May, 2015