“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, idèles 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.”

One day, in my first year as an assistant professor at MIT, while walking down one of the long corridors, I met professor Z, a respected senior mathematician with a solid international reputation. He stared at me and shouted “Admit it! All lattice theory is trivial!”