“The way to get to the top of the heap in terms of developing original research is to be a fool, because only fools keep trying. You have idea number 1, you get excited, and it flops. Then you have idea number 2, you get excited, and it flops. Then you have idea number 99, you get excited, and it flops. Only a fool would be excited by the 100th idea, but it might take 100 ideas before one really pays off. Unless you’re foolish enough to be continually excited, you won’t have the motivation, you won’t have the energy to carry it through. God rewards fools.”
“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!”
The Maoist movement decided that group theory was a reactionary subject of the old regime, and started protesting at the increasing number of professors in the subject being appointed. Demonstrations erupted outside of the maths department with protesters holding placards demanding ‘No more group theory’. One new appointee in group theory was frightened off and took a job elsewhere. During one demonstration, the students scaled the outside of the building and scrawled `Group Theory Department’ on the wall.
Letters to a young mathematician / Ian Stewart.