Thursday, January 18, 2007
Sunday, January 14, 2007
from Rota's `Indiscrete thoughts' 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
``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
Monday, January 08, 2007
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