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

Saturday, December 16, 2006

Christopher TownsendI work in locale theory and topos theory. My preoccupation is that the theory of compact Hausdorff spaces and the theory of sets have such a lot in common that they can be expressed as the same theory. Therefore I am developing axioms for a category of spaces in which the theory of compact Hausdorff spaces is dual to the theory of sets (the duality is not standard categorical duality, but is order enriched duality; the category of spaces is order enriched). A further aim is to extend this work to an axiomatization of the category of Grothendieck toposes.

Friday, December 15, 2006

PLT Online Excelente lista de libros online sobre semántica de lenguajes