| математическое: Эйлер и Фейнманн: почему 1 2 3 4 ... = -1/12 |
[Dec. 12th, 2004|04:15 pm] |
Pierre Cartier: From the combinatorics of particle interactions to special values of (multiple) zeta functions
http://swc.math.arizona.edu/dls/index.html
http://www.ihes.fr/PREPRINTS/M00/Resu/resu-M00-48.html
Cartier, Mathemagics A tribute to Euler and Feynmann
Abstract. The implicit philosophical belief of the working mathematician is today the Hilbert-Bourbaki formalism. Ideally, one works within a closed system: the basic principles are clearly enunciated once for all, including (that is an addition of twentieth century science) the formal rules of logical reasoning clothed in mathematical form.
My thesis is: there is another way of doing mathematics, equally successful, and the two methods should supplement each other and not fight. This other way bears various names: symbolic method, operational calculus, operator theory ...
In this article I make a case for this "other method" of doing mathematics, by discussing several instances where it has led to, respectively will (hopefully) lead to, fruitful insights and developments.
Cartier gave five lectures in February, 2004. Here are some relevant papers:
“Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents”, Séminaire Bourbaki 885, Mars 2001 (dvi, ps, pdf)
Several chapters from an upcoming book with Cecile De Witt. All files are pdf: Chapter 1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 9, Chapter 9 bis, Chapter 14, Chapter 16.
“Mathemagics” in postscript at the IHES preprint site
|
|
|
