**Problems and fashion in mathematical physics**

Impressive parallel developments in pure mathematics and in quantum field
theory has revived Felix Klein's vision of a "preestablished harmony
between mathematics and physics" and encouraged the appearance of a new -
we may call it "Pythagorean" - brand of mathematical physics. A telling
example is provided by "the Fock space of positive integers" introduced
by Bost and Connes [1]. Conformal field theory had an important part in
bridging the gap between mathematics and quantum field theory [2]. I
shall also cite some sharp criticisms of string theory (which pretends
to offer the modern realization of the Pythagorean dream).

- J.B. Bost, A. Connes, Hecke algebras, type III factors and phase
transition with spontaneous symmetry breaking in number theory, Selecta
Math. (New Series) 1:3 (1995) 411-457.
- I.T. Todorov, Two-dimensional conformal field theory and beyond.
Lessons from a continuing fashion, Lett. Math. Phys. 56 (2001) 151-161;
Vienna preprint ESI 986 (2001).

*Ivan Todorov*

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