Against Functional Analysis

The functional analysis thread has turned into a big love-fest, but a dissenting voice has appeared from an unexpected quarter. David Corfield spotted this interview with Gian-Carlo Rota and David Sharp. Rota says:

Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven’t. You get the feeling that the result you have discovered is forever, because it’s concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don’t get a feeling of having done an honest day’s work. Don’t get the wrong idea-combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.

This raises a disturbing possibility: I like functional analysis because it provides yet another way to avoid an honest day’s work.

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