A scorecard for Poincare

In the April issue of the Notices of AMS, Philip J Davis and David Mumford write (pdf) about Poincare’s The future of mathematics (pdf) talk delivered a century ago; there are many interesting comments on the general aspects of Poincare’s talk (specialisation, increase in the corpus of mathematics, rigour, computation,  quantitative versus qualitative, aesthetics as an element of mathematical discovery, and the linguistic elements of mathematics); they also go on to discuss more specific comments of Poincare on many different fields of mathematics (algebra, geometry,  …). Finally, there is a scorecard in which they list the developments that he had foreseen and the ones that he missed (and, he missed more than he had foreseen, obviously — though, that doesn’t, in any way, diminish what he had achieved).

Poincare’s Science and Method (of which book, the Future of mathematics talk is a chapter) is a book that I read nearly ten years ago (and enjoyed it a lot too); and, it is really nice for me to see a mathematician’s appraisal of some sections of it.

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