Mathematics, Ideas and the Physical Real

by Albert Lautman, Simon Duffy

Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics.

Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.

Genres: Philosophy, Mathematics

352 pages, Paperback

First published June 2, 2011

Reviews

[Edward Butler · Rating 5 out of 5]

A very important book for philosophers and for mathematicians alike. I say the former with more confidence than the latter, to be sure. Readers of this book are likely to fall either into the class of those who grasp the philosophy, but struggle with or must merely skim the mathematics, like myself, or those who follow the mathematics but struggle with the philosophy (as mathematician Maurice Fréchet frankly confesses in his letter to Lautman included here on p. 220f). Fernando Zalamea, in his introduction, speaks more than adequately, I suppose, to the value of Lautman's thought for today's mathematician, and of its prescience with respect to important developments in the field in the decades since Lautman's untimely and heroic death as part of the French Resistance on Aug. 1st, 1944. With respect to its philosophical import, I would say that although Lautman did not live to realize to its fullest the riches of his ideas, that he left us with enough to say that his can be the only true way forward in grasping the relationship between mathematics and Being sought since the Pythagoreans and Platonists. His tantalizing and all too brief references to the Platonic tradition, as well as to Heidegger, demonstrate an originality that can only come from a genius that encounters the works of great philosophers with no need of intermediaries, but as their equal. My only criticism is that Continuum let this edition out with an unacceptable number of errors, probably at least one on every page, sometimes serious.

[J. · Rating 5 out of 5]

Few intellectual pleasures exceed that of communing with Lautman.