Translator's Note \ Acknowledgements \ 1. Introduction Jacques Lautman \ 2. Bibliography of secondary material on the work of Albert Lautman \ 3. Albert Lautman and the Creative Dialectic of Modern Mathematics Fernando Zalamea \ 4. Preface to the 1977 Edition Jean Dieudonné \ 5. Considerations on Mathematical Logic \ 6. Mathematics and Reality \ 7. International Congress of the Philosophy of the Sciences \ 8. On the Reality Inherent to Mathematical Theories \ 9. The Axiomatic and the Method of Division \ 10. Essay on the Unity of the Mathematical Sciences in their Current Development \ 11. Essay on the Notions of Structure and Existence in Mathematics \ 12. New Research on the Dialectical Structure of Mathematics \ 13. Letter to Mathematician Maurice Fréchet \ 14. Symmetry and Dissymmetry in Mathematics and in Physics \ Bibliography \ Index.

Albert Lautman (1908-1944) was a French mathematical philosopher. An escaped prisoner-of-war, he was killed by the Nazis in Toulouse in 1944. His work in the philosophy of mathematics has since had a profound influence on modern European philosophy, in particular the work of Gilles Deleuze and Alain Badiou.
Simon Duffy is a Research Fellow in Philosophy at the University of Sydney, Australia. He is the author of The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze (Ashgate, 2006) and editor of Virtual Mathematics: The Logic of Difference (Clinamen Press, 2006).

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.