Freedom in Mathematics

Presentation of the Authors (Pierre Cartier, Jean Dhombres, Gerhard Heinzmann, Cedric Villani).- On the Origins of Mathematics.- The Relations between Mathématics and Reality.- Social and Political History of Mathematics Education.- Nature and Issues of the Mathematics Research.- Conclusion.- Annexure.

PIERRE CARTIER is academic by training, emeritus research director at the Centre national de la recherche scientifique (CNRS), and research scientist and a visitor (for indeterminate term) at the Institut des Hautes Etudes Scientifiques (IHES) of Bures-sur-Yvette. He is currently emeritus research director at the University Paris-Diderot. He is former member of the Bourbaki group. Born in 1932 in Sedan, Professor Carier, despite his provincial background, followed the path of excellence in his studies: a secondary school in his home town, followed by the lycée Saint-Louis in Paris and then the École normale superieure, and he obtained an advanced teaching degree and a doctorate in mathematics (1958). He also went to Princeton for two years; there he became acquainted with legendary figures such as Robert Oppenheimer and Andre Weil (brother of philosopher Simone Weil). Last but not least, he carried out a long military service in the marine corps against the backdrop of the Algerian war. He was then professor at the University of Strasbourg from 1961 to 1971. The years 1950-1975 were the hey-day of the Bourbaki group, of which he is one of the pillars; there he became friends with famous people like Cartan, Schwartz, Dieudonné, Chevalley, Weil, and with younger ones.

A "mathematician without borders", Professor Cartier is active within the framework of the cooperation agency of the French Mathematical Society (Cimpa). He had been working in the Paris region since 1971, and he roamed around between Parisian academic institutions: University Paris-Sud, École polytechnique, École normale supérieure. He is not a member of the French Academy of Sciences (a voluntary choice). His scientific interests are quite diverse (even eclectic), but centered around group theory and mathematical physics. He often cited thesis relates to algebraic geometry, by he also contributed to differential geometry, number theory, combinatorics, numerical analysis, probability and

"The conversations here between four leading French intellectuals ... offer rare insiders' views into the wide range of issues that inform top-down shaping of the mathematical enterprise writ large. One will find history as fresh as gossip, and students will discover perspectives that might prove crucial for timely career planning. Summing Up: Recommended. All readers." (D. V. Feldman, Choice, Vol. 54 (5), January, 2017)

"This book makes the reader a participant of an interesting conversation of two mathematicians. ... The authors complement their interesting discourse with reading lists inviting the reader to reflect further on the topics debated in the book and related issues. A very stimulating reading full of interesting thoughts and opinions." (Yuriy V. Rogovchenko, zbMATH, Vol. 1365.00010, 2017)

"It is a very engaging read. Reading this book allows one to feel like a fly on the wall of a parlor where these four great minds are discussing a number of different issues related to mathematics. ... the book contains biographical sketches of the four participants and reading lists that they each suggest for the reader who wants to think more about the topics. ... it is a very enjoyable and thought-provoking read ... ." (Darren Glass, MAA Reviews, maa.org, August, 2016)