This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani's popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political establishment.
The authors explore three major directions in their dialogue: the highly complex relationship between mathematics and reality, the subject of many debates and opposing viewpoints; the freedom that the construction of mathematics has given humankind by enabling them to develop the natural sciences as well as mathematical research; and the responsibility with which the scientific community and governments should address the role of mathematics in research and education policies.
"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)
