Birth of a Theorem: A Mathematical Adventure

Cedric Villani’s story of how he and his former student and collaborator Clement Mouhot produced the work that earned Villani the Fields Medal is probably unique in mathematical circles. Certainly there have been memoirs and the like which reveal things about the mathematician author (an example is Gian-Carlo Rota’s “Indiscrete Thoughts”) but I cannot recall a book which sets out the actual process of “slaying the beast” in such a self-effacing way. Anyone who has watched Villani lecture can appreciate that he is actually a good communicator of ideas and his book simply reflects that. Villani is not the “it is easily seen that…” type of mathematician (usually a second rate one but there are some first rate ones who engage in this type of behaviour). In the vast majority of cases this is a put down since the thing is not easily seen at all and may require detailed and specialised knowledge to truly understand. In my experience this type of mathematician is probably either “on the spectrum” or terminally arrogant. Villani has done a huge social service by actually providing a living and breathing counterexample. I can attest to this since I have had a brief email exchange with him. He is the real deal and provides a role model for more people (especially women) to get passionate about maths. Villani has not put a lot of mathematics in the book but there is some and it is best to go with the flow. If a reader has had a brush with partial differential equations as a student they will get the drift of the difficulty and enormity of the task he and Mouhot tackled. I had a triple-take at references to a norm with seven indices! The more mathematically credentialed reader can delve further and have a go at getting their minds around some of the estimates that are being made but the book is not about understanding that sort of detail. Many students are put off early in their study of mathematics by proofs or explanations which pull rabbits out of hats. The student quite rightly wonders where on earth that came from. Well, it came usually as a result of going down several blind alleys (there may be the odd exception) but the essentially dishonest mathematical communicator makes it sound as though he or she immediately saw their way through the thickets using some artifice plucked from the cosmos. The beginner is immediately defeated before even starting. Villani shows that the real world is not like that and again this is an important revelation for those interested in mathematics. Such honesty is refreshing. More professional mathematicians should read this book and reflect on the process. US mathematician Peter Casazza’s chapter in the book “I Mathematician” lays bare how some professional mathematicians act towards their colleagues (and some of it is pretty unedifying) so little wonder the public has a pretty weird idea of what mathematicians do and how they do it. It is wonderful to have someone like Cedric Villani add a palate of exuberant colour to what many people probably perceive as a thoroughly colourless profession.

A true renaissance man, the guy is a boss!