
06168005
b
2016b.00013
Villani, C\'edric
The living theorem. (Th\'eor\`eme vivant.)
Paris: Bernard Grasset (ISBN 9782246798828/pbk). 282~p. (2012).
2012
Paris: Bernard Grasset
FR
A30
A80
Zbl 1239.82017
Zbl 1241.82072
This is an extraordinary book, incomparable to all you've ever read and will ever read in the future. It is the story of a theorem and its proof by Villani and Cl\'ement Mouhot, from their first discussion about it in spring 2008 until the autumn of 2010 when their result was accepted for publication in {\it Acta Mathematica} (see [{\it C. Mouhot} and {\it C. Villani}, ``On Landau damping", Acta Math. 207, No. 1, 29201 (2011; Zbl 1239.82017); correction ibid. 207, No. 2, 391 (2011; Zbl 1241.82072)]). And this is what the author says why he wrote this book: ``On me demande souvent \`a quoi ressemble la vie d'un chercheur, d'un math\'ematicien, de quoi est fait notre quotidien, comment s'\'ecrit notre {\oe}uvre. C'est \`a cette question que le pr\'esent ouvrage tente de r\'epondre." (p. 7) Indeed does the author not only describe his everyday life as a researching mathematician delineating how he develops his ideas and the way he discusses them with other mathematicians, but he also gives a very personal account of how he manages his family life and what kind of dreams and emotions he has outside mathematics. For example, he presents parts of fancy stories he invented for his children, gives reproductions of poems that are important to him and presents a 4pages list of his favourite music pieces, ranging from Bach's Brandenburg concertos to the chansons of Catherine Ribeiro. Clearly, Villani is by no means a typical researching mathematician. Even a noninitiated reader will frequently recognize this, e.g. when Villani mentions his dream of being awarded with the Fields Medal (which actually came true in 2010), when he talks about his halfyear research residence at the Princeton Institute for Advanced Study (IAS) in 2009 or his appointment as the director of the famous Institut Henri Poincar\'e at Paris. Nevertheless, much of his description of the way he works as a researcher may well be typical for the majority of modern researching mathematicians. E.g. he gives reproductions of many emails he exchanged with Mouhot on their ongoing joint research, peppered with technical terms and {\TeX} code of formulas. There are also reproductions of excerpts of his papers in order to display (I suppose) what formulafocused mathematical texts look like. Villani not even tries to explain the formulas or their {\TeX} code. Rather, this way he merely demonstrates how mathematics is expressed technically, and that you will not understand anything of that unless you learn this complicated ``foreign language" in detail. But, on the other hand, he does actually try to explain in more general terms at least the ideas behind the stuff he is dealing with. This is mainly done in some sort of ``asides" (each of them two to four pages long) interspersing the otherwise chronological narrative in the form of a diary. These asides are written in a way accessible to the general reader, always taking up a particular keyword or theme from the main text and giving an account of related mathematical problems and results as well as the mathematicians who contributed to their development. This way readers actually get some insight into the world of mathematics and not merely into the very personal thoughts and emotions of a particular mathematician. Examples of such asides range from the Boltzmann equation and the Landau damping via Donald Knuth and his development of {\TeX} and the machinesupported proof of the fourcolour theorem to Grigori Perelman and his work on the Ricci flow. So all in all the book delivers what was promised in the preface. It does this in a very original way by staying faithful to the subject it deals with, at the risk of leaving the reader more or less at a loss. Nevertheless, I think it was worth a try to write a book on mathematics and mathematicians in this way. Whether the author was actually successful with his attempt, every reader has to judge by her or himself. For mathematicians this is definitely an interesting or at least entertaining reading. As a kind of postscript that may shed some additional light on the style of the book, I would like to cite a statement Villani makes in connection with his encounter with John Nash at the IAS. First, he tells the sad story of this great mathematician and then writes: ``Maintenant, \`a 80 ans pass\'es, il est aussi normal que vous et moi." (p. 178)
Klaus D. Kiermeier (Berlin)