Book Review: Birth of a Theorem by Cédric Villani

Have you ever thought about your ideal guest list for the best dinner party imaginable? One with never-ending conversation on a range of topics? Mine would include several favorite authors and artists. However, no truly amazing dinner party would be complete without a cohort of mathematicians (and a few physicists, but I'll leave my love of physicists for future articles). Some may think I'm joking, but those of you who have spent hours in dark corners of bars in the presence of this noble, calculating breed know why: these super-human creatures turn set theory and topology into intellectual delights for those of us who were lucky to even pass calculus. For those poor souls who have not had yet the pleasure of spontaneous, beer-infused mathematics lectures, I offer you this close analog: enjoying Birth of a Theorem: A Mathematical Adventure by Cédric Villani (translated into English from French by Malcolm DeBevoise) with a glass of wine at your side and, if you so choose, in the dark bar of your choice.

If you have ever wondered what makes a prestigious mathematician tick, this book is for you. Cédric Villani, a French mathematician turned politician, won the 2010 Fields Medal for his work on Landau damping and the Boltzmann equation. Although he received several other awards prior to this, including the Jacques Herbrand Prize, the Prize of the European Mathematical Society, the Fermat Prize, and the Henri Poincaré Prize, the Fields Medal is the mathematician's "Nobel Prize," the highest honor one can earn. The catch? It is awarded once every four years and only to mathematicians under age 40. The pressure to find a research problem and make a breakthrough at a fairly early age, therefore, is incredibly high on these young minds.

Birth of a Theorem documents Villani's struggle from promising young researcher to Fields Medal recipient, and all of the twists and turns and internal battles winning this highly coveted award takes. The story tracks his day-to-day life while developing solutions to extremely complex partial differential equations related to theoretical physics problems. No math knowledge is required, however, for Villani to transport the reader to his office, where he struggles to uncover the secrets behind these illusive problems.

Ah, the Boltzmann! The most beautiful equation in the world, as I once described it to a journalist. I fell under its spell when I was young-when I was writing my doctoral thesis. Since then I've studied every aspect of it. It's all there in Boltzmann's equation: statistical physics, time's arrow, fluid mechanics, probability theory, information theory, Fourier analysis, and more. Some people say that I understand the mathematical world of this equation better than anyone alive. -Cédric Villani, Birth of a Theorem

His prodigious writing style accompanied by diary entries, email exchanges with collaborators, and photos create an engrossing and almost literary experience. Akin to an artist's memoir, you will forget all about the problem he is trying to solve (which is only skirted around anyway) and find yourself fascinated by his process and the inner workings of his mind.

Critics have lambasted him for writing a memoir ostensibly for other mathematicians. After all, there are equations in the book! From a structural perspective, ironically, his book shares traits typifying memoirs popular with critics these days, including the deliberate interweaving of primary sources with first-person accounts of events in a time-linear fashion. His rebuke of the cheese situation in New Jersey (it's horrible, in his very French opinion), his delight in reading manga, and an entire page dedicated to his favorite songs separated by commas coupled with his fluid writing style add creative and biographical depth to what might otherwise simply be a diary of an eccentric specialist.

Since winning the Fields Medal at the end of the book, Villani has since obtained several notable professorships and research posts. In 2011 and 2013, respectively, he became a Knight of the Legion of Honor and member of the French Academy of Sciences. He has authored or co-authored 92 journal articles and scholarly publications as of this writing. In 2017, he was elected to the French legislature and reportedly has French President Emmanuel Macron's ear. Between his more recent optimal transport research and his latest 150-page report outlining France's AI strategy, both Villani's scholarly pursuits and unique methods are increasingly relevant.

Unfortunately for Villani, books filled with equations do not always go over well with literary critics and Goodreads reviewers. Do not let the opinions of English majors and recovering journalists dissuade you! Although you may not walk away from this book with any deeper understanding of statistical mechanics, you will gain deeper insight into the mind of a particular breed of human, the mathematician, and an exceptional one, at that. Villani would easily make my dinner party invite list and, hopefully, he would bring his favorite French cheeses.


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