Birth of a Theorem: A Mathematical Adventure by Cédric Villani (PDF)

Description

In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There is no book like this. This is a memoir by the author dealing with one specific piece of work he did, but he depicts this in a broad context of collaboration and communication and both pertinent and broad history of related mathematics. It really is a wonderful and interesting book. Let me also add after getting the book and looking at it quickly at first I then went to youtube to see some of his TED lectures. They are exciting and instructive in themselves. When mathematics is done at his level, we are obviously talking about very gifted people and in this case how they interact with their peers to move the mathematics further along. It is not a question of just being bright; it really is people born with a gift and then how they utilize it. No one here is lazy! How do they assume that enough progress has been made in a field to attack a key problem? He cites Andrew Wiles in the book, but in that recent famous case Wiles worked by himself for seven years in his attic office only showing one other person his work. It was not collaboration – just the opposite of what we see here. Of course Wiles ended up proving theorems in which Fermat’s Last Theorem was a corollary, but like here he had to guess that he was ready to take that step.To me the book is dynamic with energy, and it is a friendly book. He intersperses biographies, history, relationships, and seems to always develop a context. What always comes through to me is his strong collaboration with his young colleague Clement Mohout who is a gifted mathematician himself. They are not afraid of each other nor do they envy each other. It is like a father wanting to see his son do well, and it buoys up the both of them. Villani comes through in this book with so much character and class! He is forever talking to other people, visiting different places for seminars or conferences, and so inquisitive as to what others are doing.Look at Chapter 29 where he talks about John Nash, one of his mathematical heroes This is such a well known and poignant story. Villani tracks back Nash’s work which laid the foundation for some work that he did, and tells more of the Nash story which I also remember very well. He interleaves tales like this throughout the book always emphasizing relationships, symmetries, history, and context. He lays this out as important to his memoir and as a gift to us, the readers. Parenthetically, on Chapter 29 Sylvia Nasar, when she was still at the NY Times, wrote a long article, “The lost years of a Nobel laureate,” which dealt with John Nash, who had just received the Nobel Prize in Economics, and his illness and long years ill in Princeton. It was so well received that she wrote her book. Here Villani is paying additional tribute to Nash.If Richard Rogers had written a memoir with collaboration details of his work with Roger Hammerstein on South Pacific, and put in all the sweat and tears, then we would get some weak approximation to what this book is about.I am so far out of it with respect to modern mathematics, I do not dare to suggest who the book would appeal to.

⭐This book takes us through the formulation of the theorems in “On Landau damping” by Clément Mouhot and Cédric Villani. Villani is playful in real life, his research is playful, and the book is playful.This is a gem for a singular reason. One sees exactly how Villani (or a pure mathematician) goes from abstract to abstract without ever exiting the world of pure and symbolic mathematics, even though the subject concerns a very concrete real-world topic. I kept waiting for him to use simulations or even plots to see how the equations worked. But he did not … he and Mouhot had recourse to outside help (a student or an assistant) for the graphs and he camly noted that they “looked” great. Later in the book he relied on others to do the numerical work… as an afterthought. Most physicists, quants, and applied mathematicians would have played with a computer to get the intuition; Villani just worked with mathematical objects, abstract mathematical objects, and very abstract at that. And this is a big deal for the subject because it belongs to a certain class of problems that do not have analytic solutions, usually requiring numerical approaches.Landau damping is about something many people are indirectly familiar with. Some history: Fokker–Planck equation, itself the Kolmogorov forward equation, is used commonly as the law of motion of particles (hence diffusions in finance). We quants use it in the main partial stochastic differential equation. In plasma physics it is related to the Boltzman equation, which, by using mean-interraction in place of every interration (mean-field), leads to the Vlasov equation. Landau damping is (sort of) about how things don’t blow up because of some exponential decay. Proving it outside the linear version remained elusive. Villani and Mouhot set to prove it. They eventually do.One note. I read it in the English translation (because I was in a hurry to get the book), but noticed an oddity that may confuse the reader. “Calcul” in French does not mean “calculation” (in the sense of numerical calculation) but “derivation”, so the reader might be confused about calculations thinking they were numerical when Villani stayed at the abstract/symbolic level.I would have read the book in one sitting. It grips you like a detective novel.PS- Some UK BS operator, the type of journalist with an attempt at some PhD in something related to physics who thinks he knows it all and is the representative of the general public trashed the book in the Spectator. Ignore him: the fellow is clueless. Look at reviews by PRACTICING quants and mathematicians. I do not think there is another book like this one.

⭐It is apparent that Cedric is one of the most brilliant men alive. His explanation of solving difficult problems is wonderful to read and for this, I recommend the book to eager students. However, he treats the reader like an elite mathematics colleague, going off into highly rigorous proofs that don’t flow well with the rest of the book. If you can handle that, then you’ll love the book. If you can’t, well, the book will be a bit weird.

⭐In spite of the many formulas and inequalities, there was an adventure from the mind of two mathematicians ( Cedric and Clement) whom tells us how they passionately suffered in the demonstration of a theorem about damped oscillations for Boltzmann and Landau equations.

⭐I am not a Math Lover But I read this book after I saw review comments from Taleb one my favourite authors. I am happy to have taken the time and patience to complete it. Minus the various formulas and Math notations used by Cedric, it was a great experience to get into the mind and heart of a renowned Mathematician and understand how they go from the unknown to the known and derive axioms and theorems to make the world more meaning full to us. The conversational style and the honest sharing of the author’s thoughts and feelings in achieving one milestones after another was highly motivating. Moving from abstract to the concrete is a difficult art and Cedric does it in great style. I will be a better thinker thanks to the learning from this book.Recommended reading for anyone who carries a thought ” How do I understand this enigma and move to finding a solution?”.

⭐I first saw this in a bookshop in Princeton (where the author did much of the work described here) and bought it for my mathematician son-in-law. He enjoyed reading it, and so have I. Villani tries to give the reader some sense of what it’s like to be on a journey in the world of pure thought, searching for a way to prove something about a fundamental theory in physics: an equation which describes how heat flows in a fluid. Clearly, this work is abstruse in the extreme (he won a Fields Medal – viewed as the highest honour a mathematician can receive – for it), and almost impossible to describe in a way that a non-technical audience can understand; reading a book like this, I’m always reminded of Richard Feynman’s response when he was being asked too many questions by reporters after winning the Nobel Prize (“Listen, buddy, if I could tell you in a minute what I did, it wouldn’t be worth the Nobel Prize.”).However, it makes for a good story. One reason for this is that this work was done as a collaboration (unlike, for example, the famous proof of Fermat’s Last Theorem, popularized in

⭐Simon Singh’s book

⭐, which Andrew Wiles accomplished almost completely on his own), and contains a selection of their emailed correspondence so the reader can peep over their shoulders as they grapple with the proof. Once again however, this doesn’t reveal very much, partly since the maths in the emails is written using TeX, a typesetting system for mathematics, and contains sentences like [p81]”If int_0^t a(s,t) ds=O(1), everything’s fine.”which looks like gobbledygook to the uninitiated. But the book also contains interesting portraits of his colleagues and predecessors, and there’s enough about the emotions of the quest to keep the reader interested, even if it’s not clear what’s going on (I have some experience with statistical physics, but didn’t understand the relationship between his work on the Boltzmann equation and Landau damping, for example), and everyone can appreciate the joy he experiences when the work is complete and he’s rewarded for his efforts.

⭐I did not expect to understand the maths here and I did not; but the story was fun….Moments of revelation are an experience we all share.The story was like an arrow throwing dust into its passage. A 150 page proof is beyond my understanding but I am very impressed by the concept.Do read it – obsession is always interesting.

⭐I was familiar with Cedric Villani from his appearances on Numberphile. I find him to be a very interesting character and mathematician which is why I bought this book.I did struggle with the actual mathematics in the book which I could not begin to grasp (which there was a lot). However, overlooking this, I found the journey interesting enough to continue reading.A story of obsession and fascination. An insight into the life of a true mathematician.

⭐This is a tough read, even for mathematicians. Yet it is a gem. There is only one way to approach this book. Just read it, word by word, from cover to cover. Let its thoughts wash over you, and don’t worry if you understand them or not. The inside story of one of the world’s finest mathematicians is a treasure. Very few of us will get all of it, but there is plenty of joy in the parts you understand.

⭐Fascinating book, especially for an ex-mathematician, but I think this will be a good read for anyone. I’m not sure how he found time to write it but I’m very glad he did. It gives an insight into a world of creative people that most people won’t even realise exists.

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