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Birth of a Theorem: A Mathematical Adventure
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.
273 pages, Kindle Edition
First published August 1, 2012
185 people are currently reading
3412 people want to read
About the author
Cédric Villani
58 books105 followersCédric Villani is a French mathematician who has received many international awards for his work including the Jacques Herbrand Prize, the Prize of the European Mathematical Society, the Fermat Prize and the Henri Poincaré Prize.
In 2010 he was awarded the Fields Medal, the International Medal for Outstanding Discoveries in Mathematics, for his work on Landau damping and the Boltzmann equation. Often called ‘the mathematicians’ Nobel Prize’, it is awarded every four years and is viewed by some as the highest honour a mathematician can achieve.
He is a professor at Lyon University and Director of the Institut Henri Poincaré in Paris, working primarily on partial differential equations and mathematical physics.
In 2010 he was awarded the Fields Medal, the International Medal for Outstanding Discoveries in Mathematics, for his work on Landau damping and the Boltzmann equation. Often called ‘the mathematicians’ Nobel Prize’, it is awarded every four years and is viewed by some as the highest honour a mathematician can achieve.
He is a professor at Lyon University and Director of the Institut Henri Poincaré in Paris, working primarily on partial differential equations and mathematical physics.
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Displaying 1 - 30 of 211 reviews
October 27, 2018
This book contains memoirs of a mathematician, Cedric Villani, a recipient of the Fields medal. Originally written in French, I read a version that has been translated into English. The translation seems to be excellent. VIllani collaborated with Clement Mouhot, to derive and prove a theorem related to Landau damping. This is not a pure-mathematics theorem. It is based on a real physical phenomenon that occurs in plasmas. So, it is of great interest to physicists, as well to mathematicians.
The main problem with this book, is that the author does not know who its reader should be. Should the reader be a professional mathematician? Perhaps, but then why would half of the book be devoted to an exploration of how a mathematician works day-to-day? Mathematicians already know that.
Should the reader be an informed layman, with some interest in mathematics? In that case, why are there so many pages scattered throughout the book, filled with very esoteric formulas that only a true expert will understand. Many full pages in the book are filled with equations like this:
The words that accompany these pages are not of any help in understanding the equations.
The book also contains many pages of e-mail correspondence, mostly between Villani and Mouhot. This correspondence sheds a little bit of light on how a mathematician might operate during a collaboration. But again, unless you are a professional mathematician, you don't stand a chance in understanding most of the correspondence.
And besides all this, the author makes no effort at all to explain Landau damping, let alone its relationship to his theorem. Landau damping is a real physical phenomenon, with applications in several areas of physics. But having read the book, I still have no idea what it is all about. A quick glance at Wikipedia helps to understand it. But, the book does not even devote a single paragraph to explain what it is about.
The main problem with this book, is that the author does not know who its reader should be. Should the reader be a professional mathematician? Perhaps, but then why would half of the book be devoted to an exploration of how a mathematician works day-to-day? Mathematicians already know that.
Should the reader be an informed layman, with some interest in mathematics? In that case, why are there so many pages scattered throughout the book, filled with very esoteric formulas that only a true expert will understand. Many full pages in the book are filled with equations like this:
The words that accompany these pages are not of any help in understanding the equations.The book also contains many pages of e-mail correspondence, mostly between Villani and Mouhot. This correspondence sheds a little bit of light on how a mathematician might operate during a collaboration. But again, unless you are a professional mathematician, you don't stand a chance in understanding most of the correspondence.
And besides all this, the author makes no effort at all to explain Landau damping, let alone its relationship to his theorem. Landau damping is a real physical phenomenon, with applications in several areas of physics. But having read the book, I still have no idea what it is all about. A quick glance at Wikipedia helps to understand it. But, the book does not even devote a single paragraph to explain what it is about.
March 18, 2015
This entire review has been hidden because of spoilers.
December 19, 2013
If I tell that the subject of the book is 'the daily life of a mathematician during the conception of a theorem'. Everybody would agree that it sounds intimidating, but it is not. Villani is not only a top-class mathematician, but a nice writer and an 'agreable' author. The book is a nice read, and the inclusion of letters, photos and other notes make of it a really pleasant experience.
The only lacking part of the book is in the explanations about the math of his own work, I know the theorem he conceives during the story is almost half the size of the book (and that assuming mathematical notation means it's longer than the book), but he could have presented it more clearly, and even include an extra appendix for advanced readers.
The only lacking part of the book is in the explanations about the math of his own work, I know the theorem he conceives during the story is almost half the size of the book (and that assuming mathematical notation means it's longer than the book), but he could have presented it more clearly, and even include an extra appendix for advanced readers.
September 7, 2017
Cédric Villani is a flamboyant character. If you happen to catch any talk by him on the internet, you'd always find him in a three-piece suit with a scarf and a spider brooch taking in a raspy French accent. Talking of mathematical genealogy, he is a direct descendant of such greats as Jacob, Euler, Bernoulli, Lagrange, Laplace, and Poisson. Big names.
Wouldn't it be interesting to open the mind of such a person and peer into it as he went about his day ?
This book gives you the closest possible approximation to such an experience.
The book is divided into chapters corresponding to various dates during a two year period, which ends with (surprise!) him winning the coveted Fields Medal. There is not much else in terms of structure to it.
The text, written in first person, keeps going astray. One moment, he'll be telling you about an important unsolved problem in mathematics and the next he may have moved on to complaining about the lack of good cheese in New Jersey. There's an entire page containing just a comma separated list of his favourite songs. While such indiscipline may seem unpardonable for most authors, Monsieur Villani has the effect of keeping one utterly engaged. Some of the most illuminating thoughts can be found in the transcripts of the author's correspondences with his research partner.
It is fascinating to see how perspiration, perseverance and inspiration combine and feed off each other, seemingly at random to give something really beautiful. And all this in an otherwise normal human being with hobbies and worries similar to everyone else.
The book also contains interesting portraits of mathematicians and mathematical problems, giving context to the world in which the author lives and works.
I would recommend the book to anyone working in a quantitative or creative field or anyone who appreciates the labour of love.
PS - Some of the sections in the book contain really heavy mathematics, which was beyond me and as I read later, most professional mathematicians. Don't let it dissuade you from going through the rest of book. I'd say it serves to highlight the abstractness of the author's work.
Wouldn't it be interesting to open the mind of such a person and peer into it as he went about his day ?
This book gives you the closest possible approximation to such an experience.
The book is divided into chapters corresponding to various dates during a two year period, which ends with (surprise!) him winning the coveted Fields Medal. There is not much else in terms of structure to it.
The text, written in first person, keeps going astray. One moment, he'll be telling you about an important unsolved problem in mathematics and the next he may have moved on to complaining about the lack of good cheese in New Jersey. There's an entire page containing just a comma separated list of his favourite songs. While such indiscipline may seem unpardonable for most authors, Monsieur Villani has the effect of keeping one utterly engaged. Some of the most illuminating thoughts can be found in the transcripts of the author's correspondences with his research partner.
It is fascinating to see how perspiration, perseverance and inspiration combine and feed off each other, seemingly at random to give something really beautiful. And all this in an otherwise normal human being with hobbies and worries similar to everyone else.
The book also contains interesting portraits of mathematicians and mathematical problems, giving context to the world in which the author lives and works.
I would recommend the book to anyone working in a quantitative or creative field or anyone who appreciates the labour of love.
PS - Some of the sections in the book contain really heavy mathematics, which was beyond me and as I read later, most professional mathematicians. Don't let it dissuade you from going through the rest of book. I'd say it serves to highlight the abstractness of the author's work.
August 28, 2021
Someday in our university I saw a proclamation about a Math Seminar, the subject was very tempting "The Planet,Stars And Eternity" By Cedrik Villani, fields Medalist. And I went to that seminar, He was one the most inspiring mathematicians I've ever seen, He spoke about Universe, What we know about it, Newton ideas about the world, How Poincare was thinking about universe, What Equations (like boltzmann equation) tell us about our world and even, what really Math is about !
After his fantastic speech I bought his book and it took me a week to read it carefully. It was not just inspiring and enlightening about Math and science but also it was very artistic and beautiful.
After his fantastic speech I bought his book and it took me a week to read it carefully. It was not just inspiring and enlightening about Math and science but also it was very artistic and beautiful.
February 8, 2017
It's not entirely clear what the theorem is that the title refers to. And that's the biggest problem with the book: there's just too much left unexplained.
In 2010 Villani won a prestigious Fields Medal for the work covered in his book. He had enough self-confidence to make that award consciously his goal. The citation for his award reads that it is "for his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation". Unfortunately, if you want even a layperson's account of either of these topics, let alone a more detailed technical account, you'll need to search the Web. It's not in Villani's book.
A brief but helpful overview is in the award citation itself:
There's a lot of detail in the book on the day-to-day struggles of Villani and his collaborators to deal with these problems, but there's no simple statement, like the preceding, what it's all about. It's not even made clear that one of the theorems proved is about an equation known as the "Boltzmann equation" (after Ludwig Boltzman who discovered it in 1872), while a different theorem was about "Landau damping" (after Lev Landau who made the conjecture in 1946). These two problems in thoretical physics have a lot in common, since both deal with the behavior of nonsolid bulk matter (gases and plasmas). And their mathematical treatment involves complicated partial differential equations, of which Villani is a master. However, despite the similarities, the subject matter here is not just one single theorem. That's OK, but it's probably going leave readers a bit confused.
Partial differential equations (PDE) are ubiqitous in theoretical physics, and their study is an entire distinct and active field in mathematics. Any PDE describes how several related physical quantities change due to changes in several independent variables. A solution of a PDE isn't a single number, but rather a function whose value depends on the independent variables. One of those independent variables is usually time ("t"), and the functions also depend on the specific values of independent variables at a particular "initial" time t=0.
There are several especially important questions about a function that's a solution of a PDE – about the long term behavior of the function. Since the function represents a physical quantity, it cannot, in a finite time, increase in value without limit. (If it did, there would be something wrong with the equation of which it is a solution.) But in applications it's important to know how slowly or how rapidly the function changes over time. Another question is whether or not the function's values eventually settle down to a relatively stable value.
Mathematicians address these issues by trying to discover specific limits that the values of a function should not exceed. The approach is to use measures on a function, called "norms", that quantify the limits. There are many different norms that can be used, and the choice of a norm has to be based on how easy it is to use known techniques to estimate the value of the norm. Knowing how to do this effectively is the bread and butter of mathematicians who specialize in PDE, and Villani is certainly one of them. He is clearly a master at this kind of work.
But even for mathematicians who aren't PDE specialists, let alone for general readers, it's hardly possible to understand the intricacies that are involved. The book is packed full of equations. This is ordinarily considered a huge impediment to book sales, for good reasons. In the present case, most readers may overlook the bewildering profusion of formulas in the hope of understanding better what it is that mathematicians actually do. And indeed, the book is usefully read if the equations and formulas are largely ignored. Mathematicians who aren't PDE specialists will be able to understand the symbols and general form of the equations, even if they have no clue about how to analyze them. But most readers will quickly give up on trying to follow the details as being (literally) "Greek to them".
The problem here is that the book purports to help understand not just the quotidian work of mathematicians. It does that to some extent. But it sheds very little light on the creative aspect of mathematical work. Yes, Villani and his collaborators had to struggle for months with their equations to achieve significant results. But the reader is left wondering what kind of a struggle it was. Did it involve only the masterful and dogged deployment ("like a bull at a gate") of existing specialist techniques that are known to the most highly skilled in the craft? Or did it involve breakthrough creative conceptual leaps that opened up really novel perspectives on the subject matter? Was the mountain climbed through sheer strength and stamina? Or did it require the invention of entirely new methods? (And if so, how?) Most importantly, were useful techniques invented that would allow others to solve similar but different problems?
There just doesn't seem to be enough information in the book to answer these questions.
In 2010 Villani won a prestigious Fields Medal for the work covered in his book. He had enough self-confidence to make that award consciously his goal. The citation for his award reads that it is "for his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation". Unfortunately, if you want even a layperson's account of either of these topics, let alone a more detailed technical account, you'll need to search the Web. It's not in Villani's book.
A brief but helpful overview is in the award citation itself:
One of the fundamental and initially very controversial theories of classical physics is Boltzmann’s kinetic theory of gases. Instead of tracking the individual motion of billions of individual atoms it studies the evolution of the probability that a particle occupies a certain position and has a certain velocity. The equilibrium probability distributions are well known for more than a hundred years, but to understand whether and how fast convergence to equilibrium occurs has been very difficult. Villani (in collaboration with Desvillettes) obtained the first result on the convergence rate for initial data not close to equilibrium. Later in joint work with his collaborator Mouhot he rigorously established the so-called non-linear Landau damping for the kinetic equations of plasma physics, settling a long-standing debate.
There's a lot of detail in the book on the day-to-day struggles of Villani and his collaborators to deal with these problems, but there's no simple statement, like the preceding, what it's all about. It's not even made clear that one of the theorems proved is about an equation known as the "Boltzmann equation" (after Ludwig Boltzman who discovered it in 1872), while a different theorem was about "Landau damping" (after Lev Landau who made the conjecture in 1946). These two problems in thoretical physics have a lot in common, since both deal with the behavior of nonsolid bulk matter (gases and plasmas). And their mathematical treatment involves complicated partial differential equations, of which Villani is a master. However, despite the similarities, the subject matter here is not just one single theorem. That's OK, but it's probably going leave readers a bit confused.
Partial differential equations (PDE) are ubiqitous in theoretical physics, and their study is an entire distinct and active field in mathematics. Any PDE describes how several related physical quantities change due to changes in several independent variables. A solution of a PDE isn't a single number, but rather a function whose value depends on the independent variables. One of those independent variables is usually time ("t"), and the functions also depend on the specific values of independent variables at a particular "initial" time t=0.
There are several especially important questions about a function that's a solution of a PDE – about the long term behavior of the function. Since the function represents a physical quantity, it cannot, in a finite time, increase in value without limit. (If it did, there would be something wrong with the equation of which it is a solution.) But in applications it's important to know how slowly or how rapidly the function changes over time. Another question is whether or not the function's values eventually settle down to a relatively stable value.
Mathematicians address these issues by trying to discover specific limits that the values of a function should not exceed. The approach is to use measures on a function, called "norms", that quantify the limits. There are many different norms that can be used, and the choice of a norm has to be based on how easy it is to use known techniques to estimate the value of the norm. Knowing how to do this effectively is the bread and butter of mathematicians who specialize in PDE, and Villani is certainly one of them. He is clearly a master at this kind of work.
But even for mathematicians who aren't PDE specialists, let alone for general readers, it's hardly possible to understand the intricacies that are involved. The book is packed full of equations. This is ordinarily considered a huge impediment to book sales, for good reasons. In the present case, most readers may overlook the bewildering profusion of formulas in the hope of understanding better what it is that mathematicians actually do. And indeed, the book is usefully read if the equations and formulas are largely ignored. Mathematicians who aren't PDE specialists will be able to understand the symbols and general form of the equations, even if they have no clue about how to analyze them. But most readers will quickly give up on trying to follow the details as being (literally) "Greek to them".
The problem here is that the book purports to help understand not just the quotidian work of mathematicians. It does that to some extent. But it sheds very little light on the creative aspect of mathematical work. Yes, Villani and his collaborators had to struggle for months with their equations to achieve significant results. But the reader is left wondering what kind of a struggle it was. Did it involve only the masterful and dogged deployment ("like a bull at a gate") of existing specialist techniques that are known to the most highly skilled in the craft? Or did it involve breakthrough creative conceptual leaps that opened up really novel perspectives on the subject matter? Was the mountain climbed through sheer strength and stamina? Or did it require the invention of entirely new methods? (And if so, how?) Most importantly, were useful techniques invented that would allow others to solve similar but different problems?
There just doesn't seem to be enough information in the book to answer these questions.
August 19, 2015
A fun read, but utterly disjointed. Mathematical formulas stuffed in seem to only serve to make the work seem more like magic and less like work. The author or the translator seemingly cannot make up their mind on whether they want it to be a story of someone with a cool job or of the mysterious mathematical savant. I have the sneaking suspicion that you're not actually supposed to be able to read the LaTeX codes or know what an integral is when you read this book. Gotta keep up the mystery!
It's littered with translated lyrics from French songs, only tangentially related to the story. Two full pages are just a list of songs the author likes. Sure, music may be relevant to his process, but then explain! I'd rather hear what three songs really do to you, as a person, or as a mathematician, than what dozens of songs you like.
The story never really comes together, the author seems to be trying too hard to be interesting. Frankly, he almost certainly is - which is why the desperate attempt to come across as such in this book is such a waste.
It's littered with translated lyrics from French songs, only tangentially related to the story. Two full pages are just a list of songs the author likes. Sure, music may be relevant to his process, but then explain! I'd rather hear what three songs really do to you, as a person, or as a mathematician, than what dozens of songs you like.
The story never really comes together, the author seems to be trying too hard to be interesting. Frankly, he almost certainly is - which is why the desperate attempt to come across as such in this book is such a waste.
January 14, 2019
DNF. The book is too abstruse even for a math nerd like me.
January 20, 2016
From BBC Radio 4 - Book of the Week:
Rock-star mathematician Cédric Villani's magical mystery tour through the world of mathematics.
He describes the journey which sees him wrestling with and taming a new theorem that will win him the most coveted prize in his field.
Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, elation and despair.
His account unlocks what goes on inside the head of a mathematician and captures where inspiration comes from. Blending science with history, biography with myth, Villani conjures up a cast of mathematical greats including the omnipresent Einstein and Villani's personal hero, John Nash.
Read by Julian Rhind-Tutt
Translated by Malcolm DeBevoise
Abridged by Richard Hamilton
Produced by Gemma Jenkins
Rock-star mathematician Cédric Villani's magical mystery tour through the world of mathematics.
He describes the journey which sees him wrestling with and taming a new theorem that will win him the most coveted prize in his field.
Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, elation and despair.
His account unlocks what goes on inside the head of a mathematician and captures where inspiration comes from. Blending science with history, biography with myth, Villani conjures up a cast of mathematical greats including the omnipresent Einstein and Villani's personal hero, John Nash.
Read by Julian Rhind-Tutt
Translated by Malcolm DeBevoise
Abridged by Richard Hamilton
Produced by Gemma Jenkins
January 21, 2018
Every young mathematician should read Cedric Villani's mathematical adventure which led him to win many awards including the Fields Medal.
July 26, 2019
تکه هایی از متن:
همیشه به دنبال دستاورد های بزرگ مرحله افسردگی می آید و شخص کار خودش را پیش خودش کوچک میکند. خوب ببین ،کاری را که تو انجام دادی هر ابله دیگری هم میتوانست انجام دهد ، حالا برو در زندگی مسئله جدی تری پیدا بکن. چرخه تحقیقاتی ریاضی.....
این تونل تاریک کمی شبیه به مرحله کاملا تاریکی است که مشخصه ی ابتدای پروژه های تحقیقاتی در ریاضی است. یک ریاضی کار مثل کوری است که در اتاثی تاریک قرار دارد و به دنبال گربه ی سیتهی میگردد که شاید اصلا آنجا نباشد.....
اگر نپذیریم که خود را در موقعیتی آسیب پذیر قرار دهیم. پیشرفتی هم نخواهیم داشت.
همیشه به دنبال دستاورد های بزرگ مرحله افسردگی می آید و شخص کار خودش را پیش خودش کوچک میکند. خوب ببین ،کاری را که تو انجام دادی هر ابله دیگری هم میتوانست انجام دهد ، حالا برو در زندگی مسئله جدی تری پیدا بکن. چرخه تحقیقاتی ریاضی.....
این تونل تاریک کمی شبیه به مرحله کاملا تاریکی است که مشخصه ی ابتدای پروژه های تحقیقاتی در ریاضی است. یک ریاضی کار مثل کوری است که در اتاثی تاریک قرار دارد و به دنبال گربه ی سیتهی میگردد که شاید اصلا آنجا نباشد.....
اگر نپذیریم که خود را در موقعیتی آسیب پذیر قرار دهیم. پیشرفتی هم نخواهیم داشت.
March 14, 2024
A dive into Cédric Villani’s day to day experience as a world class mathematician. Includes lecture notes, theorems, interactions with other famous mathematicians, historical extracts, and his thought process (translated into english) as he proves a theorem with Clément Mouhot that wins him the Fields medal. Very entertaining, but I had to let the dense sections of mathematics wash over me to enjoy the ride.
February 7, 2017
بعد ازمدتها از یک کتاب واقعاً لذت بردم. چراکه دقیقا درک میکردم چه حس و حالی در حین پژوهش و یا زندگی دارد. و شاید قبطه میخوردم که در جغرافیای اشتباه به دنیا آمدم که گریز ناپذیر هم هست. معمولاً در نقد کتابها تمایل شخصی را کمتر وارد میکنم و بیشتر به کتاب به دید منتقد خنثی نگاه میکنم. این کتاب برای تمام کسانی که در رشته های مختلف بخصوص شخاه ریاضی-فیزیک در دانشگاه (مهندسی، فنی، علوم پایه) میخوانند توصیه میکنم. با سدریک ویلانی دراین کتاب مدتی لحظاتی از زندگی حرفه ای را تجربه میکنید، خسته میشوید، کنسرت میروید، مسافرت میروید، چرت میزنید و به بی خیالی میزنید و دوباره برمیگردید به موضوعی که رهایش کرده بودید.
شخصیت ویلانی جالب است. خشک و پشت میز نشین نیست. علائق مختلفی دارد و تک بُعدی نیست. متاسفانه دیدار شخصی با ایشان نداشتم ولی از کتابش لذت بردم و دنیای الکترونیک هم چندان انسانها از هم بی خبر نمیگذارد. موضوعی که ویلانی روی آن کار کرده، یکی از کلیدی ترین مسائل فیزیک نظری در حل معماهای متعدد انفجار بزرگ، مدل تورم و عدم تقارن ماده پاده ماده و هسته زایی در عالم اولیه هم هست. منتهی اصلا در این کتاب مجال این بحثها نیست. زندگی روزمره ی نه جندان خشک ولی فعال، یک ریاضیدان به نمایش گذاشته میشود. آنهم روزنوشتهای خود آن ریاضی دان!
سدریک ویلانی: ریاضیدان عنکبوتی
شخصیت ویلانی جالب است. خشک و پشت میز نشین نیست. علائق مختلفی دارد و تک بُعدی نیست. متاسفانه دیدار شخصی با ایشان نداشتم ولی از کتابش لذت بردم و دنیای الکترونیک هم چندان انسانها از هم بی خبر نمیگذارد. موضوعی که ویلانی روی آن کار کرده، یکی از کلیدی ترین مسائل فیزیک نظری در حل معماهای متعدد انفجار بزرگ، مدل تورم و عدم تقارن ماده پاده ماده و هسته زایی در عالم اولیه هم هست. منتهی اصلا در این کتاب مجال این بحثها نیست. زندگی روزمره ی نه جندان خشک ولی فعال، یک ریاضیدان به نمایش گذاشته میشود. آنهم روزنوشتهای خود آن ریاضی دان!
سدریک ویلانی: ریاضیدان عنکبوتی
February 15, 2020
Beautifully written, a story of mathematical adventure, a search for proof of a theorem. Cedric Villani aptly comments on a mathematician's quest as 'a search in a dark room for a black cat which in fact isn't even there', reading his story will make you believe it.
There are multiple sections in the book every now and then on famous mathematicians and their equally interesting stories & mathematical ideas. They are a treat for anyone who simply wants to admire sheer passion and imagination with which these priests of the most pristine branch of science work with.
One can safely ignore the equations and technical commentary which may seem daunting to any outsider or even to a professional mathematician outside of author's field of expertise. In spite of that, every bit of this story is enjoyable and inspirational.
There are multiple sections in the book every now and then on famous mathematicians and their equally interesting stories & mathematical ideas. They are a treat for anyone who simply wants to admire sheer passion and imagination with which these priests of the most pristine branch of science work with.
One can safely ignore the equations and technical commentary which may seem daunting to any outsider or even to a professional mathematician outside of author's field of expertise. In spite of that, every bit of this story is enjoyable and inspirational.
February 11, 2017
This is a truly beautiful book. I heard about it during a podcast and I bought it in pre-sale straight away. I am not familiar with mathematics at the level of the author, yet I was extremely curious about the creative process leading the "discovery" of a theorem. I can say the book do not disappoints. The author is extremely generous with his thoughts, ups, downs and even "off" time when working. From living in a secluded place, to manga, music or being a dad, every page its interesting and adds value to the whole.
For me, it was a great experience. I learn a lot and I really enjoyed entering the mind of a genius such as Cédric Villani.
For me, it was a great experience. I learn a lot and I really enjoyed entering the mind of a genius such as Cédric Villani.
July 14, 2019
Publicul ţintă al lui Villani nu sunt eu , absolvent de matematică, devenit corporatist şi care nu a mai lucrat cu transformata Fourier de 10 ani. Este publicul celor care fac cercetare in matematica, înţeleg formulele din limbajul Latex, un public foarte restrâns. Am citit cartea pe diagonală. Alternează reflecţii personale ale lui Villani, cu formule matematice pure, schimb de mailuri in engleză, limbaj Latex, e ceva eterogen şi cumva neglijent aşezat în aceasta carte. E felul in care Villani explică demersul lui in a deveni ceea ce e azi. De un lucru sunt sigură: Cedric Villani e un om remarcabil. Dar poate ca nu un foarte bun scriitor.
June 1, 2020
This book is about the Journal about work that Cedric Villani did on Landau Damping and Boltzmann Equation that led him to win Field's Medal which is considered the Noble prize in Mathematics.
Cedric takes you through his daily works and his flamboyant incidents are fun to read.
I had a opportunity to meet this man before I read this book, he is such a down to Earth Mathematicians whose interests ranges over a lot of things and so is this book.
If you are going to read this book, be aware about a lot of Mathematical symbols that you might not have seen or might have difficulty in comprehending!
Cedric takes you through his daily works and his flamboyant incidents are fun to read.
I had a opportunity to meet this man before I read this book, he is such a down to Earth Mathematicians whose interests ranges over a lot of things and so is this book.
If you are going to read this book, be aware about a lot of Mathematical symbols that you might not have seen or might have difficulty in comprehending!
April 16, 2015
Didn't want it to end.
December 30, 2017
CÉDRIC VILLANI est l'un de nos plus brillants mathématiciens, lauréat de l'équivalent du prix Nobel pour les mathématiques: la médaille Fields -- depuis il a un peu mal tourné puisqu'il est devenu député, mais ça c'est une autre histoire. Mais si c'est le gars qui a l'air bizarre avec les cheveux longs, un costume, une lavallière, une montre à gousset et, pour couronner le tout, il porte toujours une broche araignée. Il évoque d'ailleurs ce style atypique dans son livre, mais au risque de vous décevoir, il n'explique pas la signification de cette broche qui appartient à son domaine privé. Dans _Théorème vivant_ il raconte une partie de sa vie centrée sur la période ayant abouti à la consécration, l'obtention de la plus haute distinction dans le domaine des mathématiques.
C'est passionnant de suivre ce parcours, de vivre les hésitations, les doutes, les moments d'abattement et les illuminations. Au fil de ce travail, et notamment durant la période qu'il passe à l'_Institute for Advanced Study_ (IAS) à Princeton, il croise la route de nombreux mathématiciens, disparus ou bien vivants (l'IAS a accueilli avant lui quelques-uns des plus grands savants du siècle dernier, entre autres Albert Einstein, Kurt Gödel, Robert Oppenheimer, John von Neumann et John Nash.) Ce sera l'occasion pour lui de nous les présenter succinctement, mais toujours avec beaucoup d'admiration et de respect. Quant au sujet qu'il traite, avec son collègue Clément Mouhot, autour de l'équation de Boltzmann et de l'amortissement Landau, je dois bien avouer que je n'ai a peu près rien compris -- et je ne parle même pas des équations. Mais ce n'est pas grave, ce qui compte le plus est le cheminement, le travail. Et il en a fait du chemin puisqu'il est en plus devenu pendant cette période directeur du prestigieux Institut Henri-Poincaré. Son récit est très sobre, il semble transparent, honnête et Cédric Villani nous apparaît comme quelqu'un d'extrêmement sympathique et humain -- mais si en fait c'est un extraterrestre. On apprend qu'il est amateur de musique et de BD, si ce n'est pas un signe d'humanité.
Ce livre est très original dans sa forme -- ils n'avaient certainement jamais vu ça chez Grasset -- puisqu'il contient, en plus du récit, des échanges d'e-mails (contenant même du LaTeX), des équations et des mini biographies accompagnées de portraits au crayon -- je vous rassure c'est un dessinateur qui s'est chargé de cette dernière partout, il n'a pas tous les talents du monde, il faut pas pousser quand même. C'est en tout cas une très belle expérience de lecture et j'avoue même avoir été ému lorsqu'il raconte le passage où il apprend qu'il a été choisi pour recevoir la médaille. D'autres lectures à conseiller dans le même registre:
- Le dernier théorème de Fermat: Passionnante histoire de la résolution par Andrew Wiles de l'un des problèmes les plus connus -- en plus il est compréhensible par le commun des mortels.
- La conjecture des Poincaré: L'histoire de la résolution d'un des sept "problèmes du prix du millénaire" -- moins compréhensible.
- Feynman: La bio en BD d'un très grand physicien.
- Logicomix: La bio en BD du mathématicien Bertrand Russell
- La déesse des petites victoires: Un roman autour de Kurt Gödel qui se déroule à l'IAS.
- En cherchant Majorana: La trajectoire mystérieuse d'un génie.
http://aubonroman.com/2017/12/theorem...
C'est passionnant de suivre ce parcours, de vivre les hésitations, les doutes, les moments d'abattement et les illuminations. Au fil de ce travail, et notamment durant la période qu'il passe à l'_Institute for Advanced Study_ (IAS) à Princeton, il croise la route de nombreux mathématiciens, disparus ou bien vivants (l'IAS a accueilli avant lui quelques-uns des plus grands savants du siècle dernier, entre autres Albert Einstein, Kurt Gödel, Robert Oppenheimer, John von Neumann et John Nash.) Ce sera l'occasion pour lui de nous les présenter succinctement, mais toujours avec beaucoup d'admiration et de respect. Quant au sujet qu'il traite, avec son collègue Clément Mouhot, autour de l'équation de Boltzmann et de l'amortissement Landau, je dois bien avouer que je n'ai a peu près rien compris -- et je ne parle même pas des équations. Mais ce n'est pas grave, ce qui compte le plus est le cheminement, le travail. Et il en a fait du chemin puisqu'il est en plus devenu pendant cette période directeur du prestigieux Institut Henri-Poincaré. Son récit est très sobre, il semble transparent, honnête et Cédric Villani nous apparaît comme quelqu'un d'extrêmement sympathique et humain -- mais si en fait c'est un extraterrestre. On apprend qu'il est amateur de musique et de BD, si ce n'est pas un signe d'humanité.
Ce livre est très original dans sa forme -- ils n'avaient certainement jamais vu ça chez Grasset -- puisqu'il contient, en plus du récit, des échanges d'e-mails (contenant même du LaTeX), des équations et des mini biographies accompagnées de portraits au crayon -- je vous rassure c'est un dessinateur qui s'est chargé de cette dernière partout, il n'a pas tous les talents du monde, il faut pas pousser quand même. C'est en tout cas une très belle expérience de lecture et j'avoue même avoir été ému lorsqu'il raconte le passage où il apprend qu'il a été choisi pour recevoir la médaille. D'autres lectures à conseiller dans le même registre:
- Le dernier théorème de Fermat: Passionnante histoire de la résolution par Andrew Wiles de l'un des problèmes les plus connus -- en plus il est compréhensible par le commun des mortels.
- La conjecture des Poincaré: L'histoire de la résolution d'un des sept "problèmes du prix du millénaire" -- moins compréhensible.
- Feynman: La bio en BD d'un très grand physicien.
- Logicomix: La bio en BD du mathématicien Bertrand Russell
- La déesse des petites victoires: Un roman autour de Kurt Gödel qui se déroule à l'IAS.
- En cherchant Majorana: La trajectoire mystérieuse d'un génie.
http://aubonroman.com/2017/12/theorem...
September 16, 2023
Written in French by world famous mathematician, Cédric Villani, and translated to English with additional corrections and clarification, Birth of a Theorem: A Mathematical Adventure is a haphazard collection of thoughts about the author's mathematical journey to winning the Fields medal. This book was published a few years after the author received the Fields medal in 2010. The main issue with the book seems to be the intended audience. It tries to appeal to a wide range of people and seems to spectacularly miss almost everyone.
There are some nice illustrations of mathematicians and some passages in the book shed a light on the daily workings of an acclaimed mathematician. There are whole sections of email correspondences and mathematical theorems which are terse and pointless as far as the story telling goes. It doesn't feel like an enjoyable read.
There are some nice illustrations of mathematicians and some passages in the book shed a light on the daily workings of an acclaimed mathematician. There are whole sections of email correspondences and mathematical theorems which are terse and pointless as far as the story telling goes. It doesn't feel like an enjoyable read.
July 5, 2018
Da qualche parte ho letto che una regola aurea della divulgazione scientifica dice che a ogni formula il numero di lettori di un libro diminuisce di un terzo.
Se questa regola fosse vera questo libro, che contiene formule di matematica che fanno impallidire pure me, non avrebbe lettori.
In effetti, strictu senso, questo non è proprio un libro di divulgazione scientifica, Villani (medaglia Fields per la matematica) non ritiene di dover fare sforzi sovrumani per farvi capire qualcosa. Semplicemente racconta in presa diretta la genesi e la costruzione del teorema che gli hanno dato "gloria matematica". Libro più biografico che divulgativo, il cui tono assomiglia più a quello che si potrebbe tenere in una conversazione tra colleghi, che non sanno nulla delle vostre ricerche ma non si spaventano se parlate di integrali e norme in spazi di funzioni.
Di interessante, per certi versi, c'è proprio il coraggio di portare il lettore in una passeggiata per campi da loro poco frequentati e frequentabili. Come uno speleologo che non si senta in dovere di farvi un corso di geologia, ma semplicemente vi accompagna e lascia a voi di decidere cosa capite dello scenario inconsueto che vi si para di fronte.
Il divertente è scoprire che Villani si lascia accompagnare, nel suo viaggio matematico, da musica della più varia, da fumetti e fiabe, rari i libri. Che è un ragazzo e un uomo come tanti suoi coetanei francesi, che si culla su qualche luogo comune, che si autocompiace come tutti, che si lagna delle attese nella RER di Parigi, che, insomma, ha poco dell'immaginario del genio classico (che immaginiamo divida il suo tempo libro tra Bach e la rilettura dell'opera completa di Kant o Rousseau, al massimo, e che scorda ombrelli e chiavi di casa).
Il problema, però, è che se Villani ha molto coraggio nel suo rapporto con la matematica, né ha molto poco per quel che riguarda lui stesso. Dalla sua scrittura traspaiono bene alcune delle tipiche sofferenze di chi fa ricerca ma non traspare nulla dei suoi pensieri intimi, della sua vita privata, del suo passato. E' solo un uomo al lavoro, che parla del suo lavoro e del suo tempo libero con la profondità di un americano davanti al barbecue. Conversazione facilissima e scorrevolissima. Restarne segnati a fondo, però, è molto difficile. Se vuoi dare emozioni devi essere pronto a scoprire un pezzo di te. Anche se non ti va.
Se questa regola fosse vera questo libro, che contiene formule di matematica che fanno impallidire pure me, non avrebbe lettori.
In effetti, strictu senso, questo non è proprio un libro di divulgazione scientifica, Villani (medaglia Fields per la matematica) non ritiene di dover fare sforzi sovrumani per farvi capire qualcosa. Semplicemente racconta in presa diretta la genesi e la costruzione del teorema che gli hanno dato "gloria matematica". Libro più biografico che divulgativo, il cui tono assomiglia più a quello che si potrebbe tenere in una conversazione tra colleghi, che non sanno nulla delle vostre ricerche ma non si spaventano se parlate di integrali e norme in spazi di funzioni.
Di interessante, per certi versi, c'è proprio il coraggio di portare il lettore in una passeggiata per campi da loro poco frequentati e frequentabili. Come uno speleologo che non si senta in dovere di farvi un corso di geologia, ma semplicemente vi accompagna e lascia a voi di decidere cosa capite dello scenario inconsueto che vi si para di fronte.
Il divertente è scoprire che Villani si lascia accompagnare, nel suo viaggio matematico, da musica della più varia, da fumetti e fiabe, rari i libri. Che è un ragazzo e un uomo come tanti suoi coetanei francesi, che si culla su qualche luogo comune, che si autocompiace come tutti, che si lagna delle attese nella RER di Parigi, che, insomma, ha poco dell'immaginario del genio classico (che immaginiamo divida il suo tempo libro tra Bach e la rilettura dell'opera completa di Kant o Rousseau, al massimo, e che scorda ombrelli e chiavi di casa).
Il problema, però, è che se Villani ha molto coraggio nel suo rapporto con la matematica, né ha molto poco per quel che riguarda lui stesso. Dalla sua scrittura traspaiono bene alcune delle tipiche sofferenze di chi fa ricerca ma non traspare nulla dei suoi pensieri intimi, della sua vita privata, del suo passato. E' solo un uomo al lavoro, che parla del suo lavoro e del suo tempo libero con la profondità di un americano davanti al barbecue. Conversazione facilissima e scorrevolissima. Restarne segnati a fondo, però, è molto difficile. Se vuoi dare emozioni devi essere pronto a scoprire un pezzo di te. Anche se non ti va.
April 28, 2015
By chance, I heard Cedric Villani speak at Powells a couple of weeks ago, and it was a wonderful experience. This "rock star" mathematician is charismatic, charming, and eccentric as well as brilliant. His latest book, Birth of a Theorem, is about the journey he and his colleague take as they work to write the proof of their theorem which concerns something to do with plasmas called Landau damping. I understood nothing of the mathematics, but the talk Villani gave that enticed me was much more about the creative process, and this was the thrilling part of his story. Written in diary format, there are emails that document the frustratingly tedious and challenging mathematical exploration, and potted histories of relevant mathematicians along with delightful pencil sketches of the same. There are also musings on literature, art, and music about which Villani is an enthusiast. True, there are many italicized pages of impenetrable mathematical notations and explanations, but I simply skimmed right over them. Villani takes the reader into his own marvelous life as prize winning scholar, but he is always an appealingly normal person who misses French cheese when in Princeton, must get away to think for hours in a dark closet, and works with his papers spread all over the living room floor. Villani's book is a testament to collegiality, innovation, optimism, courage, self-awareness, and affection. Plus, he is one heck of a character. Just google the guy!
February 9, 2018
It's an absolute pleasure as Cedric Villani walks you through his mind, complete with his inner monologues as he encounters the many demons in his quest for mathematical glory. The book is written as a very personal account of a mathematician's life, in a sense that you see the passion for discovery and the disappointment at encountering failures from very close quarters. The emotion comes through in Villani's masterful writing, or at least the English translation does a good job in preserving the emotion from the original text. One amazing thing about the book is that it doesn't try to dumb things down for the casual reader at all. Every theorem, every complex idea and every academic exchange between Villani and his colleague Clement Mouhot is served to you in its pristine. At the very outset, it is made clear that the book is not a mathematical treatise.
The only negative about the book is that it may be too disorganized, and there are parts of a mathematician's life (or just anyone's life) that are not too engaging to read, so it does have dry patches. What else might irk you is that the actual "birth" of the theorem is rather unceremoniously presented, and hurried through. But I guess that's the best he could do, speaking to a largely illiterate audience. As far as the objective of the book is concerned, if it was to make the general reader appreciate the path to mathematical discovery, it does a splendid job.
The only negative about the book is that it may be too disorganized, and there are parts of a mathematician's life (or just anyone's life) that are not too engaging to read, so it does have dry patches. What else might irk you is that the actual "birth" of the theorem is rather unceremoniously presented, and hurried through. But I guess that's the best he could do, speaking to a largely illiterate audience. As far as the objective of the book is concerned, if it was to make the general reader appreciate the path to mathematical discovery, it does a splendid job.
March 23, 2017
This is a meta-book, I shall say, because it puts together different styles and pieces of information that wobble around the figure of the author, as well as its main interest in life, and what got him the Fields Medal*, Boltzmann’s Equation.
The idea behind the book is to show what happened inside Villani’s head while he was actually developing his theorem, in order to give an insight into the thought processes and style of a great mathematician. In this attempt, we are thrown into a multi-dimensional world full of different experiences, from reading manga, to listening to some particular kind of music, from childcare to administration of high-level institutes. I am going to say that sometimes this book is plainly describable as an ordered mess, but a great mess. On one page you are shown a very important theorem, and on the next one you are discussing about why L, M and N are great characters for a manga.
One of the perks of the book is the fact that ...
(continues here davidhooksite.wordpress.com/2017/03/1...)
The idea behind the book is to show what happened inside Villani’s head while he was actually developing his theorem, in order to give an insight into the thought processes and style of a great mathematician. In this attempt, we are thrown into a multi-dimensional world full of different experiences, from reading manga, to listening to some particular kind of music, from childcare to administration of high-level institutes. I am going to say that sometimes this book is plainly describable as an ordered mess, but a great mess. On one page you are shown a very important theorem, and on the next one you are discussing about why L, M and N are great characters for a manga.
One of the perks of the book is the fact that ...
(continues here davidhooksite.wordpress.com/2017/03/1...)
April 27, 2025
2025 - third re-read
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Read while on vacation. The beach, warm sun, endless careening of the unpredictable waves - the backdrop! This book is the cherry on top.
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More books like this need to written. This book is unique, it is neither a pop math nor a research monograph but a journal entry from one of the top minds of mathematics writing about the events surrounding his proof ( with his student ) of “landau damping” and subsequent events leading to his fields medal win. Here one can witness what it means to be a lifelong student of mathematics. The book is playful and contains a window into other artful side of his including playing/listening to music, food (bread, cheese), nod to books he read and liked, importance of chance, coincidences and serendipity in proving a theorem, his homage to mathematicians that inspired him etc. There were heavy doses of mathematics in the book (Norm, functional analysis, intersection of analysis and geometry and physics, Boltzmann equation) which are really not needed to be understood to appreciate the book.
-------------
Read while on vacation. The beach, warm sun, endless careening of the unpredictable waves - the backdrop! This book is the cherry on top.
================
More books like this need to written. This book is unique, it is neither a pop math nor a research monograph but a journal entry from one of the top minds of mathematics writing about the events surrounding his proof ( with his student ) of “landau damping” and subsequent events leading to his fields medal win. Here one can witness what it means to be a lifelong student of mathematics. The book is playful and contains a window into other artful side of his including playing/listening to music, food (bread, cheese), nod to books he read and liked, importance of chance, coincidences and serendipity in proving a theorem, his homage to mathematicians that inspired him etc. There were heavy doses of mathematics in the book (Norm, functional analysis, intersection of analysis and geometry and physics, Boltzmann equation) which are really not needed to be understood to appreciate the book.
January 20, 2017
This guy sounds like he loves the smell of his own farts.
August 28, 2021
This book demystifies the life of a mathematician. It is like a diary of Cédric Villani, and book even includes his raw emails with collaborators. Very close texture of how his math life and everyday thoughts are like which gradually lead to the "birth" of his theorems.
Example excerpt to get a taste of this book: "I read the message that had just appeared on my computer screen, and then read it again. Couldn’t believe my eyes.
Clément’s come up with a new plan? He wants to give up on regularization? Wants to forget about making up for the loss of regularity encoded in the time interval?
Where did all this come from? For several months now we’ve been trying to make a Newton scheme work with regularization, as in Nash–Moser—and now Clément is telling me that we need to do a Newton scheme without regularization? And that we’ve got to estimate along the trajectories, while
preserving the initial time and the final time, with two different times??
Well, maybe he’s right, who knows? Cédric, you’ve got to start paying attention, the young guys are brilliant. If you don’t watch out, they’re going to leave you in the dust!
Okay, there’s nothing you can do about it, the next generation always ends up winning … but … already?
Save the sniveling for later. First thing, you’ve got to try to understand what he’s getting at. What does this whole business of estimating really amount to, when you get right down to it? Why should it be necessary to preserve the memory of the initial time?"
Takeaway 1) So many theorems are born by mathematics/scientists/innovators thinking of it days and night, and when they were relaxing one day, the crazy idea suddenly comes up. It can also be that we work late until night, keep thinking and thinking, and suddenly, next morning when we wake up, oh we see the connection! It is a pure battle between the mathematician and the theorem.
Takeaway 2) A good university is not to teach students well, but to kindle their ability to challenge established theories, and propose new theories.
Takeaway 3) Summary of the beauty of mathematics (from Villani's point of view; I think there are also happiness from the application side): Think of the experiments that can show the Bell Curve (i.e., the law of errors), then we ask the question "why it could not be any other curves?". What math is doing here is to "replace the beautiful coincidence with a beautiful explanation." The byproduct is (a) pleasure of the mathematicians, and (b) change of the view when looking at the world.
Nice analogy to use: This book is like introducing a child observing their mathematician parent working. The child pays attention to the ups and downs of emotions, the actions, the flow of progress, etc.
---
More resources:
- Birth of a Theorem - with Cédric Villani at the Royal Institution: https://www.youtube.com/watch?v=yYwyd...
Example excerpt to get a taste of this book: "I read the message that had just appeared on my computer screen, and then read it again. Couldn’t believe my eyes.
Clément’s come up with a new plan? He wants to give up on regularization? Wants to forget about making up for the loss of regularity encoded in the time interval?
Where did all this come from? For several months now we’ve been trying to make a Newton scheme work with regularization, as in Nash–Moser—and now Clément is telling me that we need to do a Newton scheme without regularization? And that we’ve got to estimate along the trajectories, while
preserving the initial time and the final time, with two different times??
Well, maybe he’s right, who knows? Cédric, you’ve got to start paying attention, the young guys are brilliant. If you don’t watch out, they’re going to leave you in the dust!
Okay, there’s nothing you can do about it, the next generation always ends up winning … but … already?
Save the sniveling for later. First thing, you’ve got to try to understand what he’s getting at. What does this whole business of estimating really amount to, when you get right down to it? Why should it be necessary to preserve the memory of the initial time?"
Takeaway 1) So many theorems are born by mathematics/scientists/innovators thinking of it days and night, and when they were relaxing one day, the crazy idea suddenly comes up. It can also be that we work late until night, keep thinking and thinking, and suddenly, next morning when we wake up, oh we see the connection! It is a pure battle between the mathematician and the theorem.
Takeaway 2) A good university is not to teach students well, but to kindle their ability to challenge established theories, and propose new theories.
Takeaway 3) Summary of the beauty of mathematics (from Villani's point of view; I think there are also happiness from the application side): Think of the experiments that can show the Bell Curve (i.e., the law of errors), then we ask the question "why it could not be any other curves?". What math is doing here is to "replace the beautiful coincidence with a beautiful explanation." The byproduct is (a) pleasure of the mathematicians, and (b) change of the view when looking at the world.
Nice analogy to use: This book is like introducing a child observing their mathematician parent working. The child pays attention to the ups and downs of emotions, the actions, the flow of progress, etc.
---
More resources:
- Birth of a Theorem - with Cédric Villani at the Royal Institution: https://www.youtube.com/watch?v=yYwyd...
November 7, 2021
Interesantísimo libro en el que nos metemos de pasajeros en la cabeza de Cédric Villani, matemático sublime, personaje excéntrico, medalla Fields (entre otras distinciones), durante el par de años que pasan desde que se decide, con su compañero y antiguo doctorando, Clément Mahout, a atacar e intentar probar el teorema del Landau damping hasta que le dan la medalla Fields en 2010.
Son capítulos cortos, en los que nos puede tocar presenciar un poco de divulgación sobre matemáticas, algo de biografía sobre matemáticos, vivos y muertos, relatos de la vida del autor durante esos años, algunos de los cientos y cientos de correos electrónicos que intercambiaron ambos autores durante esos dos años, o directamente trozos de papers de Villani. Estos dos últimos tipos de capítulo son, incluso para muchos matemáticos, absolutamente incomprensibles (clic para ampliar):
Otras veces el autor desciende gentilmente a Tierra y nos explica los teoremas en nuestro propio lenguaje:
El conjunto, aunque salpicado por agresiones en las que el autor nos riega, inunda, sepulta bajo matemáticas de otro planeta, es una historia de una matemático muy humano, que sueña con la medalla Fields, que sabe que la tiene al alcance de la mano, pero que no se atreve a confesarlo. También es la historia de un padre y de un marido (y de la mujer, que es una santa) Es la historia de la vida de un investigador que durante los dos años que nos narra vive en Lyon (su destino como catedrático), en Princeton (6 meses, becado en el Instituto de Estudios Avanzados donde Einstein acabó sus días) y en París (como director de instituto Poincaré de investigación matemática). Es también la historia de cómo los matemáticos interaccionan unos con otros, de cómo el conocimiento se comparte y se disfruta y al mismo tiempo se apalanca para publicar y ser reconocido. En palabras de André Weil, que el autor cita,
El autor narra varios de estos episodios de lucidez extrema, en los que el problema, aparentemente intratable, le muestra un camino de solución. Digo varios y todos ellos tienen relación con partes de este mismo teorema, porque es un monstruo cuya demostración requiere 180 páginas.
Leemos un capítulo entero sobre la historia musical del autor, que parece citar su top 200 de canciones, aprendemos de su amor por LaTeX, la herramienta en la que todos hemos redactado nuestros artículos científicos y matemáticos,
El libro es muy ecléctico, tal vez como el estilo estético del autor:
En conjunto, una lectura curiosa, vertiginosa por momentos, con extensos interludios de absoluta inextricabilidad, pero que aun así me ha gustado mucho.
Son capítulos cortos, en los que nos puede tocar presenciar un poco de divulgación sobre matemáticas, algo de biografía sobre matemáticos, vivos y muertos, relatos de la vida del autor durante esos años, algunos de los cientos y cientos de correos electrónicos que intercambiaron ambos autores durante esos dos años, o directamente trozos de papers de Villani. Estos dos últimos tipos de capítulo son, incluso para muchos matemáticos, absolutamente incomprensibles (clic para ampliar):
Otras veces el autor desciende gentilmente a Tierra y nos explica los teoremas en nuestro propio lenguaje:
Imagine you’re walking through the woods on a peaceful summer’s afternoon. You pause at the edge of a pond. Everything is perfectly calm, not the slightest breeze. Suddenly the surface of the pond becomes agitated, as though seized by convulsions; a few moments later, it is sucked down into a roaring whirlpool. And then, a few moments after that, everything is calm once more. Still not a breath of air, not even a ripple on the surface from a fish swimming beneath it. So what happened? The Scheffer–Shnirelman paradox, surely the most astonishing result in all of fluid mechanics, proves that such a monstrosity is possible, at least in the mathematical world. It is not based on an exotic model of quantum probabilities or dark energy or anything of that sort. It rests on the incompressible Euler equations, the oldest of all partial differential equations, used by mathematicians and physicists everywhere to describe a perfectly incompressible fluid without any internal friction. It has been more than two hundred fifty years since Euler derived his fundamental equations, and yet not all of their mysteries have been penetrated. Indeed, they are still considered to mark out one of the most treacherous regions of the mathematical world. When the Clay Mathematics Institute set seven “millennium problems” in 2000, offering $1 million apiece for their solution, it did not hesitate to include the regularity of solutions to the Navier–Stokes equations. It was very careful, however, to avoid any mention of Euler’s equations—a far greater and more terrifying beast. And yet at first glance Euler’s equations seem so simple, so innocent, utterly devoid of guile or cunning. No need to model variations in density or to grapple with the enigmas of viscosity. One has only to write down the classical laws of conservation: conservation of mass, quantity of motion, and energy. But then … suddenly, in 1993, Scheffer showed that Euler’s equations in the plane are consistent with the spontaneous creation of energy! Energy created from nothing! No one has ever seen such bizarre behavior in fluids in the natural world! All the more reason, then, to suspect that Euler’s equations hold still more surprises in store for us. Big surprises. Scheffer’s proof is a stunning feat of mathematical virtuosity, as obscure as it is difficult. I doubt that anyone other than its author has read it carefully from beginning to end, and I am certain that no one could reconstruct its reasoning, unaided, in every detail. There was more to come. Four years later, in 1997, the Russian-born mathematician Alexander Shnirelman, renowned for his originality, presented a new proof of this staggering result. Shortly afterward Shnirelman proposed a physically realistic criterion for solutions to Euler’s equations that would prohibit pathological phenomena of the sort Scheffer had discovered. Alas! A few years ago, two brilliant young mathematicians, Camillo De Lellis, an Italian, and László Székelyhidi, a Hungarian, proved a general and still more shocking theorem that showed, among other things, that Shnirelman’s criterion was powerless to resolve the paradox. Additionally, using the techniques of convex integration, they were able to develop a new method for producing these “wild” solutions, an elegant procedure that grew out of earlier research by a number of mathematicians, including Vladimir Šverák, Stefan Müller, and Bernd Kirchheim. Thanks to De Lellis and Székelyhidi, we now realize that even less is known about Euler’s equations than we thought. And what we thought we knew wasn’t much to begin with.
El conjunto, aunque salpicado por agresiones en las que el autor nos riega, inunda, sepulta bajo matemáticas de otro planeta, es una historia de una matemático muy humano, que sueña con la medalla Fields, que sabe que la tiene al alcance de la mano, pero que no se atreve a confesarlo. También es la historia de un padre y de un marido (y de la mujer, que es una santa) Es la historia de la vida de un investigador que durante los dos años que nos narra vive en Lyon (su destino como catedrático), en Princeton (6 meses, becado en el Instituto de Estudios Avanzados donde Einstein acabó sus días) y en París (como director de instituto Poincaré de investigación matemática). Es también la historia de cómo los matemáticos interaccionan unos con otros, de cómo el conocimiento se comparte y se disfruta y al mismo tiempo se apalanca para publicar y ser reconocido. En palabras de André Weil, que el autor cita,
Every mathematician worthy of the name has experienced, if only rarely, the state of lucid exaltation in which one thought succeeds another as if miraculously, and in which the unconscious (however one interprets this word) seems to playa role. In a famous passage, Poincare describes how he discovered Fuchsian functions in such a moment. About such states, Gauss is said to have remarked as follows: "Procreare jucundum (to conceive is a pleasure)"; he added, however, "sed parturire molestum (but to give birth is painful)." Unlike sexual pleasure, this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do so at will, unless perhaps by dogged work which it seems to reward with its appearance.
El autor narra varios de estos episodios de lucidez extrema, en los que el problema, aparentemente intratable, le muestra un camino de solución. Digo varios y todos ellos tienen relación con partes de este mismo teorema, porque es un monstruo cuya demostración requiere 180 páginas.
Leemos un capítulo entero sobre la historia musical del autor, que parece citar su top 200 de canciones, aprendemos de su amor por LaTeX, la herramienta en la que todos hemos redactado nuestros artículos científicos y matemáticos,
Knuth continually worked to improve the original model. The version numbers he assigned to his program are approximations of π, ever more precisely estimated as the program was gradually perfected: after version 3.14 came version 3.141, then 3.1415, and so on. The current version is 3.1415926; according to the terms of Knuth’s will, it will change to π immediately following his death, thus fixing TEX for all eternity.
El libro es muy ecléctico, tal vez como el estilo estético del autor:
En conjunto, una lectura curiosa, vertiginosa por momentos, con extensos interludios de absoluta inextricabilidad, pero que aun así me ha gustado mucho.
June 1, 2023
¡Qué aventura extraordinaria!
Cédric Villani nos cuenta su historia de cómo llegó a obtener sus resultados en matemática y así obtener la medalla Fields, mientras nos narra un poquito de su día a día.
Me ha encantado que el autor haya incluido algunos datos históricos sobre la matemática y matemáticos porque eso hizo que la lectura sea más atractiva.
Por otro lado, veo que muchos se quejan de que este libro tiene matemática de muy alto nivel y que los correos entre Cédric y Clément son absurdamente aburridos y sin sentido. No obstante, considero que ese es el toque mágico de esta aventura. Leer correos de dos grandes matemáticos donde hablan sobre límites, decaimientos, teoremas, pruebas, etc, ¡es fascinante!
Pero si no te gusta o te interesa nada de eso, puedes saltarte esas partes y la historia se entenderá.
A parte de contar sus aciertos y desaciertos, Villani indirectamente anima a los futuros o ya matemáticos a no rendirse y a seguir pensando en ese problemita (o monstruo) hasta derribarlo.
Cédric Villani nos cuenta su historia de cómo llegó a obtener sus resultados en matemática y así obtener la medalla Fields, mientras nos narra un poquito de su día a día.
Me ha encantado que el autor haya incluido algunos datos históricos sobre la matemática y matemáticos porque eso hizo que la lectura sea más atractiva.
Por otro lado, veo que muchos se quejan de que este libro tiene matemática de muy alto nivel y que los correos entre Cédric y Clément son absurdamente aburridos y sin sentido. No obstante, considero que ese es el toque mágico de esta aventura. Leer correos de dos grandes matemáticos donde hablan sobre límites, decaimientos, teoremas, pruebas, etc, ¡es fascinante!
Pero si no te gusta o te interesa nada de eso, puedes saltarte esas partes y la historia se entenderá.
A parte de contar sus aciertos y desaciertos, Villani indirectamente anima a los futuros o ya matemáticos a no rendirse y a seguir pensando en ese problemita (o monstruo) hasta derribarlo.
September 14, 2024
A mathematicians book for mathematicians. Never seen another book at the depth of math this one ventures into - which is good and bad! I enjoyed learning about the history of math and the pioneers of various fields including snippets on the formation of popular math (and science) institutions like IAS, Henri Poincaire Insitute, etc. But damn the math is soo advanced that even with a math degree I was unable to follow most of the works embedded in this book. I did enjoy looking and trying to figure out what it meant but its scattered so often I gave up at some point as to not get stuck in the book. Even so I don’t think there’s another novel that doesn’t shy from mixing research math with a novel like this book does. For what it is I think it’s unique and demanding to understand (just the math) - like any good math textbook.
The writing actually was pretty quirky, I liked him! He writes with lots of exclamation points and enjoys painting the scenes. The tone is friendly and makes reading it that more pleasant.
The writing actually was pretty quirky, I liked him! He writes with lots of exclamation points and enjoys painting the scenes. The tone is friendly and makes reading it that more pleasant.
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