Cédric Villani

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.

A Mathematical Adventure

Birth of a Theorem

Clement Deslandes

Guillaume Deslandes

Laure Macéde Lépinay

Lorenzo Croissant

And 99 Other Classic Mathematical Riddles

Price of Cake

¿Cómo trabaja un matemático? ¿Cuáles son sus modos de invención? ¿Qué vida late tras las fórmulas y demostraciones matemáticas? En 2010, y con 37 años, Cédric Villani gana la Medalla Fields, considerada como el Premio Nobel de las matemáticas, por sus contribuciones a la física estadística y, en particular, por su formulación del teorema sobre el amortiguamiento de Landau. Este libro es un trepidante y apasionado relato en el que Villani, con su mezcla de carisma y excentricidad, de precisión y entusiasmo, da cuenta de su hazaña, desde la idea germinal hasta su resolución final como publicación. A lo largo de dos años de trabajo febril, fruto también de la colaboración de su ayudante Clément Mouhot, asistimos al desarrollo de su investigación –hecha de tanteos, dudas, rectificaciones y logros– de Lyon a Hyderabad, pasando por Kioto, París o Princeton. Un relato en forma de diario, en el que se intercalan correos electrónicos y los retratos de algunos de los grandes nombres de la matemática y la ciencia –Boltzmann, Newton, Euler, Gauss, Fourier, Kolmogórov, Nash…–, donde el lenguaje matemático más sofisticado convive con canciones, mangas y duermevelas… Cómo nace un teorema es así el testimonio apasionado y riguroso del pensamiento vivo que anima la creación matemática.

una aventura matemática

Cómo nace un teorema

Théorème vivant est le récit de la genèse d'une avancée mathématique. Nous voici emportés dans le quotidien d'un jeune chercheur de talent : un véritable « road-trip », de Kyoto à Princeton et de Lyon à Hyderabad, dont Villani tient, au jour le jour, le carnet de bord. Entre des échanges enflammés avec son collaborateur et compagnon de route, quelques refrains de chansons fredonnés au fil des équations et les histoires merveilleuses que ce père de famille raconte à ses enfants, on suit la lente et chaotique élaboration d'un nouveau théorème qui lui vaudra la plus prestigieuse distinction du monde des mathématiques.Aux antipodes de l'ouvrage de vulgarisation scientifique traditionnel, Théorème vivant est un chant passionné qui se lit comme un roman d'aventures, jalonné de portraits de quelques-uns des plus grands noms de l'histoire des mathématiques et parsemé de vertigineuses équations qui exercent sur le lecteur une irrésistible fascination.Avis à tous ceux qui gardent un souvenir cruel de l'étude des fonctions et de la résolution d'équations à plus d'une inconnue : Théorème vivant vous réconciliera avec cette science dont Cédric Villani sait comme personne, par la grâce de sa passion, transmettre la magie, la beauté et la poésie.

Théorème vivant

This is the first comprehensive introduction to the theory of mass transportation with its many—and sometimes unexpected—applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. In 1781, Gaspard Monge defined the problem of “optimal transportation” (or the transferring of mass with the least possible amount of work), with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.

Topics in Optimal Transportation

patru genii care au schimbat istoria

Visători picaţi din lună

Karol Beffa

Comment et d'où viennent les idées ? La liberté créatrice a-t-elle besoin de contraintes ? Quel rôle jouent les rituels de chacun dans l'élaboration de la pensée ? Karol Beffa et Cédric Villani répondent à ces questions dans un dialogue à bâtons rompus abordant la création dans leurs disciplines respectives, les mathématiques et la musique, qui partagent une longue histoire commune. Au fil de cette conversation, c'est le portrait de ces deux grands esprits qui se dessine et permet d'appréhender leur personnalité, leur oeuvre et leur parcours singulier. Comment devient-on mathématicien ou compositeur ? Comment s'organise une journée type dans ces métiers si singuliers ?

Les coulisses de la création

Jean Dhombres

Pierre Cartier

Gerhard Heinzmann

This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani’s popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political establishment. The authors explore three major directions in their dialogue: the highly complex relationship between mathematics and reality, the subject of many debates and opposing viewpoints; the freedom that the construction of mathematics has given humankind by enabling them to develop the natural sciences as well as mathematical research; and the responsibility with which the scientific community and governments should address the role of mathematics in research and education policies.

Freedom in Mathematics

Giuseppe Buttazzo

Luigi Ambrosio

Yann Brenier

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.

Lectures Given at the C.I.M.E. Summer School Held in Martina Franca, Italy, September 2-8, 2001

Optimal Transportation and Applications

Stefano Bianchini

Alexander Mielke

Eric A. Carlen

This volume collects the notes of the CIME course "Nonlinear PDE’s and applications" held in Cetraro (Italy) on June 23–28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of far-reaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, Hamilton-Jacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rate-independent evolution problems. The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields.

C.I.M.E. Summer School, Cetraro, Italy 2008, Editors: Luigi Ambrosio, Giuseppe Savaré

Nonlinear PDE’s and Applications

Fraydoun Rezakhanlou

François Golse

Featuring updated versions of two research courses held at the Centre Émile Borel in Paris in 2001, this book describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields. It also discusses four conjectures for the kinetic behavior of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.

Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001

Entropy Methods for the Boltzmann Equation

Hervé Pajot

Yann Ollivier

Lecture notes and research papers on optimal transportation, its applications, and interactions with other areas of mathematics.

Theory and Applications

Optimal Transportation

Yann Bonnet

Bertrand Rondepierre

marc schoenauer

charly berthet

francois levin

anne charlotte cornut

towards a french and european strategy

For a meaningful artificial intelligence

Bernard Nordlinger

Daniela Rus

This book provides an overview of the role of AI in medicine and, more generally, of issues at the intersection of mathematics, informatics, and medicine. It is intended for AI experts, offering them a valuable retrospective and a global vision for the future, as well as for non-experts who are curious about this timely and important subject. Its goal is to provide clear, objective, and reasonable information on the issues covered, avoiding any fantasies that the topic “AI” might evoke. In addition, the book seeks to provide a broad kaleidoscopic perspective, rather than deep technical details.

Healthcare and Artificial Intelligence

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.

Old and New

Optimal Transport

Luis A. Caffarelli

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2–8, 2001

Marc Schoenauer

Charly Berthet

François Levin

Anne-Charlotte Cornut

L’intelligence artificielle est entrée, depuis quelques années, dans une nouvelle ère, qui donne lieu à de nombreuses craintes et à de nombreux espoirs. Rendues possibles par des algorithmes nouveaux, la multiplication des jeux de données et le décuplement des puissances de calcul, les applications se multiplient : traduction automatique, conduite autonome, détection de cancer… Le développement de l’intelligence artificielle est amené à toucher l’ensemble des domaines et des secteurs. Les investissements dans la recherche et dans l’industrie atteignent des sommes extraordinaires, notamment aux États-Unis et en Chine. Les responsables politiques du monde entier l’évoquent dans les discours de politique générale comme un levier de pouvoir majeur. C’est que l’intelligence artificielle va désormais jouer un rôle bien plus important que celui qu’elle jouait jusqu’alors et, plus que jamais, il nous faut donner un sens à son développement. Donner un sens, c’est d’abord donner une direction, un cap, pour positionner la France et l’Europe à l’avant-garde de cette révolution naissante. C’est également lui donner une signification : l’intelligence artificielle n’a précisément de sens que si elle participe du progrès humain, social et environnemental. Dans un monde marqué par les inégalités, elle ne doit pas conduire à renforcer les phénomènes d’exclusion et la concentration de la valeur. Donner un sens, c’est enfin expliquer : démystifier ces technologies auprès de la société, mais aussi expliquer l’intelligence artificielle en elle-même, s’agissant de techniques qui restent empreintes d’une très forte opacité. Donner un sens à l’IA, voilà donc l’objectif de ce rapport.

pour une stratégie nationale et européenne

Donner un sens à l’intelligence artificielle

¿Cómo trabaja un matemático? ¿Cuáles son sus modos de invención? ¿Qué vida late tras las fórmulas y demostraciones matemáticas? En 2010, y con 37 años, Cédric Villani gana la Medalla Fields, considerada como el Premio Nobel de las matemáticas, por sus contribuciones a la física estadística y, en particular, por su formulación del teorema sobre el amortiguamiento de Landau. Este libro es un trepidante y apasionado relato en el que Villani, con su mezcla de carisma y excentricidad, de precisión y entusiasmo, da cuenta de su hazaña, desde la idea germinal hasta su resolución final como publicación. A lo largo de dos años de trabajo febril, fruto también de la colaboración de su ayudante Clément Mouhot, asistimos al desarrollo de su investigación –hecha de tanteos, dudas, rectificaciones y logros– de Lyon a Hyderabad, pasando por Kioto, París o Princeton. Un relato en forma de diario, en el que se intercalan correos electrónicos y los retratos de algunos de los grandes nombres de la matemática y la ciencia –Boltzmann, Newton, Euler, Gauss, Fourier, Kolmogórov, Nash...–, donde el lenguaje matemático más sofisticado convive con canciones, mangas y duermevelas... Cómo nace un teorema es así el testimonio apasionado y riguroso del pensamiento vivo que anima la creación matemática. Cédric Villani (1973), matemático y político francés, ha conjugado la alta investigación con la divulgación matemática. La investigación que relata este libro le mereció la Medalla Fields en 2010.

Una aventura matemática

L’autore trascina i lettori in un turbine di dubbi, problemi e istanti di grazia. - Le Monde diplomatique Questo libro è scritto da un bambino. Solo un bambino possiede la capacità innata di ripulire il mondo ogni volta che vi posa lo sguardo. - Le Figaro

La mia più grande avventura matematica

Il teorema vivente

Cédric Villani

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