Cedric Villani

Cédric Villani
Born	5 10, 1973
Birthplace	Brive-la-Gaillarde, France
Nationality	French
Occupation	Mathematician, politician, author
Known for	Work on optimal transport and Boltzmann equation; Fields Medal (2010)
Education	École Normale Supérieure (PhD)
Awards	Fields Medal (2010), Fermat Prize (2009), Henri Poincaré Prize (2009)

Cédric Patrice Thierry Villani (born 5 October 1973) is a French mathematician, author, and former politician who received the Fields Medal in 2010 for his contributions to the mathematical understanding of optimal transport, kinetic theory, and the Boltzmann equation. A former director of the Institut Henri Poincaré in Paris and a professor at the Université de Lyon, Villani has been one of the most publicly visible mathematicians in the world, known for his distinctive personal style — including his signature spider brooches and cravats — and his efforts to communicate the beauty and relevance of mathematics to broad audiences. He served as a member of the French National Assembly from 2017 to 2022, representing the fifth constituency of Essonne. Villani is the author of several books, including the memoir Birth of a Theorem (originally published in French as Théorème vivant in 2012), which offered a rare window into the creative process of mathematical research. He has been described in the media as one of France's best-known mathematicians and has used his public profile to advocate for the role of mathematics in critical thinking and public policy.

Early Life

Cédric Villani was born on 5 October 1973 in Brive-la-Gaillarde, a commune in the Corrèze department of south-central France. He grew up in a family that valued education and intellectual pursuits. From an early age, Villani demonstrated an aptitude for mathematics and the sciences, and he was drawn to the structures and patterns that underlie mathematical reasoning. His childhood in provincial France shaped a sensibility that he would later bring to his advocacy for making mathematics accessible beyond elite academic circles.

Villani's intellectual development was nurtured through the French educational system, which provides structured pathways for students with strong abilities in mathematics. He progressed through the classes préparatoires system, the competitive preparatory classes that serve as a gateway to France's grandes écoles, the elite higher education institutions. His early formation in this rigorous academic environment laid the groundwork for a career that would take him to the highest levels of mathematical achievement.

Education

Villani attended the École Normale Supérieure (ENS) in Paris, one of France's most prestigious institutions for the study of mathematics and sciences. The ENS has produced numerous Fields Medalists and has long been considered one of the world's foremost training grounds for mathematicians. At the ENS, Villani immersed himself in advanced mathematical analysis and developed interests in partial differential equations, mathematical physics, and probability theory. He completed his doctoral studies under the supervision of prominent mathematicians, focusing on the mathematical theory of kinetic equations, particularly the Boltzmann equation, which describes the statistical behavior of particles in a gas. His doctoral work established a foundation for the research that would later earn him international recognition.

Career

Mathematical Research

Villani's research has centered on several interconnected areas of mathematics, including optimal transport theory, kinetic theory, and the study of convergence to equilibrium in physical systems. His work on the Boltzmann equation — a fundamental equation in statistical mechanics that describes how the distribution of particles in a gas evolves over time — represented a major advance in understanding the mathematical properties of entropy production and the rate at which systems approach thermodynamic equilibrium.

One of Villani's most celebrated achievements was his work, carried out in collaboration with the Italian mathematician Clément Mouhot, on Landau damping, a phenomenon in plasma physics first described by the physicist Lev Landau in 1946. Landau had predicted that under certain conditions, the electric field in a plasma would decay over time even without energy dissipation, a counterintuitive result that had resisted rigorous mathematical proof for decades. Villani and Mouhot provided a full nonlinear mathematical proof of Landau damping for the Vlasov equation, a result that was described in the citation for his Fields Medal. This work required the development of new mathematical techniques and drew on ideas from several areas of analysis.

Villani's contributions to optimal transport theory also formed a central part of his research profile. Optimal transport, originally formulated by the French mathematician Gaspard Monge in 1781, concerns the problem of moving a distribution of mass from one configuration to another at minimal cost. Villani made substantial contributions to the modern mathematical framework of optimal transport, building on the foundational work of Leonid Kantorovich and others. He authored a comprehensive monograph, Topics in Optimal Transportation (2003), and later a more expansive treatment, Optimal Transport: Old and New (2009), both of which became standard references in the field.

The Fields Medal, which Villani received at the International Congress of Mathematicians in Hyderabad, India, in 2010, recognized his "proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation." The Fields Medal is awarded every four years to mathematicians under the age of 40 and is considered one of the highest honors in the discipline.

Director of the Institut Henri Poincaré

In 2009, Villani was appointed director of the Institut Henri Poincaré (IHP) in Paris, a research institute dedicated to mathematics and theoretical physics. Founded in 1928, the IHP is one of the oldest institutions of its kind and has played a central role in the French mathematical community. As director, Villani oversaw the institute's programs, conferences, and outreach activities. He used the position to promote mathematics to the public and to foster interdisciplinary connections between mathematics and other fields. His tenure at the IHP coincided with his growing public profile following the Fields Medal, and he leveraged the institution as a platform for science communication. Villani held the position of director until 2017, when he transitioned into political life.

Villani also held a professorial position associated with the IHES-Université de Lyon Chair in Analysis, through which he continued his research and teaching activities.

Public Communication of Mathematics

Beyond his research, Villani became one of the most recognizable public figures in French intellectual life, in large part because of his energetic efforts to communicate mathematics to non-specialist audiences. He gave numerous public lectures, media interviews, and conference presentations in which he articulated the role of mathematics in understanding the natural world, in technological innovation, and in the development of critical thinking skills.

In a 2015 interview with The Guardian, Villani described mathematics as being "about progress and adventure and emotion," challenging the common perception of the discipline as cold or purely abstract. He has spoken extensively about mathematics as a tool for sharpening reasoning and has argued that mathematical education can serve as "a laboratory for better thinking," a position he articulated in a 2018 interview with Forbes.

Villani delivered a public talk at the Commonwealth Club of California in April 2015, billed as "The Living Art of Mathematics," in conversation with David Eisenbud, the director of the Mathematical Sciences Research Institute. He also presented the 2013 Math for America Annual Lecture, organized by the Simons Foundation, where he addressed an audience of mathematics educators and enthusiasts.

His distinctive personal appearance — characterized by his lavallière ties, three-piece suits, and large spider brooches — made him instantly recognizable and contributed to his media profile. Journalists and commentators frequently noted that his appearance diverged from stereotypical images of mathematicians, and Villani has used this public persona to attract attention to mathematical topics.

In June 2025, Villani participated in an off-site event organized by the quantum computing company Alice & Bob in Aix-en-Provence, France, where he discussed quantum computing with the company's approximately 150 employees. The event was conducted without laptops, emphasizing in-person intellectual exchange.

Author

Villani is the author of several books aimed at both specialist and general audiences. His memoir Théorème vivant was published in France in 2012 and later translated into English as Birth of a Theorem: A Mathematical Adventure (2015). The book chronicles the process by which Villani and Mouhot developed their proof of nonlinear Landau damping, weaving together personal narrative, mathematical exposition, emails, and reflections on the creative dimensions of mathematical work. A review in Scientific American noted that the memoir offered "a glimpse into the emotional highs and lows" of mathematical research. A reviewer for The Spectator engaged with the question of how a non-specialist audience might appreciate a book so steeped in advanced mathematics, ultimately finding value in Villani's narrative of intellectual pursuit.

His earlier monographs on optimal transport — Topics in Optimal Transportation (2003) and Optimal Transport: Old and New (2009) — became standard references in the mathematical community and were instrumental in shaping the field's development in the early 21st century.

Political Career

In 2017, Villani entered French politics. He was elected to the French National Assembly as a member representing the fifth constituency of Essonne, running under the banner of La République En Marche!, the political movement founded by President Emmanuel Macron. His election was part of a broader wave of non-traditional candidates who entered the National Assembly in the 2017 legislative elections.

As a member of the National Assembly, Villani was involved in technology and science policy. In 2018, he authored a prominent report on artificial intelligence for the French government, commonly referred to as the "Villani Report," which made recommendations about France's AI strategy, including proposals related to research funding, data policy, ethics, and the economic implications of AI. The report helped shape the French government's approach to AI development.

In 2020, Villani ran as a candidate for mayor of Paris but was unsuccessful, finishing outside the leading candidates. His political career reflected a broader interest in bringing scientific and analytical perspectives to governance and public policy. He served in the National Assembly until 2022, when he did not seek re-election.

Personal Life

Villani resides in France. He is known publicly for his eccentric and carefully cultivated personal style, which includes wearing spider brooches — he has been reported to own a substantial collection — as well as lavallière neckties and formal attire that evokes a 19th-century aesthetic. His appearance has been the subject of considerable media commentary and has contributed to his recognition beyond academic circles.

Villani has spoken in interviews about his love of music, literature, and culture, and about the connections he perceives between mathematical creativity and artistic expression. He has cited influences ranging from classical music to science fiction in shaping his intellectual outlook.

Recognition

Villani has received numerous awards and honors for his mathematical work. The most prominent of these is the Fields Medal, awarded to him in 2010 at the International Congress of Mathematicians in Hyderabad, India, for his work on nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation.

Prior to the Fields Medal, Villani received the Fermat Prize in 2009, awarded for research in the areas of mathematics where Pierre de Fermat made contributions, and the Henri Poincaré Prize in 2009, awarded by the International Association of Mathematical Physics for outstanding contributions to mathematical physics. He also received the Jacques Herbrand Prize from the French Academy of Sciences.

Villani was elected as a member of the French Academy of Sciences and has held visiting positions at institutions around the world. His public lectures, books, and media appearances have earned him recognition as a leading figure in science communication. He has been featured in numerous profiles in international media, including in The Guardian, Forbes, Scientific American, and The Spectator, among other outlets.

Legacy

Villani's contributions to mathematics span both the technical and the communicative dimensions of the discipline. His research on optimal transport, kinetic theory, and Landau damping has had a lasting impact on mathematical analysis and mathematical physics, influencing subsequent research in these areas. His monographs on optimal transport have served as foundational texts for a generation of researchers.

Beyond his research, Villani's role as a public figure has contributed to a broader conversation about the place of mathematics in society. His insistence that mathematics is not merely an abstract or utilitarian discipline but one connected to creativity, emotion, and human experience has resonated with audiences worldwide. His memoir Birth of a Theorem brought the inner experience of mathematical research to a wide readership, offering a counterpoint to the perception of mathematics as remote or inaccessible.

His transition into politics, while met with mixed results, represented an unusual trajectory for a mathematician of his stature and reflected his conviction that scientific thinking has a role to play in governance and public discourse. His report on artificial intelligence for the French government remains a reference point in European discussions about technology policy.

Villani continues to be active in public life, participating in events at the intersection of science, technology, and culture. His 2025 engagement with the quantum computing company Alice & Bob is indicative of his ongoing interest in emerging technologies and their mathematical foundations.