Claire Voisin
French mathematician who disproved the generalized Hodge conjecture.
Claire Voisin (born 4 March 1962) is a French mathematician whose work centers on algebraic geometry. She has made significant contributions to the study of variations of Hodge structures and mirror symmetry, and authored several books on Hodge theory. In 2002, she demonstrated that a generalized version of the Hodge conjecture—one of the seven Millennium Prize Problems carrying a one-million-dollar prize—is false for compact Kähler varieties.
Voisin’s career includes a series of major honors. She received the European Mathematical Society Prize in 1992 and the Servant Prize from the French Academy of Sciences in 1996. The Sophie Germain Prize came in 2003, and in 2008 she won the Clay Research Award for disproving the Kodaira conjecture on deformations of compact Kähler manifolds. The year before, she was awarded the Ruth Lyttle Satter Prize in Mathematics for solving the generic case of Green’s conjecture on syzygies of canonical curve embeddings—a problem that had occupied algebraic geometers for over two decades (the full conjecture remains open for arbitrary curves). In 2016, she became the first woman to hold a chair in mathematics at the Collège de France, where she was elected to the Chair of Algebraic Geometry that same year and continues to hold it as of the latest known information. That same year, she received the Gold Medal of the CNRS, France’s highest scientific award. She shared the Shaw Prize in Mathematical Sciences with János Kollár in 2017, and in 2023 received the BBVA Foundation Frontiers of Knowledge Award in Basic Sciences jointly with Yakov Eliashberg. In 2024, she became the first woman to win the Crafoord Prize in Mathematics.
Voisin has been elected to numerous academies: the French Academy of Sciences, the German Academy of Sciences Leopoldina (2009), the Academia Europaea (2014), the U.S. National Academy of Sciences as a foreign associate (2016), the Royal Society as a Foreign Member (2021), and the American Academy of Arts and Sciences as an International Honorary Member (2022). She was an invited speaker at the 1994 International Congress of Mathematicians (ICM) in Zürich and a plenary speaker at the 2010 ICM in Hyderabad. She served on the Mathematical Sciences jury for the Infosys Prize from 2017 to 2019, and was named an MSRI Clay Senior Scholar for 2008–2009 and again in spring 2019.
Quick Facts
- Birth Date
- 1962-03-04
- Birth Place
- Saint-Leu-la-Forêt, Île-de-France
- Fields
- Mathematics
- Workplaces
- Pierre and Marie Curie University / École Polytechnique / Collège de France
- Education
- École Normale Supérieure / Paris-Sud 11 University
- Doctoral Advisor
- Arnaud Beauville
- Known For
- Algebraic geometry / Hodge theory
Facts from the source article.
Lore & Background
Claire Voisin was born on 4 March 1962. She is a member of the French Academy of Sciences and was elected to the chair of algebraic geometry at the Collège de France in 2016, becoming the first woman to hold a chair in mathematics there; she still holds this position as of the latest known information. In 2002, she proved that the generalization of the Hodge conjecture for compact Kähler varieties is false. The Hodge conjecture is one of the seven Clay Mathematics Institute Millennium Prize Problems selected in 2000, each with a prize of one million US dollars.
Voisin won the European Mathematical Society Prize in 1992 and the Servant Prize in 1996. She received the Sophie Germain Prize in 2003 and the Clay Research Award in 2008 for her disproof of the Kodaira conjecture on deformations of compact Kähler manifolds.
Reader's Guide
Claire Voisin's significance lies in her deep contributions to algebraic geometry, particularly in Hodge theory and mirror symmetry. Her 2002 disproof of the generalized Hodge conjecture for compact Kähler varieties was a landmark result, showing that a natural extension of one of the Millennium Prize Problems is false. She also disproved the Kodaira conjecture on deformations of compact Kähler manifolds and solved the generic case of Green's conjecture on syzygies, a problem that had resisted solution for over two decades. Her work has reshaped understanding of algebraic cycles and Hodge structures. Voisin's numerous honors, including the Crafoord Prize, Shaw Prize, and CNRS Gold Medal, reflect her standing as one of the leading mathematicians of her generation. She has also been a trailblazer as the first female mathematician member of the Collège de France and the first woman to win the Crafoord Prize in Mathematics.
Frequently Asked Questions
Who is Claire Voisin?
Claire Voisin is a French mathematician born on 4 March 1962 who specializes in algebraic geometry. She is widely recognized for her deep work on Hodge structures, mirror symmetry, and several landmark disproofs in the field.
What is Claire Voisin's most famous result?
In 2002 she proved that a generalized form of the Hodge conjecture—one of the seven Millennium Prize Problems—fails for compact Kähler varieties. This single counterexample overturned a long-standing belief and reshaped how researchers approach that conjecture.
What other major conjectures has Claire Voisin disproved or solved?
Beyond the Hodge result, she disproved the Kodaira conjecture and resolved the generic case of Green's conjecture. She has also authored influential books that made Hodge theory more accessible to a broader mathematical audience.
What major honors has Claire Voisin received?
She was awarded the European Mathematical Society Prize in 1992 and the Servant Prize from the French Academy of Sciences. These recognitions reflect her sustained impact on algebraic geometry over several decades.
What area of mathematics does Claire Voisin work in?
Her research sits at the intersection of algebraic geometry, complex geometry, and Hodge theory. She is particularly known for studying variations of Hodge structures and their connections to mirror symmetry.
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