Yvonne Choquet-Bruhat (French: [ivɔn ʃɔkɛ bʁy.a] ; 29 December 1923 – 11 February 2025) was a French mathematical physicist now best remembered for her investigation of the mathematics of general relativity. Her proof that the Einstein field equations can be expressed as a well-posed initial-value problem was listed by the journal Classical and Quantum Gravity as one of thirteen "milestone" results in general relativity in an issue published in the centennial anniversary of its birth in 2015. She also studied non-Abelian gauge theory, relativistic hydrodynamics, and supergravity.
Choquet-Bruhat was the first woman to be elected to the French Academy of Sciences and was a Grand Officer of the Legion of Honour.
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Early life and education
Yvonne Bruhat was born in Lille on 29 December 1923 in an intellectual family. Her mother was philosophy professor Berthe Hubert and her father was physicist Georges Bruhat, who died in 1945 in the Sachsenhausen concentration camp. He was sent there after refusing to divulge information on the French Resistance to Nazi occupation. Her brother François Bruhat also became a mathematician.
Bruhat attended secondary school in Paris, earning her Baccalauréat in 1941, at the top of her class. She received the silver medal for physics in the prestigious Concours Général national competition. In her view, mathematics and the natural sciences were the best ways to understand the Universe. Uncertain whether to study medicine, physics, or mathematics, she decided on the last. She wanted to research rather than teach, as was more usual for women at the time. From 1943 to 1946 she studied at the École normale supérieure de jeunes filles (a girls' school, also known as the École normale de Sèvres) near Paris.
Career
From 1946 to 1949, she was an assistant at the École normale supérieure. In 1947, Bruhat undertook research under the supervision of mathematical physicist André Lichnerowicz, who invited her to be his doctoral student after seeing her excellent marks on an examination for future high-school teachers. But unlike most mathematicians at the time, she did not want to follow the trend towards increasing abstraction and preferred to remain close to physics, motivated by her desire to better understand nature. Jean Leray, an expert on the theory of partial differential equations, suggested that she investigate whether or not the Einstein field equations of general relativity were well-posed. This became the topic of her dissertation, for which she earned her doctorate in 1951. While it was known that the equations of motion derived from Newton's laws of motion and gravitation yielded unique solutions with initial conditions, whether this was true for Einstein's gravitational field equations remained unproven until her landmark thesis.
Her work guaranteed the predictability of the universe as described by general relativity. Her work also lent credence to gravitational waves, predicted by general relativity, but initially doubted by Einstein, who thought that they were merely a mathematical artefact of coordinate choices. In two papers published in 1916 and 1918, Einstein had only shown that waves were solutions to the linearized gravitational field equations. Bruhat demonstrated that this was also true for the fully non-linear equations. She expressed the Einstein field equations in vacuum using harmonic coordinates, previously introduced by Théophile De Donder and Cornelius Lanczos, in which case they become non-linear hyperbolic partial differential equations, and as such could describe the propagation of waves. While Georges Darmois had already tackled the problem for analytic solutions, Bruhat's proof applied to non-analytic cases as well.
She also showed that gravitational waves could not propagate at an arbitrary speed; they must travel at the speed of light in vacuum. Causality was therefore not violated. With the 2017 detection of both gravitational and electromagnetic waves from GW170817, the merger of two neutron stars in the galaxy NGC 4993, Bruhat's faith in her mathematical work was vindicated by multi-messenger astronomy.
With some help from Leray, Bruhat and her first husband, Léonce Fourès, were offered fellowships at the Institute for Advanced Study (IAS) in Princeton, New Jersey, in the academic year 1951–51. During her time there, she met a number of scientific luminaries, including the Institute director, J. Robert Oppenheimer, former scientific director of the Manhattan Project, John Archibald Wheeler, who became her friend, and John von Neumann, who showed her an early electronic computer he built called the IAS machine. She also met Albert Einstein, father of general relativity, whom she remembered as a kind and friendly man. She presented her work to him on his blackboard. She described this as a happy time in her life. After their time at the IAS, she and her husband accepted positions at the University of Marseille.
Technical research contributions
Choquet-Bruhat's best-known research deals with the mathematical nature of the initial data formulation of general relativity. A summary of results can be phrased purely in terms of standard differential geometric objects.
An initial data set is a triplet (M, g, k) in which M is a three-dimensional smooth manifold, g is a smooth Riemannian metric on M, and k is a smooth (0,2)-tensor field on M.
Given an initial data set (M, g, k), a development of (M, g, k) is a four-dimensional Lorentzian manifold (M, g) together with a smooth embedding f : M → M and a smooth unit normal vector field along f such that f *g = g and such that the second fundamental form of f, relative to the given normal vector field, is k.
In this sense, an initial data set can be viewed as the prescription of the submanifold geometry of an embedded spacelike hypersurface in a Lorentzian manifold.
An initial data set (M, g, k) satisfies the vacuum constraint equations, or is said to be a vacuum initial data set, if the following two equations are satisfied:
R
g
−
|
k
|
g
2
+
(
tr
g
k
)
Personal life and death
In 1947, she married fellow mathematician Léonce Fourès. Their daughter Michelle is an ecologist. Her doctoral work and early research was under the name Yvonne Fourès-Bruhat. In 1960, Bruhat and Fourès divorced.
The following year she married the mathematician Gustave Choquet and changed her last name to Choquet-Bruhat. She and Choquet had two children: a son, neuroscientist Daniel, and a daughter, medical doctor Geneviève.
Her memoir, from her academic and personal life, was translated into English in 2018.
Choquet-Bruhat died on 11 February 2025 in Merignac, France (33700), at the age of 101.
Major publications
Articles
Y. Fourès-Bruhat (1951). "Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires". Acta Mathematica. 88: 141–225. doi:10.1007/bf02392131. Zbl 0049.19201. Wikidata Q56048465.
Choquet-Bruhat, Yvonne; Geroch, Robert. Global aspects of the Cauchy problem in general relativity. Comm. Math. Phys. 14 (1969), 329–335. doi:10.1007/BF01645389 MR 0250640
Survey articles
Bruhat, Yvonne. The Cauchy problem. Gravitation: An introduction to current research, pp. 130–168, Wiley, New York, 1962.
Choquet-Bruhat, Yvonne; York, James W. Jr. The Cauchy problem. General relativity and gravitation, Vol. 1, pp. 99–172, Plenum, New York-London, 1980.
Choquet-Bruhat, Yvonne. Positive-energy theorems. Relativity, groups and topology, II (Les Houches, 1983), 739–785, North-Holland, Amsterdam, 1984.
Choquet-Bruhat, Yvonne. Results and open problems in mathematical general relativity. Milan J. Math. 75 (2007), 273–289.
Choquet-Bruhat, Yvonne. Beginnings of the Cauchy problem for Einstein's field equations. Surveys in differential geometry 2015. One hundred years of general relativity, 1–16, Surv. Differ. Geom., 20, Int. Press, Boston, MA, 2015.
Technical books
Choquet-Bruhat, Yvonne; DeWitt-Morette, Cécile; Dillard-Bleick, Margaret. Analysis, manifolds and physics. Second edition. North-Holland Publishing Co., Amsterdam-New York, 1982. xx+630 pp. ISBN 0-444-86017-7
Choquet-Bruhat, Yvonne; DeWitt-Morette, Cécile. Analysis, manifolds and physics. Part II. North-Holland Publishing Co., Amsterdam, 1989. xii+449 pp. ISBN 0-444-87071-7
Honours and awards
Médaille d'Argent du Centre National de la Recherche Scientifique, 1958
Prix Henri de Parville of the Académie des Sciences, 1963
Member (since 1965), Comite International de Relativite Generale et Gravitation (President 1980–1983)
Member, Académie des Sciences, Paris (elected 1979)
Elected to the American Academy of Arts and Sciences 1985
Association for Women in Mathematics Noether Lecturer, 1986
Commandeur de la Légion d'honneur, 1997
Dannie Heineman Prize for Mathematical Physics, 2003
She was elevated to the 'Grand Officier' and 'Grand Croix' dignities in the Légion d'Honneur in 2008.
In 2026, Choquet-Bruhat was announced as one of 72 historical women in STEM whose names are proposed to be added to the 72 men already celebrated on the Eiffel Tower. Anne Hidalgo, the Mayor of Paris, announced this on the recommendation of a committee led by Isabelle Vauglin of Femmes et Sciences and Jean-François Martins, which represents the operating company that manages the Eiffel Tower.