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Haïm Brezis

Quick Info

Born
1 June 1944
Riom-ès-Montagnes, Auvergne, France
Died
7 July 2024
Jerusalem, Israel
Summary
Haïm Brezis was a French mathematician whose remarkable contributions made him a world leading specialist on mathematical analysis and partial differential equations. He was awarded the Leroy P Steele Prize for Lifetime Achievement in 2024.

Biography

Haïm Brezis was the son of Yaakov Brezis (known as Mico) and Rivka (known as Becky). Yaakov Brezis was a Romanian Orthodox Jew who had left Romania to live in Paris near the beginning of the 1930s. Romania and France always had close connections and one of Yaakov's uncles had taken philosophy courses at the Sorbonne. We should explain at this point where the name Breszis came from. It is the initials of the Hebrew name "Ben Rabbi Chalom Zelig." We will say a little more below about the complications Haïm Brezis had with his name. Yaakov lived in Paris until the outbreak of World War II when the German invasion of France meant that Paris became extremely dangerous for a Jew. He went to the Massif Central and it was there that he met Rivka. In fact Rivka's parents were Orthodox Jews from the Krakow region of Poland and they had emigrated to Germany during World War I. Rivka had attended primary school in Germany until the racial laws of 1933. She then went with her parents to Holland where she attended high school and was awarded a baccalaureate. In 1942 Rivka escaped from Holland with her parents and they lived in the Massif Central as refugees.

Yaakov and Rivka had no official documents and certainly could not have a civil marriage. Their fathers carried out a religious marriage in secret and Haïm Brezis, their first child, was born in Riom-ès-Montagnes, a small village in Auvergne where they had made their home. Haïm explained in [8]:-
I was born a few days before the Allied landings. My grandmother had come on foot from very far away and whispered the news in my mother's ear, who was still bedridden in the clinic. My parents named me Haïm, which means Life in Hebrew. ... I was registered with the civil registry under the name Jean-Jacques Vienne and, even twenty years later, I had a lot of trouble getting rid of this false identity when I needed administrative documents!
Immediately after his birth, however, the situation became even more dangerous and [8]:-
... when the threats worsened, [my parents] retreated to a shepherd's hut deep in the woods. I spent the first weeks of my life practically in the forest. At the age of one month I had pyloric stenosis ...
By the end of August 1944 Paris was liberated from the Germans and when Haïm was six months old his parents left the Massif Central and went to Paris where they their home. Yaakov was a furrier and set up his business the Latin Quarter of Paris, on Rue Claude-Bernard. Haïm explained [8]:-
His shop was located next to the synagogue on Rue Vauquelin and the Rabbinical School. Many members of the community would stop by to chat with my father and confide in him. Sometimes they brought a donation for the synagogue. Others came to ask for support. He was very generous. He also maintained special relationships with the teachers and students of the Rabbinical School, who often came into his shop to greet him.
Although Haïm had been given that Hebrew name, as we explained above, he could not be registered with a Hebrew name so his birth had been registered as Jean-Jacques Vienne. Even when he began has schooling in Paris his name was a problem since Haïm was not on the list of acceptable French names. He became known as Rémi Brézis, the French insisting on putting an acute accent on Brézis. It was not until he was 22 years old that he was able to insist that his name was Haïm Brezis.

Let us note at this point that Haïm Brezis was the eldest of his parents three children. He had a brother David Brezis (1947-2020), born in Paris on 29 November 1947, who became a research fellow in philosophy at the Centre national de la recherche scientifique. His youngest brother was Mayer L Brezis, born in Paris on 26 July 1949, who studied medicine at Tel Aviv University, was trained as an internist and nephrologist at Harvard, and became professor of medicine at the Hadassah-Hebrew University Medical Centre.

Haïm's mother voluntarily ran a Jewish school in Paris. He said [8]:-
I received my first Hebrew lessons in the family setting. From the age of three, I began to read Hebrew, before French. When I arrived at school, the teacher was astonished that I persisted in writing French from right to left ...
His formal schooling began at the Lycée Montaigne which was originally associated with the Lycée Louis-le-Grand. It had taken the name Lycée Montaigne in 1891. After studying at this school he moved to the Lycée Henri IV. This Lycée originally occupied the buildings of the former Sainte Geneviève Abbey, became the École Centrale du Panthéon, then the Lycée Napoléon in 1804, and after several more changes had become the Lycée Henri IV in 1873. It was at this school that Brezis began to become passionate about mathematics, particularly the problem solving aspect of the subject. He loved solving mathematical problems, continuing this during the school holidays. He was taught mathematics by I Salanskis who gave Brezis a lot of confidence by telling him that he should study at the École Normale Supérieure and pursue a career in mathematics.

Brezis followed this advice and applied to sit the entrance examinations to the École Normale Supérieure. When, however, he had to take these examinations on a Saturday, he did not attend for religious reasons. He said in [7]:-
... the École Normale Supérieure on rue d'Ulm had slammed the door in the face of citizen Brezis, who persisted in respecting his religious convictions and refusing to write on Saturdays.
He, therefore entered the Université Pierre et Marie Curie in 1962 to begin his studies of university level mathematics. Beginning in his first year, he took courses from outstanding mathematicians such as Claude Chevalley, François Bruhat, and Roger Godement. Later he was inspired by lecturers like Gustave Choquet and Laurent Schwartz. After the award of his Diplôme d'études approfondies (DEA), Brezis asked Choquet to suggest a topic for his Doctorat de 3e cycle [8]:-
Before talking to me about mathematics, he asked me the question: "Do you have a scholarship?" I replied: "No, my parents help me live." I had no idea that one could even apply for a scholarship. He replied: "Yes, you must apply for a scholarship, it is independent of the parents' status. Unfortunately, the deadline has passed." He picked up the phone and called the scholarship office: "I have a student here who did not know the deadlines. I am responsible for the delay; he absolutely must have a scholarship." Thanks to him, I received this scholarship.
Choquet suggested that Brezis work on fixed point theorems and gave him a pile of Félix Browder's papers to read. Seeing a poster in the library of the Henri Poincaré Institute advertising the Séminaire de mathématiques supérieures Ⓣ in Montreal from June to August 1965 with Browder giving a lecture course on Problèmes non-linéaires Ⓣ, he immediately took a flight to Montreal. He was allowed to attend the lectures even though he had not registered for the conference. Also at this conference he attended a course of lectures by Guido Stampacchia on Équations elliptiques du second ordre à coefficients discontinus Ⓣ and a course by Shmuel Agmon on Unicité et propriétés de convexité dans les problèmes différentiels. Ⓣ While at this conference he became very interested in partial differential equations.

After he returned to Paris, Brezis asked people which French mathematician was working on topics closest to Browder and was told to talk to Jacques-Louis Lions who was a Professor in the Faculty of Science of the University of Paris. He found talking to Lions very encouraging and began to follow some of the ideas that Lions had suggested. He continued to work on his dissertation Les opérateurs monotones Ⓣ advised by Choquet and was awarded the Doctorat de 3e cycle in 1966. Choquet advised him to apply for a position at the CNRS and he received a four year appointment. He then continued working towards his Doctorat d'État advised by Jacques-Louis Lions.

While working towards his Doctorat d'État, Brezis received invitations to visit Guido Stampacchia, Felix Browder and Louis Nirenberg. The first invitation was to the University of Pisa in 1967 where he spent a month with Guido Stampacchia. While in Pisa he also met Ennio De Giorgi who held the Chair of Mathematical Analysis at the Scuola Normale Superiore in Pisa. A visitor to Pisa at that time was Shmuel Agmon from Jerusalem and he quickly developed a friendship with Brezis. After his visit to Pisa, Brezis left for a long stay at the Courant Institute of Mathematical Sciences in New York visiting Louis Nirenberg. His third invitation, in the early 1970s, was to Felix Browder at the University of Chicago. Perhaps it was Louis Nirenberg who had the greatest influence on Brezis [8]:-
Working closely with Louis Nirenberg, I had the privilege of seeing a great mathematician at work When he was stuck and out of ideas, he would suggest going for a coffee, a walk in Greenwich Village and a bookstore tour, or even visiting an exhibition. When he returned, he was back on top form and bubbling with inspiration. I also learned not to call him too early in the morning: after spending the evening at the movies, he might have spent the night working until dawn on a problem that was worrying him. Ready to share his impressions of a film, Louis is often disappointed by my poor film knowledge! He is delighted to be able to recommend a nice hotel in Tuscany or a little-known museum in London. He is always available to write a warm letter of recommendation for a young person looking for a job or to help a colleague in difficulty. A luminous and very modest man, Louis has become for me the living model of a Master in the deepest sense of the term.
Brezis began publishing and had eleven papers in print in 1967-68: Une généralisation des opérateurs monotones Ⓣ; Méthodes d'approximation et d'itération pour les opérateurs monotones Ⓣ; Fonctions duales relativement à une forme bilinéaire Ⓣ; Sur certains problèmes unilatéraux hyperboliques Ⓣ; Inéquations d'évolution abstraites Ⓣ; Sur une classe de problèmes d'évolution non linéaires Ⓣ; Les opérateurs monotones Ⓣ; Sur certains problèmes non linéaires Ⓣ; Sur la régularité de la solution d'inéquations elliptiques Ⓣ; Méthodes d'approximation et d'itération pour les opérateurs monotones Ⓣ; and Équations et inéquations non linéaires dans les espaces vectoriels en dualité. Ⓣ

Brezis submitted his two Doctorat d'État theses - Première thèse: Problèmes unilatéraux. Deuxième thèse: Groupes de difféomorphismes et mouvement d'un fluide incompressible Ⓣ - in 1971 and was awarded the degree in the following year. We note that by the time he was awarded his Doctorat d'État he had 38 papers in print. In 1973 he published his first book, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert Ⓣ based on a course on nonlinear analysis he had delivered in Paris in 1970-71. For more information about this book, see THIS LINK.

In 1972 Brezis was appointed to the Pierre and Marie Curie University (the University of Paris-VI) and in 1973 he delivered the Peccot lectures at the Collège de France on Les semigroupes de contractions non linéaires. Ⓣ In 1976 he was promoted to full professor at the University of Paris-VI. He held this position until he retired from the Pierre and Marie Curie University in 2007; he was made Professor Emeritus in the following year. In addition to his roles at the University of Paris-VI he served as a lecturer at the École Polytechnique in Paris from 1973 to 1985. In 1987 he accepted an offer from Rutgers University in New Jersey, USA as Distinguished Visiting Professor spending several months there every year; he held this appointment until 2022 when he became Emeritus. He was also a regular visitor at the Technion, Haifa, Israel between 2008 and 2022.

In 1978 Brezis visited Jerusalem and sought out Michal Govrin because of an article she wrote about her journey to Poland. Even before this meeting Michal Govrin (born 24 November 1950) had studied for a Ph.D. in theatre and literature in Paris and had spoken to Brezis on the telephone concerning his activities in an association aiming to achieve peace in the Middle East. Haïm Brezis and Michal Govrin Brezis were married in 1982 and had two children. Their daughter Rachel-Shlomit Brezis (born 1984) became a developmental psychologist specialising in autism. She was awarded a PhD in Psychology from the University of Chicago in 2011 and (as of 2025) works at the Interdisciplinary Center Herzliya, Israel. Miriam-Rivka Brezis (born 1988) is (in 2025) a student/intern at the Tel Aviv Sourasky Medical Center, Israel.

When Brezis was elected as International Member of the National Academy of Sciences in 2003 he gave the following summary of his research contributions [18]:-
My mathematical research has been devoted to the study of solutions of nonlinear partial differential equations and to a variety of problems in mathematical physics and differential geometry, involving such equations. In the past decade, my students and I have investigated models arising in the Thomas-Fermi theory of atoms and molecules, in the theory of liquid crystals and in superconductors. This includes a detailed mathematical analysis of singularities: line and point defects, Ginsburg-Landau vortices, etc. In the closely related problems of global geometry, blow-up phenomena and the appearance of singularities are associated with critical exponents and lack of compactness in the variational formulation. I have been able to classify all possible singular behaviour in many cases, using new techniques and ideas from various sectors of mathematics: calculus of variations, nonlinear functional analysis, estimates in Sobolev spaces of solutions of nonlinear partial differential equations, Fourier analysis and the topology of Sobolev manifolds.
His outstanding work led to him being awarded a number of prestigious prizes including the Ampère Prize (1985), the Eugène Catalan Prize (1990), and the Leroy P Steele Prize for Lifetime Achievement (2024). For more details of these prizes and Brezis' research contributions which led to the awards, see THIS LINK.

As a Ph.D. advisor, Brezis has a remarkable record. The Mathematics Genealogy Project lists 60 students who have been awarded a Ph.D. with Brezis as their thesis advisor. The most famous is Pierre-Louis Lions who was awarded his Ph.D. in 1979 for his thesis Sur quelques classes d'équations aux dérivees partielles non linéaires et leur résolution numérique Ⓣ. He went on to win a Fields Medal in 1994.

Let us end this biography by quoting the tribute from the Académie des Sciences following Brezis' death in 2024 [19]:-
We are very sad to inform you of the death of Haïm Brezis on 7 July 2024, at the age of eighty. He was elected correspondent on 24 November 1986, and then a member on 13 June 1988, in the Mathematics section and in the Intersection of Applications of Science.

Haïm Brezis's early work focused on the theory of monotone operators. His book "Maximum Monotone Operators and Semigroups of Contractions in Hilbert Spaces" (1973) presents his main results on these operators, which in reality constitute the state of the art at the time. This is practically still the case today, and this remarkable work remains an essential reference for the mathematical community, with applications in unexpected fields.

A second series of his works is devoted to various aspects of variational equations and inequalities. His doctoral thesis, "Unilateral Problems" (1972), in the form of a 168-page article, establishes optimal regularity results for these equations (elliptic, parabolic, or hyperbolic). At the same time, Haïm Brezis also studied semilinear elliptic equations with highly irregular data, in the space of integrable functions or measures. In particular, he obtained crucial results concerning the existence of solutions with optimal conditions. These results, of major influence, are still regularly used, testifying to their relevance and timelessness.

In the 1980s, Haïm Brezis worked on quasi-invariant elliptic equations invariant under the action of a non-compact group, which posed new difficulties. This is the natural framework for many problems in geometry or physics. He developed a method for obtaining solutions for many problems of this type. This approach involves an energy associated with the problem, and showing that it reaches values ​​below a certain critical value makes it possible to overcome the lack of compactness induced by the non-compact group. This magisterial work has had and still has a considerable impact.

In the 1990s, Haïm Brezis explored the Ginzburg-Landau equations (with complex values), which were used in particular in the theory of superconductivity and superfluids. These equations contain a small parameter linked, for example, to phase transition phenomena. Haïm Brezis gave a very precise description of the asymptotic behaviour of solutions when this small parameter tends towards 0 with the appearance of vortices and their properties. His book "Ginzburg Landau Vortices", with Fabrice Bethuel and Frédéric Hélein (1994), contains the fundamental results on this subject. This book has inspired and still inspires a great deal of research and constitutes the essential mathematical reference on the subject.

These topics naturally led Haïm Brezis, starting in the 1990s, to become interested in Sobolev spaces of applications between two manifolds, a theme straddling analysis and geometry. Brezis's profound results on this subject established fundamental properties. For example, with Hoai-Minh Nguyen, he obtained very precise estimates of the Jacobian of a function between two spheres of the same dimension.

Haïm Brezis also did considerable work in the training of researchers, in advanced teaching, and in the dissemination of research.

In France, his Functional Analysis course at Jussieu, which was crowded with students, was packed for years. His book "Functional Analysis - Theory and Applications" (1983), which resulted from it, is considered a bible on the subject. Translated into ten languages, it has contributed greatly to the training of numerous analysts worldwide.

Haïm Brezis created and then directed the book series "Progress in Nonlinear Differential Equations and Their Applications," which has published over a hundred books since 1988. He was editor-in-chief of the Journal of the European Mathematical Society (JEMS) for twelve years (2003-2015). Under his leadership, JEMS became a leading journal. His contribution to our journal "Comptes Rendus Mathématique" and to our institution, through his active participation in numerous committees, has been invaluable.

Haïm Brezis founded an impressive school, having supervised 58 theses and counting more than a thousand descendants. His scientific work and influence have been recognised by numerous distinctions. He was a member or foreign member of nine academies (including the American Academy of Arts and Sciences and the National Academy of Sciences) and a Doctor Honoris Causa or Honorary Professor of eleven universities. The most recent distinction, the prestigious Steele Prize for Lifetime Achievement, was awarded to him in 2024 by the American Mathematical Society in recognition of his entire work.

Haïm Brezis was one of the most influential mathematicians of the last fifty years worldwide. His impact, touching many areas of mathematics, his legacy, and his influence are exceptional.

With our deep regret and sincere greetings,
The Bureau of the French Academy of Sciences.
Other Mathematicians born in France

References (show)

  1. 1985 Prix Ampère (Électricité de France) - Le prix est décerné à M Haïm Brezis, Mathématicien, Professeur à l'Université Pierre-et-Marie-Curie, La Vie des sciences, Académie des sciences (11 January 1985).
    https://archive.wikiwix.com/cache/index2.php?url=https%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k5471020z%2FtexteBrut#federation=archive.wikiwix.com&tab=url
  2. 2024 Prizes, Notices of the American Mathematical Society 71 (4) (2024), 534-557.
  3. H Berestycki, M Bertsch, F E Browder, L Nirenberg, L A Peletier and L Véron (eds.), Perspectives in Nonlinear Partial Differential Equations In Honor of Haïm Brezis (American Mathematical Society, 2007).
  4. H Berestycki, M Bertsch, F E Browder, L Nirenberg, L A Peletier and L Véron, Preface, in Perspectives in Nonlinear Partial Differential Equations In Honor of Haïm Brezis (American Mathematical Society, 2007), vii.
  5. H Berestycki, M Bertsch, F E Browder, L Nirenberg, L A Peletier and L Véron, On Haïm Brezis, in Perspectives in Nonlinear Partial Differential Equations In Honor of Haïm Brezis (American Mathematical Society, 2007), ix-xv.
  6. H Berestycki and J-M Coron, Preface, Chinese Annals of Mathematics 38 (1) (2017), i-viii.
    https://sites.math.rutgers.edu/~brezis/PUBlications/CAMvol38.pdf
  7. H Brezis, Allocution de Haïm Brezis le 22 Juin 2004 à l'Université Pierre et Marie Curie lors de la réeption en l'honneur de son 60eme anniversaire, in Perspectives in Nonlinear Partial Differential Equations In Honor of Haïm Brezis (American Mathematical Society, 2007), xvii-xx.
  8. H Brezis and J Vauthier, Haïm Brezis. Un Mathématicien Juif (Beauchesne, 1999).
  9. B Calvert, Review: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, by Haïm Brezis, Mathematical Reviews MR0348562 (50 #1060).
  10. F Catrina, Review: Functional analysis, Sobolev spaces and partial differential equations, by Haïm Brezis, Mathematical Association of America (28 April 2011).
    https://web.archive.org/web/20151018141846/https://www.maa.org/publications/maa-reviews/functional-analysis-sobolev-spaces-and-partial-differential-equations
  11. A Chinni, Review: Sobolev maps to the circle - from the perspective of analysis, geometry, and topology, by Haïm Brezis and Petru Mironescu, Mathematical Reviews MR4390036.
  12. David Brezis, École Normale Supérieure (2001).
    https://archive.wikiwix.com/cache/index2.php?url=http%3A%2F%2Fwww0.ens.fr%2Fumr8547%2FPersonnels%2FBREZIS.html#federation=archive.wikiwix.com&tab=url
  13. Décès de Haim Brézis, Société Mathématique de France (8 July 2024).
    https://smf.emath.fr/actualites-smf/deces-de-haim-brezis
  14. M Govrin, Speech given by Michal Govrin on 22 Jun 2004 at the Université Pierre et Marie Curie at the reception in honor of Haïm Brezis's 60th birthday, in Perspectives in Nonlinear Partial Differential Equations In Honor of Haïm Brezis (American Mathematical Society, 2007), xxi-xxiii.
  15. M Govrin, Jewish Literary Manifesto (in First Person Feminine), michalgovrin.com (2021).
    https://michalgovrin.com/en/m_essays/jewish-literary-manifesto-in-first-person-feminine/
  16. Haïm Brezis Awarded 2024 Steele Prize for Lifetime Achievement, American Mathematical Society News (5 December 2023).
    https://www.ams.org/news?news_id=7259
  17. Haïm Brézis: Obituary, Académie des Sciences (2024).
    https://www.academie-sciences.fr/en/node/2524
  18. Haïm Brézis: International Member, National Academy of Sciences (2025).
    https://archive.wikiwix.com/cache/index2.php?url=http%3A%2F%2Fwww.nasonline.org%2Fmember-directory%2Fmembers%2F20004883.html#federation=archive.wikiwix.com&tab=url
  19. Haïm Brézis, Académie des Sciences (9 December 2009).
    https://www.academie-sciences.fr/pdf/membre/BrezisH_bio1209.pdf
  20. Haïm Brézis: Membre honoraire 1997, Institut Universitaire de France (2022).
    https://archive.wikiwix.com/cache/index2.php?url=https%3A%2F%2Fwww.iufrance.fr%2Fles-membres-de-liuf%2Fmembre%2F594-haim-brezis.html#federation=archive.wikiwix.com&tab=url
  21. Haïm Brézis: Membre associee, Royal Academy of Science, Letters and Fine Arts of Belgium (5 January 2002).
    https://archive.wikiwix.com/cache/index2.php?url=https%3A%2F%2Facademieroyale.be%2Ffr%2Fl-academie-royale-classes-classe-sciences-membres-detail%2Frelations%2Fhaim-brezis%2F#federation=archive.wikiwix.com&tab=url
  22. Haïm Brézis, mathématicien chevalier de la Légion d'honneur, La France en Israël (11 May 2012).
    http://web.archive.org/web/20160303170918/http://www.ambafrance-il.org/Haim-Brezis-chevalier-de-la-Legion
  23. Laudatio a Monsieur le Professeur Haïm Brezis, de l'Université Pierre et Marie Curie, à l'occasion de remise du titre de Docteur Honoris Causa de l'Université "Alexandru Ioan Cuza" de Iaşi, Université Alexandru Ioan Cuza (28 October 2010).
    https://web.archive.org/web/20130921055721/http://www.uaic.ro/uaic/bin/download/University/doctor_honoris_causa/LaudatioBrezisfinalFR.pdf
  24. J Mawhin, Éloge de Haïm Brezis, La Thérésienne (2025).
    http://web.archive.org/web/20250318073217/https://popups.uliege.be/2593-4228/index.php?id=1889
  25. Mayer L Brezis, Professor of Medicine, University of Jerusalem (2013).
    https://web.archive.org/web/20131020213002/http://www.huji.ac.il/dataj/controller/ihoker/MOP-STAFF_LINK?sno=9844462&Save_t=
  26. Prof Haïm Brézis, Journal of Fixed Point Theory and Applications 15 (1) (2014), 1-2.
  27. Rachel Shlomit Brezis, PhD, Sagol Center for Brain and Mind, Israel (2025).
    https://web.archive.org/web/20180917181840/http://www.sagolcenter.org.il/wp-content/uploads/2016/06/Rachel-Shlomit-Brezis-CV-2016.pdf
  28. V D Radulescu, Review: Functional analysis, Sobolev spaces and partial differential equations, by Haïm Brezis, Mathematical Reviews MR2759829 (2012a:35002).
  29. G Tesxhi, Review: Functional analysis, Sobolev spaces and partial differential equations, by Haïm Brezis, Monatshefte für Mathematik 165 (3-4) (2012), 601-602.
  30. Haïm R Brézis, Mathematics Genealogy Project (2025).
    https://www.genealogy.math.ndsu.nodak.edu/id.php?id=39923&fChrono=1

Additional Resources (show)

Other pages about Haïm Brezis:

  1. Haïm Brezis Books
  2. Haïm Brezis Prizes

Other websites about Haïm Brezis:

  1. Mathematical Genealogy Project
  2. MathSciNet Author profile
  3. zbMATH entry
Written by J J O'Connor and E F Robertson
Last Update September 2025