1.1. The Peccot Lectures.

Since 1885, thanks to an endowment from the family of the mathematician Claude-Antoine Peccot, the Collège de France has rewarded each year young mathematicians under 30 years of age who have distinguished themselves in the field of theoretical or applied mathematics.

The Peccot course is a one-semester mathematics course at the Collège de France. Each course is given by a mathematician under the age of thirty who has distinguished themselves by their promising first work. The course consists of a series of lectures which allow the winner to present their recent research. Being a lecturer on a Peccot course is a distinction that often foreshadows an exceptional scientific career; among them are future holders of the Fields medal, the Abel prize, academicians and professors at the Collège de France. The first to deliver the Cours Peccot were Émile Borel (1899-1902), Henri Lebesgue (1902-03) and René Baire (1903-04).

1.2. Haïm Brezis's Peccot Lectures.

Haïm Brezis delivered the Peccot lectures at the Collège de France on Les semigroupes de contractions non linéaires in 1973.

2.1. The Petit d'Ormoy, Carrière, Thébault Prize.

The Petit d'Ormoy, Carrière, Thébault Prize is a mathematics prize of the French Academy of Sciences. It has been awarded in this form since 1943.

2.2. Haïm Brezis awarded the Prize.

Haïm Brezis was awarded the Petit d'Ormoy, Carrière, Thébault Prize in 1976.

3.1. The Ampère Prize.

The Ampère Prize of Electricity of France is a scientific prize awarded annually by the French Academy of Sciences. Founded in 1974 by Electricity of France in honor of André-Marie Ampère, whose 200th birthday was celebrated in 1975, it rewards one or more French scientists for outstanding research work in the field of mathematics or physics.

3.2. Citation for Ampère Prize to Haim Brezis in 1985.

Haim Brezis is a mathematician, professor at the Pierre and Marie Curie University in Paris.

Haïm Brezis is one of the world's leading specialists in functional analysis, a relatively new discipline currently forging concepts and methods enabling the mathematical attack of profoundly new nonlinear problems, capable of realistically modelling complex mechanical, physical, chemical, and biological situations.

Haïm Brezis' contributions to this discipline are of the utmost importance:

- comprehensive study of the regularity of solutions to variational inequalities for second-order elliptic and parabolic operators;

- resolution of free boundary problems and study of the regularity of this boundary, problems encountered in gas dynamics, plasticity, and the dynamics of multiphase media, etc.;

- systematic study of nonlinear evolution problems - Schrödinger-type equations in particular - and the behaviour of solutions for large timescales;

- completely new and sometimes surprising results through equations generalising Thomas Fermi's equation.

Through his remarkable contributions, which highlight simple, new phenomena, rigorously established using methods of rare elegance, Haïm Brezis has indisputably placed himself among the greatest names in functional analysis of recent decades.

4.1. The Eugène Catalan Prize.

The Eugène Catalan Prize is awarded every five years by the Royal Academy of Science, Letters and Fine Arts of Belgium. The aim of the award is to recognise a scholar who has made important progress in pure mathematics. The prize, created in honour of the mathematician Eugène Charles Catalan, was first given in 1969. The original criteria specified Belgian or French scholars.

4.2. Haim Brezis awarded the Eugène Catalan Prize.

Haim Brezis was awarded the Eugène Catalan Prize by the Royal Academy of Science, Letters and Fine Arts of Belgium in 1990.

5.1. The Ky Fan Award

In the fall of 1999, Ky Fan and his wife, Yu-Fen Fan, made a gift of approximately $1 million to the AMS. The funds will be used to establish the Ky and Yu-Fen Fan Endowment. Income from the endowment will support mathematics in China and mathematically talented high school students in the U.S.

"The gift from Ky and Yu-Fen Fan reflects their commitment to supporting mathematics, particularly in their home country of China, where there is much talent but few resources," said AMS president Felix E Browder. "Their generosity is remarkable."

Funds from the Ky and Yu-Fen Fan Endowment will primarily be devoted to a program for fostering collaborations between Chinese mathematicians and mathematicians in other parts of the world, especially North America. The program will provide grants to Chinese mathematics departments to bring in visitors from the rest of the world as well as grants to North American departments to bring in visitors from China. There will also be support for occasional conferences in China and for improving mathematics library holdings in Chinese institutions. In addition, the endowment will provide small grants to assist programs in the U.S. that nurture mathematically talented high school students. Half of the Fans' gift will go into the endowment, and the other half into a gift annuity (whereby the donor receives an annuity and the unused portion becomes a donation).

Ky Fan is an emeritus professor of mathematics at the University of California, Santa Barbara. Born on September 19, 1914, in Hangchow, China, he received his B.S. degree from Peking University (1936) and his D.Sc. degree from the University of Paris (1941). He was a member of the Institute for Advanced Study in Princeton from 1945 to 1947 and held positions at the University of Notre Dame, Wayne State University, and Northwestern University before going to U.C., Santa Barbara, in 1965. Elected a member of the Academia Sinica in 1964, Fan served as the director of the Institute of Mathematics there from 1978 to 1984.

Fan was a student and collaborator of M Fréchet and was also influenced by John von Neumann and Hermann Weyl. The author of approximately 130 papers, Fan made fundamental contributions to operator and matrix theory, convex analysis and inequalities, linear and nonlinear programming, topology and fixed point theory, and topological groups. His work in fixed point theory, in addition to influencing nonlinear functional analysis, has found wide application in mathematical economics and game theory, potential theory, calculus of variations, and differential equations.

"The Ky and Yu-Fen Fan Endowment addresses groups that have deep reservoirs of talent in need of cultivation and resources," Browder said. "The AMS is profoundly grateful to Ky and Yu-Fen Fan. The impact of their generosity will be felt for years to come."

5.2. Ky Fan Award to Haim Brezis.

Haïm Brezis received the Ky Fan Award from the American Mathematical Society in 2001.

6.1. The Steele Prize.

The Leroy P Steele Prize was established by the American Mathematical Society in 1970 in honour of George David Birkhoff, William Fogg Osgood, and William Caspar Graustein. It was endowed under the terms of a bequest from Leroy P Steele. From 1970 to 1976 one or more prizes were awarded each year for outstanding published mathematical research; most favourable consideration was given to papers distinguished for their exposition and covering broad areas of mathematics. In 1977 the Council of the American Mathematical Society modified the terms under which the prizes were awarded. In 1993, the Council formalised three categories of the prize by naming each of them: (1) The Leroy P Steele Prize for Lifetime Achievement; (2) The Leroy P Steele Prize for Mathematical Exposition; and (3) The Leroy P Steele Prize for Seminal Contribution to Research.

6.2. Haim Brezis wins the Steele Prize for Lifetime Achievement.

The 2024 Steele Prize for Lifetime Achievement is awarded to Haïm Brezis:-

... for his outstanding and seminal contributions in several fields of Nonlinear Functional Analysis and Partial Differential Equations, and for his remarkable influence in mathematics, in particular through his exceptional training of PhD students. His book "Functional Analysis, Sobolev Spaces and Partial Differential Equations" has been used for forty years as a classical textbook in many universities worldwide; first published in French in 1983, it has been reprinted, expanded, and translated into eight languages.

6.3. Citation for Haim Brezis.

The 2024 Steele Prize for Lifetime Achievement is awarded to Haïm Brezis for his outstanding and seminal contributions in several fields of Nonlinear Functional Analysis and Partial Differential Equations, and for his remarkable influence in mathematics, in particular through his exceptional training of PhD students.

Brezis has greatly contributed to leading and shaping the fields of Nonlinear Analysis and Partial Differential Equations and how the main questions are posed. He has started and animated several different areas of analysis, for example maximal monotone operators, gradient flows and weak notions of degree. His papers contain gems with beautiful unexpected statements. His philosophy of action, which always starts with simple and easily understandable questions, has been adopted by many of his numerous students. Although a pure mathematician at heart, his mathematics has often been motivated by, or found its way back to, applications, for example to liquid crystals and to Ginzburg-Landau vortices in the theory of superconductivity.

Brezis is a fine lecturer and expositor. His beautiful book on Functional Analysis, Sobolev Spaces and Partial Differential Equations, first published in French in 1983 and then reprinted and expanded along the years and translated into eight different languages, has been used for forty years as a classical textbook in many universities worldwide.

The legacy of Haïm Brezis is measured not only by his work but also by that of his students and associates, many of whom have had, and continue to have, outstanding careers. He has supervised 58 PhD theses. In addition to his role as a teacher, leader and researcher, he has contributed greatly to the community through his many editorial roles and through influential posts such as Vice-President of the American Mathematical Society.

6.4. Biographical Note for Haim Brezis.

Haïm Brezis was born in 1944 in Riom-es-Montagnes, a hamlet in the mountainous Auvergne region of France. His parents were Jewish refugees hiding under precarious conditions in the woods surrounding this hamlet. After WWII they settled in Paris, where Haïm received his entire education in various institutions of the celebrated Latin Quarter. He earned a Doctorate in 1971 from the Université de Paris, under the supervision of G Choquet and J L Lions.

In 1972 he was appointed at the Université Paris VI (Associate Professor 1972-1976, Full Professor 1976-2007, Emeritus since 2008).

In 1987 he accepted an offer from Rutgers as Distinguished Visiting Professor for several months every year; he held it until 2022 when he became Emeritus. He was also a regular visitor at the Technion (2008-2022).

Brezis is a member of Académie des Sciences, Paris. He is a foreign member of the American Academy of Arts and Sciences, the National Academy of Sciences, USA, and several European national academies (Belgium, Italy, Romania, Spain).

He received Honorary degrees from various universities in Belgium, Greece, Israel, Italy, Netherlands, Romania, and Spain. He holds a Honorary Professorship from the Institute of Mathematics, Academia Sinica, Beijing, from Fudan University, and from Beijing Normal University.

6.5. Response from Haim Brezis.

I am delighted to have been awarded the 2024 Steele Prize for lifetime achievement and honoured by the generous citation.

My encounter with Partial Differential Equations (PDEs) was accidental. During the 1960's French academia (perhaps still under the influence of Bourbaki) largely overlooked PDEs, with the notable exception of J-L Lions. Given my interest in Nonlinear Functional Analysis, my PhD advisor, Choquet, gave me papers by F. Browder to read. Some of them contained applications to PDEs that I did not yet understand, and so I taught myself basic PDEs. With Lions' support, I later deepened my understanding of the field under three leading experts who became my mentors and collaborators: Browder (Chicago), Nirenberg (NYU), and Stampacchia (Pisa).

Later, in the early 1970s, I witnessed in France a revolution: Students were encouraged to learn PDEs because of their potential applications to many real-life problems. I received a position at the University of Paris where I taught PDEs to large groups of outstanding students (including from École Normale Supérieure and Polytechnique). I had to generate open problems for my PhD students. Many of them and their descendants have become leaders in PDEs and adjacent fields. I was fortunate to work with brilliant collaborators to whom I am immensely grateful. Their list is much too long to be inserted in the limited space I have here.

Today, PDEs are thriving in France and worldwide; many new results and research directions have emerged, and some challenging open problems remain. Looking back, fifty years later, I am proud to have been part of this success story.

Member, Académie des Sciences Paris, 1988.

Member, Academia Europaea, 1989.

Foreign member, Romanian Academy, 1993.

Foreign member, American Academy of Arts and Sciences, 1994.

Foreign member, Royal Academy of Sciences, Madrid, 2000.

Foreign member, Royal Academy of Sciences, Belgium, 2002.

Foreign member, National Academy of Sciences, USA, 2003.

Foreign member, Accademia dei Lincei, 2010.

Foreign member, Società Nazionale di Scienze, Lettere e Arti, Napoli, 2019.

Doctor Honoris Causa, Catholic University of Louvain-la Neuve, 1996.

Doctor Honoris Causa, Technion, Haifa, 1998.

Honorary Professor, Academia Sinica, Beijing, 1999.

Honorary Professor, Fudan University, Shanghai, 1999.

Doctor Honoris Causa, University of Bucharest, 2000.

Doctor Honoris Causa, Universidad Autonoma de Madrid, 2001.

Doctor Honoris Causa, University of Leiden, 2002.

Honorary Professor, Beijing Normal University, 2005.

Doctor Honoris Causa, SISSA (Scuola Intern. Sup. Studi Avanzati), Italy, 2006.

Doctor Honoris Causa, University of Iasi, Romania, 2010.

Doctor Honoris Causa, National Technical University, Athens, 2016.

M Haïm Brézis is Professor Emeritus at Pierre and Marie Curie University and Distinguished Visiting Professor at Rutgers University in New Jersey (SUA) and the Technion in Haifa, Israel.

Professor Haïm Brézis is one of the most important mathematicians of recent decades, and his research has profoundly influenced the theory of nonlinear partial differential equations. He ranks among the greatest mathematicians of the century who laid the foundations of this field, which is so important for mathematical physics, alongside Jacques Hadamard, Jean Leray, Juliusz Shauder, Jacques-Louis Lions, Felix Browder, Luis Nirenberg, Tosio Kato, and Kosaku Yosida. His work on nonlinear equations with monotone and pseudo-monotonic operators, nonlinear contraction semigroups, variational inequalities, and, more recently, the variational theory of Ginzburg-Landau equations, has profoundly influenced many mathematicians, including those at Iasi.

His treatises on functional analysis and the theory of maximally monotone operators in Hilbert spaces are undoubtedly among the most influential monographs in the field, rivalling in popularity those of Hille-Yosida and Kosaku Yosida.

In the early 1960s, nonlinear functional analysis made remarkable progress thanks to George Minty's (1962) work on the equivalence in Hilbert spaces between the maximal monotonicity of the nonlinear operator A and the surjection of the operator I+A. This spectacular result, developed by Felix Browder for reflexive spaces, proved to be decisive for the theory of the existence of elliptic nonlinear equations, being the starting point for the theory of nonlinear evolution equations, established by Yukio Komura and Tosio Kato (1967) and subsequently developed by many mathematicians, including Haïm Brezis.

In 1967, a young mathematician from Paris, Haïm Brézis, announced and published a profound extension of the theory of maximal monotone operators for a class of operators called pseudo-monotonic, which had a great impact on the mathematical community. This was the starting point of a remarkable scientific career, marked by many other equally spectacular discoveries, including: the regularity of solutions to elliptic and parabolic variational inequalities with a profound impact on the theory of free boundary problems, the regularising effect of contraction semigroups associated with subgradient-type operators, the semigroup realisation of the equation of porous media, the Ginzburg-Landau equation, the theory of periodic solutions for the nonlinear wave equation. To all this we add the important results of convex analysis, the theory of adjacent spaces and domains. His results are remarkable for the subtlety of the idea, for the beauty and for the perfection of the argument. Everything that bears the signature of Haïm Brezis has the consistency and durability of text chiselled in stone.
...
Professor Haïm Brézis is not only a great scholar, but also a conscience of the civilised world, taking a public stand on some of the serious problems of contemporary society. It should be emphasised that Haïm Brezis is linked to Romania both by his family origins and by the established relations with the academic community and Romanian mathematicians. He is particularly linked to the "Alexandru Ioan Cuza" University, which he visited in 1993.

Given his brilliant personality and his special relationship with the "Alexandru Ioan Cuza" University, we have the joy and honour to solemnly confer, in this anniversary year, the title of Doctor Honoris Causa on Professor Haïm Brezis.