Yves François Meyer

Quick Info

19 July 1939
Paris, France

Yves Meyer is a French mathematician who has made major contributions in different areas: for example he solved the Calderón conjecture and founded the mathematical theory of wavelets. He has won major prizes including the Abel Prize and the Princess of Asturias Award.


When Yves Meyer was born, his father was a pharmacist running a pharmacy at 17 boulevard du Temple, Paris. Sadly, however, his mother and father seldom lived together. Yves wrote [34]:-
My father never wished to live with us, even when I was a baby.
The "us" in this quote is Yves, his sister Danièle (born 1938), and his mother. Yves's father enrolled in the Army in 1944 and was sent to the Pharmacy Department in Rabat Hospital in Morocco. Yves, his sister and mother remained in Paris until 1945 when, against the wishes of Yves' father, they went to Rabat. There they lived in one room in a cheap hotel, while Yves' father continued to live and work at Rabat Hospital. After two years in Rabat, Yves' father moved to the Pharmacy Department in Tunis Hospital in Tunisia. This time the whole family travelled together in a slow train, the journey taking almost a week. It was extremely hot in a train without air conditioning [34]:-
In Tunis we lived for two years in a tiny room in a hotel. Afterwards we obtained housing in a suburb of Tunis. Then my father enrolled as a volunteer to Indochina. My mother stayed in Tunis. The French war in Indochina was a tragedy and ended with the Diên Biên Phu disaster. My father returned to Tunis in 1953 and decided finally to try to live with us. I was fourteen.
There were two High Schools in Tunis when Meyer was growing up there, the Collège Sadiki and the Lycée Carnot. He studied at the Lycée Carnot where the [31]:-
... teachers were outstanding. I was mostly attracted by humanities. I eventually switched to mathematics. What certainly played a seminal role in my way of thinking was the everyday life in Tunis. The Tunis of my childhood was a melting pot where people from all over the Mediterranean sea had found a peaceful exile. Italian, Maltese, Sepharades, Berberes, Arabs and French were living together. As a child I was obsessed by the desire of crossing the frontiers between these distinct ethnic groups. But I was limited by my ignorance of the languages which were spoken in the streets of Tunis.
Meyer's mother was his first teacher and, when he attended the Lycée Carnot, she insisted he study Greek and Latin. This had the consequence that he took no science subjects, although he was well educated in mathematics. He loved the humanities but had a special talent for mathematics. Beauty was especially important to him and when he was a teenager he wanted to be an artist [16]:-
I was more interested in humanities. I was in love with Socrates and Plato, and I am still reading Plato right now, day after day, night after night. ... The point is that I am a bad writer. That is my bad side. So, I took mathematics because I was gifted - I was unusually gifted in mathematics. I cannot explain that. I understood mathematics from the inside in a very natural way. When I was in high school, I understood mathematics by myself and not by listening to my teachers.
One event which took place while Meyer was at the Lycée Carnot turned out to be quite influential. Jean-Pierre Kahane visited Tunis and gave a talk to a general audience on his research on trigonometric series. Meyer said [17]:-
He gave a talk - and he is a very good speaker - in such a way that I understood what he was talking about. I was a student in high school. I was truly fascinated. I was fascinated by his personality. ... It was quite exceptional and I would like to say that this influenced my work.
After his father returned to Tunis in 1953 the family lived there until August 1956 when Meyer's father received a position back in France and they went to Strasbourg, the city where his father had been born [34]:-
Compared to Tunis Strasbourg was hell. In 1956 the German influence was still strong. People were speaking a German dialect and had kept some traditional German values of the nineteenth century. I was quite unhappy there but this lasted only one year.
He spent a year in Strasbourg preparing to take the entrance examinations for the Grands Écoles. He was still confused whether he wanted to make a career in mathematics or in the humanities. At this stage he found mathematics easy but the humanities was his real joy. He realised, however, that he had more talents in mathematics than in the humanities and he also felt that mathematics offered more career prospects for him so, rather reluctantly, he chose to specialise in mathematics. He took the entrance examinations for entry into the Grands Écoles and was ranked first. He now had to chose whether to study at the École Normale Supérieure or the École Polytechnique. His mother was in no doubt that he should enter the École Polytechnique which made things hard for him since he preferred the École Normale Supérieure. He said [34]:-
The École Normale Supérieure leads to a professorship either in high school where the alumni are given a position immediately after graduating, or for those who are gifted in research and willing to start a Ph.D. program, eventually to a position at the University. The École Normale Supérieure did not offer a graduate programme. If you enter École Polytechnique you will likely become a manager, an important person. This was not my goal. I was still influenced by Socrates. I did not want to be involved in the industrial development of my country.
He entered the École Normale Supérieure de la Rue d'Ulm in Paris in 1957 along with around 40 science students and 40 arts students. Although he studied mathematics, Meyer was far more at home talking to the students studying humanities. Later he would come to understand that he did not love mathematics at this stage because he found it too easy. He graduated in 1960 and, with the Algerian War taking place between France and Algeria, he undertook three years of military service. He could have avoided being drafted at this time by continuing to study for a doctorate but chose not to take that route. He was, however, strongly opposed to the war which he described as "unjust", so was happy the military offered him an alternative to fighting in Algeria.

Meyer taught at the Prytanée national militaire in La Flèche, a city roughly half way between Paris and the west coast of France, from 1960 to November 1962. This military school provided secondary level education as well as giving preparatory classes for students going on the study at military academies. Perhaps it was hard for someone who found high school and university mathematics so easy to appreciate the difficulties that most students encounter. Perhaps, as he himself said, he was not methodical and organised enough to be a good teacher. Certainly these three years at the Prytanée national militaire convinced him that he was not suited to high school teaching.

In 1963 he married Anne Limpaler; they went on to have two children. In the same year of 1963, after his military service ended, Meyer was appointed as a teaching assistant at the University of Strasbourg. He was one of fourteen teaching assistants in the Department of Mathematics which had fourteen full professors. A teaching assistant undertook research for a doctorate but they were essentially unsupervised finding their own research problems in any area of mathematics. Meyer was very happy there sharing one big room with all the other teaching assistants. After reading Antoni Zygmund's book Trigonometric Series, which he found fascinating, he started working on open problems in this area. He wrote twelve chapters of a thesis on the results he had obtained then asked Pierre Cartier, who was one of the professors at Strasbourg, who would supervise him. Cartier suggested that Meyer contact Jean-Pierre Kahane who was a Professor in the Faculty of Sciences of Paris Sud at Orsay. Carrying his twelve typed chapters, Meyer took the train to Orsay to ask Kahane if he would be his thesis advisor. Kahane told him that, since he had enough material for a doctorate in his twelve chapters, he did no need a thesis advisor.

Meyer submitted his work to the University of Strasbourg for his doctorate. Only at that stage, however, did he discover that Elias Stein, who was working with Alberto Calderón at the University of Chicago, had been working on the same problems and had proved stronger results. During his oral examination, he kept explaining [34]:-
I obtained this theorem but Elias Stein proved a much better result ...
Paul-André Meyer, who had been appointed to the University of Strasbourg in 1964, was on the committee examining Meyer's thesis. He told Meyer:-
Yves, it is not your role to criticise your results, it is the role of the committee.
It was an unfortunate experience but nevertheless he was awarded his doctorate in 1966. In that year he was appointed to a temporary position at the Faculty of Sciences of Paris Sud at Orsay. He now changed research area but again was led to problems by falling in love with a book. This time it was the book Ensembles parfaits et séries trigonométriques written by Jean-Pierre Kahane and Raphaël Salem and published in 1963. Salem had died in 1963 leaving a number theory problem unsolved and Meyer decided to search for a solution. This problem on Diophantine approximation, involving Pisot and Salem numbers, took him three years to solve. It was a remarkable achievement and he was asked to lecture on it in the Section 'Exceptional Sets in Analysis' at the International Congress of Mathematicians held in Nice, France in 1970. He delivered the lecture Nombres de Pisot et Analyse Harmonique . His achievement was also marked with being named Peccot lecturer in 1968-69 and the award of the Salem Prize in 1970.

For more information about the awards to Meyer of Cours Peccot and the Salem Prize, see THIS LINK.

Details of Meyer's work on Diophantine approximations and Pisot numbers are contained in a series of papers, but are also set out in his first book Algebraic numbers and harmonic analysis (1972). It is remarkable that ideas in this book were so far ahead of their time that it was many years later that their full significance became understood. Let us try to explain this. A Delone set DD is a subset of Rn\mathbb{R}^{n} such that there exists a large R0R_{0} such that every ball of radius R0R_{0} contains at least one point of DD and there exists a small R1R_{1} such that every ball of radius R1R_{1} contains at most one point of DD. A Meyer set is a Delone set DD such that the set of differences DDD-D is also a Delone set. Meyer studied Meyer sets (which he called 'model sets') in the 1972 book. In 1974 Roger Penrose, without knowing Meyer's work, introduced the related idea of an aperiodic tiling called a Penrose tiling. Dan Shechtman, also without knowing anything about Meyer's contributions, investigated crystalline materials lacking a periodic structure and published results on these substances called quasicrystals in 1984. Shechtman was awarded the Nobel Prize in Chemistry in 2011 for his discovery of quasicrystals. It was Enrico Bombieri and the Canadian mathematician Robert Moody who realised that Meyer's study of Meyer sets in his 1972 book had set up the mathematical structure of quasicrystals.

In 1982 Meyer, with help from Alan McIntosh and Ronald Coifman, solved what was known as Calderón's conjecture in the theory of singular integral operators. Meyer and Coifman were already trying to solve the conjecture but were not close to the solution. During visits to Coifman at the University of Chicago, Meyer often had useful discussions with Alberto Calderón and Antoni Zygmund. McIntosh became involved in an unexpected way. Meyer's colleagues were protesting a decision by the Minister of Education and were refusing to give graduate courses. Meyer, who always liked to be different, decided he would give a graduate course. Alan McIntosh (1942-2016) was an Australian mathematician who had been awarded a Ph.D. from the University of California, Berkeley in 1966 advised by Frantisek Wolf. He worked at Macquarie University in Sydney, Australia from 1967 but spent the year 1980 as a Professeur Invité at the Université Paris VI. He attended Meyer's graduate course and immediately stood out from the other students who were attending. Meyer had lunch with him once a week and soon discovered that McIntosh was also thinking about Calderón's conjecture. When at Berkeley, McIntosh had been influenced by Tosio Kato and he was looking at a conjecture of Kato's which, if solved, would prove Calderón's conjecture. Meyer said [17]:-
McIntosh explained that the problem I was trying to solve could be rephrased in the terminology of Kato. As soon as I got this information, I discussed with Coifman the possibility of solving the problem through this new formulation. Coifman was excited and wrote a kind of draft version of the solution. Then I returned to France and I managed to find the missing points. So, without my discussion with McIntosh, who knows if the problem would have been solved by me?
Although the mathematics we have described above is a very important contribution by Meyer, nevertheless he is best known for his discovery of wavelets. Before we describe this, however, we should look at how Meyer's career progressed. He had been appointed to the Université d'Orsay in 1966, and remained there when it changed to become the University of Paris-Sud (Paris XI) in 1971. In 1980 he left Orsay to take up an appointment as Professor at the École Polytechnique. After six years in that role, in 1986 he was appointed as a professor at the Centre de Recherche en Mathématiques de la Décision at the Université Paris-IX Dauphine. The Centre is a joint research unit whose research themes cover most of applied mathematics. In 1995 he took up a research position at Centre National de la Recherche Scientifique, holding this for four years before becoming a professor at the École Normale Supérieure de Cachan in 1999. In 2009 he retired, becoming Professor Emeritus at École Normale Supérieure de Cachan.

Let us explain how Meyer became interested in applied mathematics. Up to 1983 he had very much thought of himself as a pure mathematician. By the autumn of that year, now as a professor at the École Polytechnique, he was a colleague of Charles Goulaouic who worked on partial differential equations. Meyer wrote [34]:-
Goulaouic was dying of cancer. My mathematical talent could not even improve the ultrasound examination of his liver. I was helpless in front of such human suffering and distress.
The International Space Station began to be planned in the early 1980s and in 1984 the European Space Agency joined the project. Jacques-Louis Lions asked Meyer to look at the problem of controlling vibrations that the Space Station might encounter; he solved the problem and published his solution in the paper Étude d'un modèle mathématique issu du contrôle des structures déformables (1985) [34]:-
Then I emerged from depression, and understood for the first time in my life that my skills in pure mathematics could be used in real-life problems. In my research I then abolished the frontier between pure and applied mathematics.
Let us explain how Meyer's work [40]:-
... began the "wavelet revolution" of signal processing in the late 1980s and early 1990s, with the wavelet transform now being routinely used in many basic signal processing tasks such as compression (e.g. in the JPEG2000 image compression format) and denoising, as well as more modern applications such as compressed sensing (reconstructing a signal using an unusually small number of measurements).
It began for Meyer standing beside the photocopy machine in the École Polytechnique one day in 1984 waiting for his friend Jean Lascoux, Head of the Department of Mathematical Physics at the École Polytechnique, to finish Xeroxing papers for his colleagues. Turning to Meyer, Lascoux handed him a preprint of a paper by Jean Morlet and Alex Grossmann about wavelets. The paper used results by Calderón that were very familiar to Meyer but authors of the paper [16]:-
... had the fantastic idea that this could be a revolution in signal processing. So that was a fantastic step. I was immediately excited by the paper and by the way it was written. They were working at the Centre de Physique Théorique in Marseille. So I took the first train to Marseille and I joined the group.
There were three in the group at Marseille, Jean Morlet, Alex Grossman and Ingrid Daubechies. Meyer said [17]:-
I discussed with Ingrid and then I had the idea to try to find an orthonormal basis of wavelets, which would make everything trivial on the algorithmic level. It took me three months of intense work but that is nothing compared to the seven years I spent proving Calderón's conjecture. In just three months, I found the basis.
Charles Chui writes in his review of Meyer's book Wavelets and operators (1992) [8]:-
Yves Meyer learnt about the work of Morlet and the Marseille group and immediately recognised the connection of Morlet's algorithm to the notion of resolution of identity in harmonic analysis due to A Calderón in 1964. He then applied the Littlewood-Paley theory to the study of "wavelet decomposition". In this regard, Yves Meyer may be considered as the founder of this mathematical subject, which we call wavelet analysis. Of course, Meyer's profound contribution to wavelet analysis is much more than being a pioneer of this new mathematical field. For the past ten years, he has been totally committed to its development, not only by building the mathematical foundation, but also by actively promoting the field as an interdisciplinary area of research.
For more details about Meyer's work on wavelets, see the information we give about his books on the topic at THIS LINK.

Meyer has been awarded major prizes for his contributions to wavelets. The International Mathematical Union and the Deutsche Mathematiker-Vereinigung awarded Meyer the Carl Friedrich Gauss Prize for Applications of Mathematics in 2010 [7]:-
... for fundamental contributions to number theory, operator theory and harmonic analysis, and his pivotal role in the development of wavelets and multiresolution analysis.
He was awarded the Abel prize in 2017 [1]:-
... for his pivotal role in the development of the mathematical theory of wavelets.
For more information about this award to Meyer, see THIS LINK.

In 2020 Meyer and Ingrid Daubechies were jointly awarded the Princess of Asturias Award for Technical and Scientific Research. The jury gave reasons for their choice [2]:-
Yves Meyer and Ingrid Daubechies have led the development of the modern mathematical theory of wavelets, which are like mathematical heartbeats that enable us to approach Van Gogh and discover his style or to listen to the music enclosed in the apparent noise of the Universe, among many other applications of all kinds. In short, they enable us to visualise what we cannot see and listen to what we cannot hear.
For more information about this award to Meyer, see THIS LINK.

We gave some details above about Meyer's address to the International Congress of Mathematicians in Nice, France, in 1970. He was also an invited speaker at the 1982 Congress in Warsaw in 1983 when he presented the paper Intégrales singulières, opérateurs multilineares, analyse complexe et équations aux dérivées partielles to the 'Real and Functional Analysis' Section. He was also an invited speaker at the 1990 Congress in Kyoto when he gave the talk Wavelets and Applications in the 'Applications of Mathematics to the Sciences' Section.

In addition to the awards mentioned above, Meyer was elected to the Académie des Sciences in 1993, elected as an International Member of the American National Academy of Sciences in 2014, and elected a Foreign Member of the Spanish Academy of Exact, Physical and Natural Sciences in January 2018. He has also been elected as a Foreign Honorary Member of the American Academy of Arts and Sciences in 1994, a fellow of the American Mathematical Society in 2013 and as a Member of the Royal Norwegian Academy of Sciences and Letters.

Let us end this biography with a quote from [62]:-
To his exceptional creative quality, Meyer combines an open and generous personal attitude that deserves to be highlighted as an example for present and future generations.
This quote is illustrated by Meyer's own words [34]:-
The success of my research is mostly due to my friends. Let me single out Raphy Coifman, and praise a friendship over more than forty years. Working with Alexander Olevskii is a blessing. The success of my research is also due to my incredible students. I shared so much with them. We are a family. Alberto Calderón was my spiritual father and my love and gratitude have no bounds.

References (show)

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  30. Mathematicians behind JPEG files honored by Spanish award, phys.org (23 June 2020).
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  56. Yves Meyer, Member, Académie des Sciences.
  57. Yves Meyer élu à la National Academy of Sciences, Académie des Sciences (29 April 2014).
  58. Yves Meyer, Ingrid Daubechies, Terence Tao and Emmanuel Candès, Princess of Asturias Awards (2020).
  59. Yves Meyer receives the Abel Prize, ICIAM Newsletter 5 (2) (April 2017), 6-7.
  60. Yves Meyer Awarded Abel Prize, Notices of the American Mathematical Society 64 (6) (2017), 592-594.
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Written by J J O'Connor and E F Robertson
Last Update March 2024