French mathematician Yves Meyer was today awarded the 2017 Abel Prize for his work on wavelets, a mathematical theory with applications in data compression, medical imaging and the detection of gravitational waves.

Meyer, 77, will receive 6 million Norwegian krone (about £600,000) for the prize, which recognises outstanding contributions to mathematics and is awarded by the Norwegian Academy of Science and Letters.

The Abel Prize has been awarded annually since 2003 and was last year won by Briton Andrew Wiles for his work on solving Fermat’s Last Theorem. It is considered by many to be a maths equivalent of the Nobel Prize, which has no prize for mathematics.

The Norwegian Academy released the following biography of Meyer this morning, written by Philip Ball, which explains his work in an accessible way. I’m reprinting it here in full.

A biography of Yves Meyer

Yves Meyer, professor emeritus at the École normale supérieure Paris-Saclay in France, proves that, in contrast to what F. Scott Fitzgerald said about American lives; in mathematics a life can indeed have a second act, and perhaps even several more. Having made important contributions in the field of number theory early in his career, Meyer’s boundless energy and curiosity prompted him to work on methods for breaking down complex mathematical objects into simpler wavelike components – a topic called harmonic analysis. This led him in turn to help construct a theory for analysing complicated signals, with important ramifications for computer and information technologies. Then he moved on again to tackle fundamental problems in the mathematics of fluid flow.

That tendency to cross boundaries was with him from the start. Born on 19 July 1939 of French nationality, he grew up in Tunis on the North African coast. “The Tunis of my childhood was a melting pot where people from all over the Mediterranean had found sanctuary,” he said in a 2011 interview. “As a child I was obsessed by the desire of crossing the frontiers between these distinct ethnic groups.”

Meyer entered the élite École normale supérieure de la rue d’Ulm in Paris in 1957, coming first in theentrance examination. “If you enter ENSUlm, you know that you are giving up money and power,” he later said. “It is a choice of life. Your life will be devoted to acquiring and transmitting knowledge.”

After graduating, Meyer completed his military service as a teacher in a military school. But despite his deep commitment to education and his students, he wasn’t suited to the role. “A good teacher needs to be much more methodical and organised than I was,” he admits. Moreover, he was uncomfortable with being the one who was “always right”.“To do research,” Meyer has said, “is to be ignorant most of the time and often to make mistakes.” Nevertheless, he feels his experience of high school teaching shaped his life: “I understood that I was more happy to share than to possess.”

He joined the University of Strasbourg as a teaching assistant, and in 1966 he was awarded a PhD there – officially under Jean-Pierre Kahane, but Meyer assertsthat, like some others in France at that time, he essentially supervised himself. He became a professor of mathematics first at the Université Paris-Sud (as it is now known), then the École Polytechnique and the Université Paris-Dauphine. He moved to the ENS Cachan (recently renamed the ENS Paris-Saclay) in 1995, where he worked at the Centre of Mathematics and its Applications (CMLA) until formally retiring in 2008. But he is still an associate member of the research centre.

Searching for structure

Yves Meyer’s work has, in the most general terms, been concerned with understanding mathematical functions with complex and changing forms: a character that can be described by so-called partial differential equations. Fluid flow, for example, is described by a set of such equations called the Navier- Stokes equations, and in the 1990s Meyer helped to elucidate particular solutions to them – a topic that ranks among the biggest challenges in maths.



Meyer’s interest in what might be called the structures and regularities of complicated mathematical objects led him in the 1960s to a theory of “model sets”: a means of describing arrays of objects that lack the perfect regularity and symmetry of crystal lattices. This work, which arose from number theory, provided the underpinning theory for materials called quasicrystals, first identified in metal alloys in 1982 but prefigured by quasi-regular tiling schemes identified by mathematical physicist Roger Penrose in 1974. The discovery of quasicrystals by materials scientist Dan Shechtman earned him the 2011 Nobel Prize in chemistry. Meyer has sustained his interest in quasicrystals, and together with Basarab Matei in 2010 he helped to elucidate their mathematical structure.

In the 1970s Meyer made profound contributions to the field of harmonic analysis, which seeks to decompose complex functions and signals into components made of simple waves. Along with Ronald Coifman and Alan McIntosh, he solved a long-standing problem in the field in 1982 by proving a theorem about a construction called the Cauchy integral operator. This interest in harmonic decomposition led Meyer into wavelet theory, which enables complex signals to be “atomised” into a kind of mathematical particle called a wavelet.

Wavelet theory began with the work of, among others, physics Nobel laureates Eugene Wigner and Dennis Gabor, geophysicist Jean Morlet, theoretical physicist Alex Grossmann, and mathematician Jan-Olov Strömberg. During a conversation over the photocopier at the École Polytechnique in 1984, Meyer was handed a paper on the subject by Grossmann and Morlet, and was captivated. “I took the first train to Marseilles, where I met Ingrid Daubechies, Alex Grossmann and Jean Morlet”, he says. “It was like a fairy tale. I felt I had finally found my home.”

Breaking down complexity

From the mid-1980s, in what he called a “second scientific life”, Meyer, together with Daubechies and Coifman, brought together earlier work on wavelets into a unified picture. In particular, Meyer showed how to relate Grossmann and Morlet’s wavelets to the work of Argentinian mathematician Alberto Calderón, which had supplied the basis for some of Meyer’s most significant contributions to harmonic analysis. In 1986 Meyer and Pierre Gilles Lemarié-Rieusset showed that wavelets may form mutually independent sets of mathematical objects called orthogonal bases.



Coifman, Daubechies and Stéphane Mallat went on to develop applications to many problems in signal and image processing. Wavelet theory is now omnipresent in many such technologies. Wavelet analysis of images and sounds allows them to be broken down into mathematical fragments that capture the irregularities of the pattern using smooth, “well-behaved” mathematical functions. This decomposition is important for image compression in computer science, being used for example in the JPEG 2000 format. Wavelets are also useful for characterising objects with very complex shapes, such as so-called multifractals, and Meyer says that they prompted his interest in the Navier- Stokes equations in the mid-1990s.

In the past twenty years Meyer’s passion for the structure of oscillating patterns has led him to contribute to the success of the Herschel deep-space telescope mission, and he is working on algorithms to detect cosmic gravitational waves. Meyer’s contribution to image processing is also wide-ranging. In 2001 he proposed a mathematical theory to decompose any image into a “cartoon” and a “texture”. This “cartoon plus texture” algorithm is now routinely used in criminal investigations to extract digital fingerprints from a complex background.

In such ways, Meyer’s work has a relevance extending from theoretical areas of mathematics such as harmonic analysis to the development of practical tools in computer and information science. As such, it is a perfect example of the claim that work in pure mathematics often turns out to have important and useful real-world applications.

An intellectual nomad

Meyer is a member of the French Academy of Science and an honorary member of the American Academy of Arts and Sciences. His previous prizes include the Salem (1970) and Gauss (2010) prizes, the latter awarded jointly by the International Mathematical Union and the German Mathematical Society for advances in mathematics that have had an impact outside the field. The diversity of his work, reflected in its broad range of application, reflects his conviction that intellectual vitality is kept alive by facing fresh challenges. He has been quoted as saying that when you become too much an expert in a field then you should leave it – but he is wary of sounding arrogant here. “I am not smarter than my more stable colleagues,” he says simply. “I have always been a nomad – intellectually and institutionally.”

Some feel that Meyer has not yet had the recognition his profound achievements warrant, perhaps because he has been so selfless in promoting the careers of others and in devoting himself to mathematical education as well as research. “The progress of mathematics is a collective enterprise,” he has said. “All of us are needed.”

He has inspired a generation of mathematicians who have gone on to make important contributions in their own right. His collaborator on wavelet theory Stéphane Mallat calls him a “visionary” whose work cannot be labelled either pure or applied mathematics, nor computer science either, but simply “amazing”. His students and colleagues speak of his insatiable curiosity, energy, generosity and openness to other fields. “You must dig deeply into your own self in order to do something as difficult as research in mathematics,” Meyer claims. “You need to believe that you possess a treasure hidden in the depths of your mind, a treasure which has to be unveiled.”

I blog about maths for The Guardian here. I also have a puzzle blog for The Guardian, in which I set a puzzle every two weeks. Here’s the last one. My puzzle book Can You Solve My Problems? is just out in the US. It is already out in the UK with a slightly different subtitle.