**Jacques-Louis Lions** was a French mathematician who produced an enormous volume of original work in many different areas.

- Lions was deeply attached to the town that he grew up in, and it always remained as a place to return to whenever possible throughout his life.
- In 1946 Lions left the Collège de Grasse and studied for one year at the Lycée Félix-Faure in Nice.
- Most students from the École Normale Supérieure went on to become school teachers but Lions, and his friend and fellow student Bernard Malgrange, decided that they wanted to become university teachers.
- Spending 1950-51 at the École Normale Supérieure, Lions was awarded a grant from the National Centre for Scientific Research to enable him to undertake doctoral studies which he did at the University of Nancy under the supervision of Laurent Schwartz.
- In becoming a student of Schwartz, Lions was being supervised by an outstanding mathematician who had the previous year won a Fields medal.
- Lions was one of several students who Schwartz directed to take this new approach and his doctoral thesis developed what has become the standard variational theory of linear elliptic and evolution equations.
- Lions received his Docteur ès sciences in 1954 and he was appointed Maître de Conférences at Nancy.
- During the years 1954 to 1957 Lions held a number of visiting appointments in the United States, India and Japan.
- It is an impossible task to indicate all the areas in which Lions worked, his output was so enormous; Mathematical Reviews lists 529 papers and books under his name.
- We make this point before we say anything about the mathematics he studied since as soon as we mention topics he studied the reader should be aware that Lions would be studying many other problems which we are not mentioning at the same time.
- This said, let us remark that Lions was very fond of collaborating with other mathematicians and during his time at Nancy he was collaborating with several Italian mathematicians.
- The work which Lions did in this area, both by himself and in collaboration with Magenes, was included in their three volume treatise Problèmes aux limites non homogènes et applications Ⓣ(Problems with inhomogeneous boundary and applications).
- Lions followed this pattern when he was appointed Professor in the Faculty of Science of the University of Paris in 1963.
- Although at this stage Lions did not publish on the topic, the lecture notes from graduate courses he gave on numerical analysis began to circulate and be used to set up numerical analysis courses in other institutions.
- In 1966, in addition to his post in the Faculty of Science, Lions became a part-time professor at the École Polytechnique; an appointment he held until 1986.
- One notable feature of this work is that Lions introduces an infinite dimensional version of the Riccati equation in it.
- Let us describe one or two more major treatises by Lions.
- Perhaps the most outstanding contribution by Lions was the vast treatise Mathematical analysis and numerical methods for science and technology which he wrote with Robert Dautray.
- With this incredible output of work it is hard to believe that Lions would have time for anything else.
- Given this unbelievably wide remit, Lions set up Committee 2000 with himself as chairman, setting himself the target of completing the task by the year 2000.
- He succeeded, and the report was handed personally by Lions to President Chirac on 25 January 2000 in a ceremony at the Elysée Palace.
- We have mentioned a few honours that Lions received.
- In 2003 three volumes of 'Selected works of Jacques-Louis Lions' were published.
- In spite of what Lions himself liked to call the 'truly diabolical' complexity of the set of partial differential equations, boundary conditions, transmission conditions, nonlinearities, physical hypotheses, etc., that appeared in those models, Lions, in collaboration with Roger Temam and Shou Hong Wang, was able to study the questions of the existence and uniqueness of solutions, to establish the existence of attractors, and to do a numerical analysis of these models.
- The variety of topics that Lions tackled in the above works is very impressive.
- In a long series of notes published in the Comptes Rendus until 2001, Lions returned to numerical analysis, and in particular to parallel computation and domain decomposition methods.
- Always in search of new subjects, Lions even pursued the study of a problem of dislocation in crystallography, a problem that no one really knew how to tackle.
- One cannot help being struck by the quality, diversity and novelty of the mathematics used in this immense body of work, and by Lions's ability to decipher among the applications some vast areas that had been thought to be inaccessible.
- Like John von Neumann, for whom he expressed profound admiration, Jacques-Louis Lions was a visionary who understood very quickly that the use of increasingly powerful computing tools could revolutionize the modelling of phenomena and improve our knowledge and mastery of the physical world as long as the corresponding mathematics was created and developed.

Born 2 May 1928, Grasse, Alpes-Maritimes, France. Died 17 May 2001, Paris, France.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive