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View one larger picture. Biography Jacques Dixmier 's parents were both school teachers. His father taught languages, French, Latin and Greek.

In , when Jacques was nine years old, the family moved to Versailles. It was in Versailles that Jacques studied for his baccalaureate. The first year that he studied there he had a poor mathematics teacher but that was only for one year and, for every year after that, he had an outstanding mathematics teacher.

In fact he said later in life that it was almost certainly due to the high quality of the mathematics teaching that he decided that mathematics was the subject for him. He said [ 6 ] :- Even there I had a very good teacher in mathematics.

After his baccalaureate, Dixmier remained in Versailles to prepare for his university studies in mathematics. His main teachers were Henri Cartan and Gaston Julia. In fact he was fortunate to have Henri Cartan as a lecturer since he was on the faculty at Strasbourg but he could not return there since the Germans controlled the university. Julia gave a course every year in advanced mathematical analysis. This sort of course But we were very anxious to have a diploma as soon as possible because of the war; you did not know what could happen in a few months!

Julia was an extremely good teacher and we understood him. In fact the level of his course about Hilbert space was not very high but we understood almost everything. As a result, Hilbert space became for me as familiar as ordinary space. That was certainly the reason for my research orientation later on. It is very important to be completely familiar with the basics of your subject. Henri Cartan taught a calculus course but he had modified the course to present it in the style of Bourbaki [ 3 ] :- The main point was to introduce us to so-called modern algebra groups, rings, vector spaces, Therefore, Henri Cartan 's lectures were combining a rather standard course on calculus but in the spirit of the not yet published volume of Bourbaki , entitled 'Functions of a real variable'.

In the more "modern" or "advanced" part, we were told about integers mod p, Grassmann calculus, Fourier transforms, and fixed-point theorems.

Henri Cartan knew how to involve us in the class We were seventeen in the class However, the class was [ 3 ] After consulting the class, he decided to teach a course on Lie groups.

Dixmier joined the resistance which was a dangerous thing to do. He attended a few meetings but was never part of any armed resistance. During the vacation between Dixmier's second and third years the war came to an end. On the night of 4 August , the Gestapo arrested a student who was absent from Rue d'Ulm. Dixmier was there at the time [ 6 ] :- There is something which concerned me personally that I still do not understand. I heard some noise but I did not know what had happened. Two officers of the Gestapo were there.

They shouted out and I was taken completely by surprise. They fired and I don't understand how I was not wounded. They took me and I was sent to detention in an office. They were deported, and Bruhat died at the Buchenwald concentration camp. It was during this year - 46 that he worked on his thesis, advised by Gaston Julia.

Julia also lived in Versailles and his children had been taught by Dixmier's parents. However, Dixmier did not find relations with Julia straightforward [ 6 ] :- I think he was a very good mathematician. He was not an easy person. As you probably know, he was politically at the extreme right and hoped for a German victory during the war. Although Julia did not directly suggest the problem that Dixmier worked on for his thesis, it was Julia 's lectures on Hilbert spaces that inspired him [ 6 ] :- I was certainly inspired by some of the things he had told us - generally speaking, on Hilbert space.

In my thesis, I studied some particular subspaces, non-closed but not arbitrary - very special subspaces; my entire thesis is concerned with this class of subspaces. In - 47 he continued to work at the Centre National de la Recherche Scientifique and was helped in his research by Roger Godement.

However, Godement now was a great help to Dixmier, telling him about unitary representations and showing him results on this topic which he had proved but had not published.

By this time Dixmier was married and his wife continued to work as a secondary school teacher. They had a one room apartment in Paris and travelled a lot to their respective jobs.

He said [ 6 ] :- We travelled a lot and travelling by train from Paris to Toulouse was not easy at all in This was the year that he was invited to become a member of the Bourbaki team [ 6 ] :- One day in , Serre and Samuel , who both knew me, approached me and asked whether I would accept becoming a member of Bourbaki.

At the time, this was extremely flattering; I jumped at it! In a new position was created in Dijon. This was just one of many new positions that were being created around France since there was a large increase in student numbers and the government tried to cope with this increase by expanding the universities. Living in Paris and working in Toulouse was certainly not an ideal thing for anyone to do, so Dixmier decided that, since Dijon was much closer to Paris, he would apply for the position there.

Speaking about the beginning of his time in this position, he said [ 6 ] :- The number of students was enormous. During the first 2 or 3 years, I had students. He spent the rest of his career in Paris. Dixmier wrote some excellent books. Everywhere the concepts studied are presented with the utmost brevity and clarity For the graduate student it is a masterpiece of pedagogical writing, being succinct, wonderfully self-contained and of exceptional precision. Later he worked on enveloping algebras and finally on invariant theory and partition theory.

MathSciNet lists published items for Dixmier up to There his main areas of research are given as 'Functional analysis', 'Nonassociative rings and algebras', and 'Topological groups and Lie groups'.

When writing books, Dixmier liked to follow the style of Bourbaki but when he lectured his style was very different from that of his colleagues. He spoke about this when interviewed [ 6 ] :- I have certainly a philosophy [ about lecturing ] that differs from most of my colleagues. In order to make good talks, I prepared them word for word. Most of my colleagues think that this is a far too formal attitude, that you have to rely on inspiration.

I do not believe that at all. I have often heard the opinion that it is good to get stuck; otherwise students do not understand that there is a real difficulty. I must say, I do not agree at all. I was usually very careful to write in big letters, to avoid talking into the blackboard and so on.

I really wanted to be different from Arnaud Denjoy ; it is said that, during a lecture, he thought a, he said b, he wrote c, and d would have been correct! After the second lecture, I left; it was hopeless for me. Well, not for everyone; Gustave Choquet was a pupil of Denjoy. I know that the written work of Denjoy is very good. But as a teacher, he was terrible. For written text, I must admit that I like the Bourbaki style! During his career, he supervised 20 Ph.

He spent five years at IHES. Here is the publisher's description:- For years, you've been hearing about quantum mechanics, a major 20 th -century discovery, so certain terms have become familiar and they stir your imagination: wave functions, particle interaction, uncertainty principle, Feynman diagrams. At times, you find yourself dreaming about whimsical photons, disturbing experiments and their unexpected results, but you don't have the time to spend hundreds of hours on difficult mathematical and scientific studies that, at best, would make you understand the relevance of Richard Feynman 's quip: "If you think you understand quantum mechanics, you don't understand quantum mechanics.

It gives you a front-row seat in the quantic theatre, and you'll be amazed at what you see. Dixmier received several prestigious prizes and medals for his outstanding contributions. Author of books used for decades in France as well as Russia and the United States, Jacques Dixmier has been for thirty years at the University Pierre and Marie Curie a generous head of the school, who has promoted theses that are landmarks.

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## Mathematics Genealogy Project

Jacques Dixmier born is a French mathematician. Dixmier received his Ph. In upon the initiative of Jean-Pierre Serre and Pierre Samuel , Dixmier became a member of Bourbaki , in which he made essential contributions to the Bourbaki volume on Lie algebras. From Wikipedia, the free encyclopedia. French mathematician. This article may be expanded with text translated from the corresponding article in German.

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## Jacques Dixmier

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