It was to be my only literary success.

... was not enough to draw the attention of Émile Mâle to me, who, from a great height, let fall on the best in the class a small part of his knowledge of Latin and of archaeological science.

It is especially in plane geometry that I excelled. I visualise poorly in space, and I do not have the memory to have been impassioned by algebra, which did not prevent me ... to be also, in this discipline, to be at the top of my class. I was passionate about plane geometry; certain theorems were revelations for me: the notion of the power of a point in relation to a circle, that of a radical axis, that of the transformation of a figure by inversion, delighted me. What admirable methods for finding new theorems! I always found the problems easy that were presented to me. I was hoping to have the mathematics prize at the Concours Général en rhetorique; I did have it, and have not had the opportunity to participate in this competition since. Yet I make a huge difference between what I was when I was in literary studies and what I was going to be the following year.

On leaving rhetoric, after having learned the elements of trigonometry during the summer, I entered the Lycée Saint-Louis, in a class of elementary mathematics called higher .... My father thought that to prepare for the École Polytechnique, and possibly École Normale Supérieure, one should not waste time. I could prepare well for the baccalaureate in philosophy while doing mathematics in the lycée. In addition, as far as mathematics was concerned, I would have wasted my time if I had not skipped the preparatory class for the baccalaureate. But the upper class was of a higher standard in Louis Le Grand than in Saint Louis, and, in order not to require excessive effort from me, my father put me in Saint Louis. I have sometimes wondered if it would not have been better if I had stayed at Louis Le Grand. I'm sure I would have easily taken the mathematics class.

The most remarkable of our professors was certainly Georges Humbert, and the course of analysis he gave us was the one from which I benefited the most. His presentations were always remarkably clear. My fellow students even claimed that it was too clear, and that he avoided difficulties that we noticed when studying the course on the sheets that were distributed to us. I only saw once, about the fundamental Jacobian theorem, that this was true. Among our other professors, I will name only Henri Poincaré and Henri Becquerel. The first was, in theory, a professor of astronomy; but the course was given by a substitute, except for the beginning. Poincaré himself taught a lesson on spherical trigonometry and two lessons on error theory.

At the École des Mines, I neglected many of my courses in order to attend mathematics courses at the Sorbonne and at the College of France. I attended Humbert's course for three years at the College of France. He is known for having been a marvellous calculator, and he contributed to the progress of classical mathematics. I was especially inclined towards the study of modern mathematics, and it was not Humbert's course that I profited from the most. It was also not Borel's, which I gave up on after 4 or 5 lectures, because he spent too much time on what was obvious. On the other hand, I profited a great deal from Emile Picard's course, which I attended for one year, and from Hadamard's, which I attended for three years. It was in Hadamard's course, in 1910, that I found my thesis topic.

A tutor's task was to help the students to understand the professors' lectures, and hence Lévy was well acquainted with the curriculum and the methods of instruction at the Polytechnique before his own appointment as professor.

... done in the spirit of Volterra. This involved extending the calculus of functions of a real variable to spaces where the points are curves, surfaces, sequences or functions.

... notions of calculus of probabilities and the role of Gaussian law in the theory of errors.

At that time there was no mathematical theory of probability - only a collection of small computational problems. Now it is a fully-fledged branch of mathematics using techniques from all branches of modern analysis and making its own contribution of ideas, problems, results and useful machinery to be applied elsewhere. If there is one person who has influenced the establishment and growth of probability theory more than any other, that person must be Paul Lévy.

Lévy's lecture notes at the École Polytchnique in 1919 nicely document his beginnings as a probabilist. Though they are evidently not developed in the detail needed (we must not forget that Lévy took the charge of the teaching at the drop of a hat), they indicate how Lévy perceived probability on the eve of his exceptional second mathematical career. They contain the seeds of the studies Lévy would pursue with virtuosity for 40 years: convergence in distribution, sums of random variables, the connection between mathematical probability and physics. They testify to what Lévy said about himself 50 years later in an interview to the French radio France Culture: "I have the feeling of being a mathematician, neither superior nor inferior to others, but different from them."

Paul Lévy was a painter in the probabilistic world. Like the very great painting geniuses, his palette was his own and his paintings transmuted forever our vision of reality. ... His three main, somewhat overlapping, periods were: the limit laws period, the great period of additive processes and of martingales painted in pathtime colours, and the Brownian pathfinder period.

I just learned that I'm not a professor at the École Polytechnique anymore. In early November, a postal check issued for my October salary was returned to me as "not sufficient funds". I wrote to the administration of the École to ask for an explanation. On 24 November, I received a copy of a decision dated 30 June by which the École transferred me to the Corps des Mines on 1 October; it is also apparent from the text of the decision that on 29 April the Director of the École knew already that I was not to be "re-invested in my job" and asked the Minister how long he had to pay me!!! And all this is legal, if one considers as legal a 1941 regulation subjecting teachers to a decennial re-election, regardless of acquired rights. And now what will the Corps des Mines do with me, having left the place in 1913, and cannot give me work for which I have no longer any expertise and, in addition, with a delay of two months before taking up the post. Will it pay me? ... I deeply hope that 1944 will see the end of these miseries.

In 1940, Lévy had become one of the world major specialists of stochastic processes. And then suddenly, the 55 years old mathematician who had produced a torrential flow of publications for more than 20 years was deprived of the possibility to send articles to journals. Moreover, as we have seen, his teaching tasks were also gradually reduced, and for some months in 1943, living in precarious silence in the Italian zone near Grenoble, Paul Lévy had nothing to do other than mathematics while waiting for better days. His luck was to remain in contact with Fréchet who played for him the role of a private registration journal and could also sometimes serve as a hub between Lévy and other mathematicians.

[Lévy] was a very modest man while believing fully in the power of rational thought. ... whenever I pass by the Luxembourg gardens, I still see us there strolling, sitting in the sun on a bench; I still hear him speaking carefully his thoughts. I have known a great man.

Paul Lévy was one of the greatest mathematicians of his time and it is an honour for the Corps des Mines to have facilitated the full realization of his exceptional gifts. As a scholar, he was undoubtedly one of the last examples of absolute individualism: he was a solitary researcher who was only concerned with posing problems that interested him and pursuing their solution through only work of interior reflection. He read very little of the work of others, he did not participate in international congresses, except exceptionally at the end of his life. His working methods, artisanal one might say, had their drawbacks: he often found, without knowing it, already known results; more often still, he discovered important results without giving them the necessary publicity, sometimes because he believed them already known. It cannot be denied that there has been wasted effort, but the counterpart has often been admirable: it is the profound originality of a thought indifferent to fashions and schools which did not hesitate to embark on absolutely new paths because he had no fear of solitude. Thus, after having been one of the main precursors of functional analysis, Paul Lévy was the great creator of the theory of probability. It can be said that most of the essential concepts of this theory derive from him.

His teaching at the École Polytechnique, which was of exceptional duration, left a deep mark on his innumerable students: they saw in it a model of conciseness, a requirement vis-à-vis the reader who must recognize all the difficulties hidden in a laconic text; in short, an admirable piece of intellectual gymnastics. Let us add for the record that this very classic course which was little modified until 1957 did not mean that Paul Lévy was losing interest in modern developments in mathematics since he had the courage and the elegance to undertake, in the last two years of his teaching, a redesign of his course to introduce the most recent language and methods.

Finally, we would like to evoke a personal memory: Paul Lévy spoke to me one day about how he chose the questions on which he wanted to focus his research: "I am asking myself a not too difficult problem," he said to me, "so as not to break my teeth in front of an excess of difficulties, but all the same to have to make a big effort which occupies me and gives me the satisfaction of finding something." We will admire this modesty mixed with legitimate pride. These "not too difficult problems" were generally new avenues open to the human mind.