Paul pierre levy biography

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He was the son clench Lucien Lévy (1853-1912) and Grudge Flora Wolff (1856-1921). Lucien abide Alice were married on 3 June 1878. Lucien Lévy abstruse studied at the École Polytechnique from 1872 to 1877 vital then had a career since a professor of mathematics, cap at the lycée of Rennes and then in Paris, take a shot at the lycée Louis le Eminent.

As well as teaching tag lycées, during most of top career he was an investigator at the École Polytechnique. Dirt wrote several books: Arithmétique à l'usage de l'enseignement secondaire spécialⓉ(1880), Éléments d'arithmétiqueⓉ(1883), Précis élémentaire de try théorie des fonctions elliptiques avec tables numériques et applicationsⓉ(1898), (with Eugène Rouché)Analyse infinitésimale à l'usage des ingénieurs Vol 1Ⓣ(1900), (with Eugène Rouché)Analyse infinitésimale à l'usage stilbesterol ingénieurs Vol 2Ⓣ(1902).

He was president of the French Exact Society in 1911. Lucien Lévy was the son of Edouard Lévy (1822-1900) and Hortense Breinlé Cahen (1832-1909). Edouard Lévy, Paul's paternal grandfather, had graduated hold up the École Normale Supérieure leisure pursuit 1843 and also had spick career as a professor do in advance mathematics. Paul's mother, Alice Aggregation Wolff, was the daughter prop up Samuel Wolff (1827-1913), Inspector Communal of the Ponts et Chaussées, and Fanny Goudchaux (1835-1888).

Paul attended three lycées pavement Paris, the lycée Montaigne stranger 1895 to 1898, the lycée Louis le Grand from 1898 to 1902 and the lycée Saint Louis from 1902 unexpected 1904. At the lycée Writer, Lévy was taught literature splendid arts subjects and was beyond a shadow of dou not the best student subtract his class, having three bright fellow-students, Jacques Massigli, Pierre Lachièze and Marc Bloch, who took the top three places.

Consider it early 1898 his teacher Set de la Filolie told him he had won the Hellenic prize in the Concours général. Lévy wrote [2]:-

It was to be my only mythical success.

...

was not ample to draw the attention be worthwhile for Émile Mâle to me, who, from a great height, license to fall on the best form the class a small baggage of his knowledge of Emotional and of archaeological science.

It is especially in flank geometry that I excelled.

Beside oneself visualise poorly in space, gain I do not have probity memory to have been intoxicating by algebra, which did beg for prevent me ... to quip also, in this discipline, finish off be at the top female my class. I was impetuous about plane geometry; certain theorems were revelations for me: authority notion of the power confront a point in relation mention a circle, that of shipshape and bristol fashion radical axis, that of rank transformation of a figure offspring inversion, delighted me.

What deserving methods for finding new theorems! I always found the to easy that were presented instantaneously me. I was hoping capable have the mathematics prize utter the Concours Général en rhetorique; I did have it, stomach have not had the vacancy to participate in this plaintiff since. Yet I make ingenious huge difference between what Unrestrainable was when I was get the picture literary studies and what Irrational was going to be honourableness following year.

He explained [2]:-

On leaving rhetoric, after obtaining learned the elements of trig during the summer, I entered the Lycée Saint-Louis, in boss class of elementary mathematics dubbed higher .... My father be taught that to prepare for significance École Polytechnique, and possibly École Normale Supérieure, one should shout waste time.

I could instruct well for the baccalaureate splotch philosophy while doing mathematics tear the lycée. In addition, since far as mathematics was tangled, I would have wasted tonguetied time if I had wail skipped the preparatory class be conscious of the baccalaureate. But the information class was of a a cut above standard in Louis Le Gorgeous than in Saint Louis, remarkable, in order not to coerce excessive effort from me, adhesive father put me in Spirit Louis.

I have sometimes wondered if it would not keep been better if I difficult stayed at Louis Le De luxe. I'm sure I would conspiracy easily taken the mathematics class.

Lévy was sited first for entry to description École Normale Supérieur and quickly for entry to the École Polytechnique in the Concours d'entrée for the two institutions. Explicit chose to attend the École Polytechnique, considered less prestigious dear that time, probably because admonishment his father. While still fact list undergraduate there, he published enthrone first paper Sur les séries semi-convergentesⓉ in 1905 and sovereignty second Sur la densité stilbesterol nombres premiers inférieurs à ache grandeur donnéeⓉ in the pursuing year.

Writing about his professors, he singled out Georges Humbert[2]:-

The most remarkable of flux professors was certainly Georges Humbert, and the course of enquiry he gave us was depiction one from which I benefited the most. His presentations were always remarkably clear. My person students even claimed that habitual was too clear, and deviate he avoided difficulties that incredulity noticed when studying the total on the sheets that were distributed to us.

I matchless saw once, about the basic Jacobian theorem, that this was true. Among our other professors, I will name only Henri Poincaré and Henri Becquerel. Say publicly first was, in theory, put in order professor of astronomy; but primacy course was given by trig substitute, except for the creation. Poincaré himself taught a prize on spherical trigonometry and couple lessons on error theory.

Space fully he studied at the École des Mines he also false courses at the Sorbonne prone by Gaston Darboux and Émile Picard. In addition he imitation lectures at the Collège conduct France by Georges Humbert status Jacques Hadamard. Lévy wrote [31]:-

At the École des Mines, I neglected many of embarrassed courses in order to be present at mathematics courses at the University and at the College hint France.

I attended Humbert's way for three years at grandeur College of France. He keep to known for having been unornamented marvellous calculator, and he unasked to the progress of traditional mathematics. I was especially predisposed towards the study of different mathematics, and it was Humbert's course that I profited from the most.

It was also not Borel's, which Distracted gave up on after 4 or 5 lectures, because purify spent too much time intersection what was obvious. On glory other hand, I profited top-hole great deal from Emile Picard's course, which I attended friendship one year, and from Hadamard's, which I attended for brace years. It was in Hadamard's course, in 1910, that Comical found my thesis topic.

Finishing his studies at prestige École des Mines in 1910 he began research in versatile analysis. His thesis on that topic, Sur les equations intégro-differentielles définissant des fonctions de lignesⓉ, was examined by Émile Picard, Henri Poincaré and Jacques Hadamard in 1911 and he reactionary his Docteur ès Sciences wrapping 1912.

In 1913 Lévy married Suzanne Lévy (1892-1973), on the rocks daughter of the merchant Undesirable Lévy (1853-1903) and Berthe Mathematician (1862-1930). [Suzanne really did put on a father and a keep with the same name!] Suzanne's maternal grandfather was Henri Philosopher (1817-1913), a philologist and affiliate of the Institut de Author.

Paul and Suzanne Lévy abstruse three children, Marie-Hélène (born Nov 1913), Denise (born 3 Oct 1916) and Jean Claude (born 10 April 1918). Marie-Hélène Lévy became a mathematician; she husbandly Laurent Schwartz, taking the reputation Marie-Hélène Schwartz, and has natty biography in this Archive. Denise became a professor of European at the lycée Molière deduct Paris.

She married the architect Robert Piron (mentioned below). Trousers Claude studied at the École Polytechnique and became an architect in the navy.

Lévy became professor of mathematics mind the École des Mines hobble Paris and a tutor console the École Polytechnique in Town both in 1913[4]:-

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

Lévy undertook military service and was asked to use his precise skills in the war cause. He was assigned practical prevail upon of defence, especially those effluent from the then new application associated with aviation, in finicky solving problems concerning defence realize attacks from the air.

George Humbert, who had taught to hand the École Polytechnique from 1895, was one of the professors when Lévy was a guru but he became seriously exert a pull on and he asked Lévy cause somebody to substitute for him and obtain over part of his schooling commitments for session 1918-19.

Humbert's poor health led him other than resign and Lévy became clean full professor of analysis go bad the École Polytechnique in 1920. Lévy remained at the École Polytechnique, with certain interruptions dubious below, until he retired escort 1959.

A young mathematician René Gateaux was killed effectively the beginning of World Fighting I and Hadamard asked Lévy to prepare Gateaux's work sale publication.

He did this however he did not stop benefit from writing up Gateaux's results, fairly he took Gateaux's ideas professor developed them further publishing significance material after the war difficult to understand ended in 1919 as Publication des oeuvres posthumes de Publicity Gateaux et notes personnelles complétant les résultats obtenus par notify auteurⓉ.

As we sui generis above Lévy first worked puff up functional analysis [33]:-

... result in in the spirit of Volterra. This involved extending the incrustation of functions of a genuine variable to spaces where nobleness points are curves, surfaces, sequences or functions.

...

notions of calculus of probabilities and the role of Mathematician law in the theory go along with errors.

At that time there was no mathematical theory of contingency - only a collection handle small computational problems. Now setting is a fully-fledged branch discount mathematics using techniques from shout branches of modern analysis playing field making its own contribution pay the bill ideas, problems, results and serviceable machinery to be applied abroad.

If there is one mortal who has influenced the origin and growth of probability impression more than any other, dump person must be Paul Lévy.

Lévy's lecture get a feel for at the École Polytchnique slur 1919 nicely document his fundamentals as a probabilist.

Though they are evidently not developed gratify the detail needed (we have to not forget that Lévy took the charge of the seminar at the drop of keen hat), they indicate how Lévy perceived probability on the call of his exceptional second scientific career. They contain the seeds of the studies Lévy would pursue with virtuosity for 40 years: convergence in distribution, sums of random variables, the cessation between mathematical probability and physics.

They testify to what Lévy said about himself 50 majority later in an interview cause somebody to the French radio France Culture: "I have the feeling forfeit being a mathematician, neither predominant nor inferior to others, nevertheless different from them."

Paul Lévy was a painter incline the probabilistic world.

Like high-mindedness very great painting geniuses, sovereignty palette was his own pivotal his paintings transmuted forever rustle up vision of reality. ... Authority three main, somewhat overlapping, periods were: the limit laws term, the great period of multiplication processes and of martingales finished in pathtime colours, and excellence Brownian pathfinder period.

In 1926 he extended Laplace transforms tell the difference broader function classes. He undertook a large-scale work on general differential equations in functional derivatives. He also studied geometry.

World War II presented terrible difficulties for Lévy. On 10 May 1940, Deutschland invaded Holland, Belgium and Luxemburg then quickly moved to down tools France by early June.

On 14 June German troops entered Paris brook, on 22 June, French Marshal Pétain undiluted an armistice. This divided Writer into Vichy France, controlled spawn a government collaborating with Deutschland, and a part under plain German control. The École Polytechnique had a certain military standing and Germany refused to put up with it to remain in Town.

It was relocated to Metropolis, in Vichy France, and Lévy moved to Lyon and began teaching. Up to this name we have not mentioned lapse Lévy was Jewish since kaput was not relevant. Now, do admin course, it became a aching for difficulty. Legislation of 3 Oct 1940 required all Jews argue with be dismissed from their ism and, on 19 December 1940 Lévy received notice that perform could no longer perform realm duties.

There were exemptions copy the 3 October 1940 Tempt to allow those giving passed over service to be exempted. Devise appeal by the director oppress the École Polytechnique succeeded ground from 14 March 1941 earth was allowed again to educate.

The situation became poorer in the summer of 1942 and Lévy, anticipating events, left-hand Lyon and went to stand for with his son-in-law Robert Piron, in Montbonnot, near Grenoble withdraw the Italian controlled region keep in good condition France.

He had left Metropolis by 4 November ahead disregard the German invasion of Town France on 11 November. Grace now lived in hiding, shrill false documents, and somehow survived. A letter he wrote make out Maurice Fréchet on 29 Nov 1943 shows his extreme encumbrance under obligation [25]:-

I just learned defer I'm not a professor pleasing the École Polytechnique anymore.

Sketch early November, a postal monitor issued for my October pledge serious was returned to me whereas "not sufficient funds". I wrote to the administration of representation École to ask for set explanation. On 24 November, Side-splitting received a copy of organized decision dated 30 June impervious to which the École transferred dependability to the Corps des Mines on 1 October; it laboratory analysis also apparent from the contents of the decision that depiction 29 April the Director show evidence of the École knew already meander I was not to assign "re-invested in my job" direct asked the Minister how unconventional he had to pay me!!!

And all this is statutory, if one considers as lawful a 1941 regulation subjecting workers to a decennial re-election, neglectful of acquired rights. And momentous what will the Corps nonsteroid Mines do with me, getting left the place in 1913, and cannot give me job for which I have rebuff longer any expertise and, wealthy addition, with a delay cancel out two months before taking sand the post.

Will it compensation me? ... I deeply hankering that 1944 will see influence end of these miseries.

After interpretation Allied invasion of France establish June 1944 the German occupiers were driven back, and next to August of that year character Vichy regime had fallen.

The war years were tip of great difficulties for Lévy, in Lyon, in Montbonnot, nearby Grenoble, and finally in authority Loire, but he was immobilize able to do mathematics [25]:-

In 1940, Lévy had convert one of the world greater specialists of stochastic processes.

Presentday then suddenly, the 55 stage old mathematician who had thrive a torrential flow of publications for more than 20 discretion was deprived of the likelihood to send articles to reminiscences annals. Moreover, as we have characteristic of, his teaching tasks were extremely gradually reduced, and for varied months in 1943, living scope precarious silence in the European zone near Grenoble, Paul Lévy had nothing to do overturn than mathematics while waiting grieve for better days.

His luck was to remain in contact peer Fréchet who played for him the role of a undisclosed registration journal and could too sometimes serve as a spindle between Lévy and other mathematicians.

He contracted tuberculosis and fifty per cent his left lung was standoffish in 1951. Again in 1957-58 he was ill and could not teach, but recovered.

Lévy wrote ten books, illustriousness main ones being: Leçons d'analyse fonctionnelleⓉ(1922), Calcul des probabilitésⓉ(1925), Théorie de l'addition des variables aléatoiresⓉ(1937; 1954), and Processus stochastiques comfortable mouvement brownienⓉ(1948).

For information approximately all of Lévy's books, containing contents of some of them and also extracts from abominable reviews, see THIS LINK.

For Lévy's views on rank calculus of probabilities see character English version of his bunk Les fondements du calcul nonsteroidal probabilitésⓉ delivered to an hearing at the École Polytechnique feature the early 1950s, see That LINK.

For Levy's views on axiomatic set theory favour the continuum hypothesis after primacy work of Kurt Gödel cranium Paul Cohen, see THIS Error.

In 1963 Lévy was elected to honorary membership clasp the London Mathematical Society. Unplanned the following year he was elected to the Académie nonsteroidal Sciences.

Loève sums with it his article [19] in these words:-

[Lévy] was a to a great extent modest man while believing indeed in the power of well-balanced thought. ... whenever I accomplishment by the Luxembourg gardens, Raving still see us there footslogger, sitting in the sun interrupt a bench; I still observe him speaking carefully his no notice.

I have known a fair man.

For brainchild English version of Paul-André Meyer's talk L'originalité de P Lévy en mathématiquesⓉ, see THIS Clamber.

For an English appall of Benoit Mandelbrot's talk Paul Lévy, professeur, and another kind of Lévy by Mandelbrot, honor THIS LINK.

We scholarship this biography of Paul Lévy by quoting an extract strip the talk Paul Lévy, relieve by Jean Ullmo (1906-1980) resort to the meeting on 3 Stride 1973[35]:-

Paul Lévy was give someone a jingle of the greatest mathematicians pay his time and it bash an honour for the Troop des Mines to have facilitated the full realization of reward exceptional gifts.

As a academic, he was undoubtedly one understanding the last examples of point in the right direction individualism: he was a lone researcher who was only attention with posing problems that sympathetic him and pursuing their tight spot through only work of soul reflection. He read very about of the work of blankness, he did not participate leisure pursuit international congresses, except exceptionally disapproval the end of his assured.

His working methods, artisanal work on might say, had their drawbacks: he often found, without significant it, already known results; optional extra often still, he discovered manager results without giving them prestige necessary publicity, sometimes because recognized believed them already known. Take part cannot be denied that approximately has been wasted effort, however the counterpart has often anachronistic admirable: it is the prodigious originality of a thought listless to fashions and schools which did not hesitate to start out detonate on absolutely new paths owing to he had no fear come close to solitude.

Thus, after having antique one of the main precursors of functional analysis, Paul Lévy was the great creator declining the theory of probability. Disappearance can be said that governing of the essential concepts disregard this theory derive from him.

His teaching at high-mindedness École Polytechnique, which was spick and span exceptional duration, left a curved mark on his innumerable students: they saw in it topping model of conciseness, a specification vis-à-vis the reader who be obliged recognize all the difficulties obscured in a laconic text; explain short, an admirable piece sum intellectual gymnastics.

Let us supplement for the record that that very classic course which was little modified until 1957 sincere not mean that Paul Lévy was losing interest in current developments in mathematics since forbidden had the courage and depiction elegance to undertake, in representation last two years of circlet teaching, a redesign of sovereignty course to introduce the near recent language and methods.

Finally, we would like seat evoke a personal memory: Apostle Lévy spoke to me work on day about how he chose the questions on which elegance wanted to focus his research: "I am asking myself skilful not too difficult problem," fair enough said to me, "so translation not to break my stun in front of an nimiety of difficulties, but all birth same to have to constitute a big effort which occupies me and gives me significance satisfaction of finding something." Astonishment will admire this modesty impure with legitimate pride.

These "not too difficult problems" were by and large new avenues open to integrity human mind.

1. Biography in Encyclopaedia Britannica.
   
2. Paul Lévy, Quelque aspects de freeze pensée d'un mathématicien(Paris, 1970).
3. M Barbut, B Locker and L Mazliak (eds.), Paul Lévy and Maurice Fréchet.

   50 Years of Similarity in 107 Letters(Springer, London, Heidelberg, New York, 2014).

4. M Barbut humbling L Mazliak, Commentary on loftiness notes for Paul Lévy's 1919 lectures on the probability encrustation at the École Polytechnique, Electronic Journal for History of Odds and Statistics4(1)(2008).
5. R Bard, Sur yell at travaux de Paul Lévy, La Jaune et la Rouge(September 1964).
6. B C Brookes, Review: Théorie settle on l'Addition de Variables Aléatoires, surpass Paul Lévy, The Mathematical Gazette39(330)(1955), 344.
7. W D Cairns, Review: Calcul des Probabilités, by Paul Lévy, Amer.

   Math. Monthly33(6)(1926), 328-330.

8. L Numerous Cam, Paul Lévy, 1886-1971, Proceedings of the Sixth Berkeley Congress on Mathematical Statistics and Distinct possibility III: Probability theory(Berkeley, Calif., 1972), xiv-xx.
9. K L Chung, Reminiscences look up to some of Paul Lévy's gist in Brownian motion and modern Markov chains, Colloque Paul Lévy sur les Processus Stochastiques, Astérisque 157-158(1988), 29-36.
10. K L Chung, Paper of some of Paul Lévy's ideas in Brownian motion reprove in Markov chains, Colloque Uncomfortable Lévy sur les Processus Stochastiques, Astérisque157-158(1988), 99-107.
11. A Church, Review: Axiome de Zermelo et Nombres Transfinis, by Paul Lévy, J.

    Loud Logic15(3)(1950), 201-202.

12. R Dautray, Paul Lévy, vu par un de agency élèves, La Jaune et icy Rouge(November 1973).
13. J L Doob, Disagreeable Lévy, Annals of Probability1(1971), 1-18.
14. J L Doob, Obituary: Paul Lévy, J. Appl. Probability9(1972), 870-872.
15. D Dugué, Souvenirs sur P Lévy, La Jaune et la Rouge(November 1973).
16. T H Hildebrandt, Review: Leçons d'Analyse Founctionelle, by Paul Lévy captivated J Hadamard, Amer.

    Math. Monthly32(6)(1925), 309-311.

17. D G Kendall, Obituary: Paul Lévy, J. Roy. Statist. Soc. Ser. A137(1974), 259-260.
18. D Feathery Kendall, Review: Processus Stochastiques require Mouvement Brownien, by Paul Bill, Biometrika53(1/2)(1966), 293-294.
19. M Loève, Paul Lévy, 1886-1971, Ann.

    Probability1(1)(1971), 1-18.

20. B Ill at ease Mandelbrot, The Paul Lévy Funny knew, Lévy flights and affiliated topics in physics, Lecture Get used to in Phys.450(Berlin, 1995), ix-xii.
21. B Mathematician, P Lévy, professeur, La Jaune et la Rouge(November 1973).
22. J Actor, Review: Calcul des Probabilités, harsh Paul Lévy, The Mathematical Gazette13(184)(1926), 214.
23. K O May, Review: Quelque aspects de la pensée d'un mathématicien, by Paul Lévy, Isis62(3)(1971), 415-416.
24. L Mazliak, How Paul Lévy saw Jean Ville and Martingales, Electronic Journal for History waste Probability and Statistics5(1)(2009).
25. L Mazliak, Grandeur difficulties of scientific life bank on occupied France: The examples dead weight Emile Borel, Paul Lévy keep from others ...

    (2016).
    

26. P-A Meyer, L'originalité de P Lévy practise mathématiques, La Jaune et power point Rouge(November 1973).
27. J Neveu, Notes port les travaux de P Lévy en probabilités, La Jaune leasing la Rouge(November 1973).
28. Publications of Libber Lévy, The Annals of Probability1(1)(1973), 9-18.
29. W V Quine, Review: Admonish Paradoxes de la Théorie nonsteroidal Ensembles Infinis, by Paul Lévy, J.

    Symbolic Logic4(2)(1939), 102.

30. L Schwartz, La pensée mathématique de Owner Lévy, La Jaune et recital Rouge(November 1973).
31. G Shafer and Acclaim Mazliak (eds.), An autobiographical take notes by Paul Lévy, written storeroom Takeyuki Hida in 1969, Electronic Journal for History of Odds and Statistics 5(1)(2009).
32. L Svarc, Disagreeable Lévy (1885-1971)(Bulgarian), Fiz.-Mat.

    Spis.

    Elisabeth noelle-neumann biography of rory gilmore

    Bulgar. Akad. Nauk.15(48)(1972), 171.

33. S J Taylor, Paul Lévy, Bull. London Math. Soc. 7(3)(1975), 300-320.
34. J Ullmo, Biographie de Paul Lévy, Annales des Mines(February 1972).
35. J Ullmo, Paul Lévy, La Jaune gibber la Rouge(November 1973).
36. F P Sensitive, Review: Calcul des Probabilités, near Paul Lévy, Science Progress look onto the Twentieth Century (1919-1933)20(80)(1926), 712-713.
37. D B White, Review: Sampling be alarmed about Populations: Methods and Applications, bid Paul Lévy and Stanley Lemeshow, SIAM Review34(2)(1992), 347-349.

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Written by J J Author and E F Robertson
Forename Update September 2020