Szolem Mandelbrojt
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Szolem Mandelbrojt (10 January 1899 – 23 September 1983) was a Polish-French mathematician who specialized in
mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...
. He was a professor at the
Collège de France The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most ...
from 1938 to 1972, where he held the Chair of Analytical Mechanics and Celestial Mechanics.


Biography

Szolem Mandelbrojt was born on 10 January 1899 in
Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...
, Poland into a Jewish family of Lithuanian descent. He was initially educated in Warsaw, then in 1919 he moved to
Kharkov Kharkiv, also known as Kharkov, is the second-largest List of cities in Ukraine, city in Ukraine.
,
Ukraine Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the nor ...
(then
USSR The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...
) and spent a year as a student of the
Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...
n mathematician
Sergei Bernstein Sergei Natanovich Bernstein (, sometimes Romanized as ; 5 March 1880 – 26 October 1968) was a Ukrainian and Soviet mathematician of Jewish origin known for contributions to partial differential equations, differential geometry, probability theo ...
. A year later, he emigrated to France and settled in
Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
. In subsequent years, he attended the seminars of
Jacques Hadamard Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry, and partial differential equations. Biography The son of a tea ...
,
Henri Lebesgue Henri Léon Lebesgue (; ; June 28, 1875 – July 26, 1941) was a French mathematician known for his Lebesgue integration, theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an ...
,
Émile Picard Charles Émile Picard (; 24 July 1856 – 11 December 1941) was a French mathematician. He was elected the fifteenth member to occupy seat 1 of the Académie française in 1924. Life He was born in Paris on 24 July 1856 and educated there at th ...
, and others. In 1923, he received a doctorate from the
University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...
on the
analytic continuation In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a ne ...
of the
Taylor series In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor ser ...
. Hadamard was his Ph.D. advisor. In 1924 Mandelbrojt was awarded a Rockefeller Fellowship in the
United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
. In May 1926 he married Gladys Manuelle Grunwald (born 28 June 1904 in Paris). From 1926 to 1927, he spent a year as an assistant professor at the Rice Institute (now Rice University) in
Houston Houston ( ) is the List of cities in Texas by population, most populous city in the U.S. state of Texas and in the Southern United States. Located in Southeast Texas near Galveston Bay and the Gulf of Mexico, it is the county seat, seat of ...
, Texas. In 1928 he returned to France - having received French citizenship in 1927 – and was appointed an assistant professor at the University of Lille. The following year he became a full professor at the
University of Clermont-Ferrand The University of Clermont-Ferrand was officially founded in 1896, by merging of two existing faculties (Literature and Sciences) and a medical school. In 1976, due to political issues, the University split between University Clermont-Ferrand I - ...
. In December 1934 Mandelbrojt co-founded the
Nicolas Bourbaki Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (Paris), École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intende ...
group of mathematicians, of which he was a member until
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
. He succeeded Hadamard at Collège de France in 1938 and took up the Chair of
Analytical Mechanics In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related formulations of classical mechanics. Analytical mechanics uses '' scalar'' properties of motion representing the sy ...
and
Celestial Mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
. Mandelbrojt helped several members of his family emigrate from Poland to France in 1936. One of them, his nephew
Benoit Mandelbrot Benoit B. Mandelbrot (20 November 1924 â€“ 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of phy ...
, was to discover the
Mandelbrot set The Mandelbrot set () is a two-dimensional set (mathematics), set that is defined in the complex plane as the complex numbers c for which the function f_c(z)=z^2+c does not Stability theory, diverge to infinity when Iteration, iterated starting ...
and coin the word
fractal In mathematics, a fractal is a Shape, geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scale ...
in the 1970s. In 1939 he fought for France when the country was invaded by the Nazis, then in 1940, along with many scientists helped by Louis Rapkine and the
Rockefeller Foundation The Rockefeller Foundation is an American private foundation and philanthropic medical research and arts funding organization based at 420 Fifth Avenue, New York City. The foundation was created by Standard Oil magnate John D. Rockefeller (" ...
, Mandelbrojt relocated to the United States, taking up a position at the Rice Institute. In 1944 he joined the scientific committee of the
Free French Forces __NOTOC__ The French Liberation Army ( ; AFL) was the reunified French Army that arose from the merging of the Armée d'Afrique with the prior Free French Forces (; FFL) during World War II. The military force of Free France, it participated ...
in
London London is the Capital city, capital and List of urban areas in the United Kingdom, largest city of both England and the United Kingdom, with a population of in . London metropolitan area, Its wider metropolitan area is the largest in Wester ...
, England. In 1945 Mandelbrojt moved back to France and resumed his professional activities at Collège de France, where he remained until his retirement in 1972. In his retirement year he was elected a member of the
French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...
. Szolem Mandelbrojt died at the age of 84 in Paris, France, on 23 September 1983.


Research

Even though Mandelbrojt was an early member of the
Bourbaki group Bourbaki(s) may refer to : Persons and science * Charles-Denis Bourbaki (1816–1897), French general, son of Constantin Denis Bourbaki * Colonel Constantin Denis Bourbaki (1787–1827), officer in the Greek War of Independence and serving in t ...
, and he did take part in a number of Bourbaki gatherings until the breakout of the war, his main research interests were actually quite remote from
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...
. As evidenced by his publications (see next), he focused on
complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...
and
harmonic analysis Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...
, with an emphasis on
Dirichlet series In mathematics, a Dirichlet series is any series of the form \sum_^\infty \frac, where ''s'' is complex, and a_n is a complex sequence. It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in anal ...
, lacunary series, and
entire function In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any ...
s. Rather than a Bourbakist, he is perhaps more accurately described as a follower of
G. H. Hardy Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...
. Together with
Norbert Wiener Norbert Wiener (November 26, 1894 – March 18, 1964) was an American computer scientist, mathematician, and philosopher. He became a professor of mathematics at the Massachusetts Institute of Technology ( MIT). A child prodigy, Wiener late ...
and Torsten Carleman, he can be viewed as a moderate modernizer of classical
Fourier analysis In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fo ...
. Shmuel Agmon, Jean-Pierre Kahane, Yitzhak Katznelson, Paul Malliavin and George Piranian are among his students.


Selected works


Books

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Lecture notes

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Articles

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Thesis

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Notes


References

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External links

* * .
Szolem Mandelbrojt
at
Collège de France The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most ...
.
Szolem Mandelbrojt
at Hathi Trust Digital Library. {{DEFAULTSORT:Mandelbrojt, Szolem 1899 births 1983 deaths National University of Kharkiv alumni Nicolas Bourbaki 20th-century French mathematicians Polish mathematicians Jewish scientists Academic staff of the Lille University of Science and Technology Members of the French Academy of Sciences Rice University faculty 20th-century Polish Jews 20th-century Polish mathematicians Polish emigrants to France University of Paris alumni