Charles Jean De La Vallée Poussin
   HOME

TheInfoList



OR:

Charles-Jean Étienne Gustave Nicolas, baron de la Vallée Poussin (; 14 August 18662 March 1962) was a Belgian
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. He is best known for proving the
prime number theorem In mathematics, the prime number theorem (PNT) describes the asymptotic analysis, asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by p ...
. The King of Belgium ennobled him with the title of
baron Baron is a rank of nobility or title of honour, often Hereditary title, hereditary, in various European countries, either current or historical. The female equivalent is baroness. Typically, the title denotes an aristocrat who ranks higher than ...
.


Biography

De la Vallée Poussin was born in
Leuven Leuven (, , ), also called Louvain (, , ), is the capital and largest City status in Belgium, city of the Provinces of Belgium, province of Flemish Brabant in the Flemish Region of Belgium. It is located about east of Brussels. The municipalit ...
,
Belgium Belgium, officially the Kingdom of Belgium, is a country in Northwestern Europe. Situated in a coastal lowland region known as the Low Countries, it is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeas ...
. He studied
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
at the
Catholic University of Leuven University of Leuven or University of Louvain (; ) may refer to: * Old University of Leuven (1425–1797) * State University of Leuven (1817–1835) * Catholic University of Leuven (1834–1968) * Katholieke Universiteit Leuven or KU Leuven (1968 ...
under his uncle Louis-Philippe Gilbert, after he had earned his
bachelor's degree A bachelor's degree (from Medieval Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate degree awarded by colleges and universities upon completion of a course of study lasting three to six years ...
in
engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...
. De la Vallée Poussin was encouraged to study for a doctorate in
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
and mathematics, and in 1891, at the age of just 25, he became an
assistant professor Assistant professor is an academic rank just below the rank of an associate professor used in universities or colleges, mainly in the United States, Canada, Japan, and South Korea. Overview This position is generally taken after earning a doct ...
in mathematical analysis. De la Vallée Poussin became a professor at the same university (as was his father, Charles Louis de la Vallée Poussin, who taught
mineralogy Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, and physical (including optical mineralogy, optical) properties of minerals and mineralized artifact (archaeology), artifacts. Specific s ...
and
geology Geology (). is a branch of natural science concerned with the Earth and other astronomical objects, the rocks of which they are composed, and the processes by which they change over time. Modern geology significantly overlaps all other Earth ...
) in 1892. De la Vallée Poussin was awarded with Gilbert's chair when Gilbert died. While he was a professor there, de la Vallée Poussin carried out research in mathematical analysis and the theory of numbers, and in 1905 was awarded the Decennial Prize for Pure Mathematics 1894–1903. He was awarded this prize a second time in 1924 for his work during 1914–23. In 1898, de la Vallée Poussin was appointed as the correspondent to the Royal Belgian Academy of Sciences, and he became a Member of the Academy in 1908. In 1923, he became the President of the Division of Sciences. In August 1914, de la Vallée Poussin escaped from Leuven at the time of its destruction by the invading
German Army The German Army (, 'army') is the land component of the armed forces of Federal Republic of Germany, Germany. The present-day German Army was founded in 1955 as part of the newly formed West German together with the German Navy, ''Marine'' (G ...
of
World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...
, and he was invited to teach at
Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
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 ...
. He accepted this invitation. In 1918, de la Vallée Poussin returned to Europe to accept professorships 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 ...
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 ...
and at the Sorbonne. After the war was over, de la Vallée Poussin returned to Belgium, The International Union of Mathematicians was created, and he was invited to become its President. Between 1918 and 1925, de la Vallée Poussin traveled extensively, lecturing in
Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...
,
Strasbourg Strasbourg ( , ; ; ) is the Prefectures in France, prefecture and largest city of the Grand Est Regions of France, region of Geography of France, eastern France, in the historic region of Alsace. It is the prefecture of the Bas-Rhin Departmen ...
, and
Madrid Madrid ( ; ) is the capital and List of largest cities in Spain, most populous municipality of Spain. It has almost 3.5 million inhabitants and a Madrid metropolitan area, metropolitan area population of approximately 7 million. It i ...
. and then in the United States where he gave lectures at the Universities of Chicago, California, Pennsylvania, and Brown University, Yale University, Princeton University, Columbia University, and the Rice Institute of Houston. He was awarded the ''Prix Poncelet'' for 1916. De la Vallée Poussin was given the titles of Doctor Honoris Causa of the Universities of Paris, Toronto, Strasbourg, and Oslo, an Associate of the Institute of France, and a Member of the
Pontifical Academy of Sciences The Pontifical Academy of Sciences (, ) is a Academy of sciences, scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the progress of the mathematical, physical, and natural sciences and the study ...
, Nazionale dei Lincei, Madrid, Naples, Boston. He was awarded the title of Baron by King Albert I of the Belgians in 1928. In 1961, de la Vallée Poussin fractured his shoulder, and this accident and its complications led to his death in
Watermael-Boitsfort Watermael-Boitsfort (French language, French, ) or Watermaal-Bosvoorde (Dutch language, Dutch, ; ), often simply called Boitsfort in French or Bosvoorde in Dutch, is one of the List of municipalities of the Brussels-Capital Region, 19 municipal ...
, near
Brussels, Belgium Brussels, officially the Brussels-Capital Region, (All text and all but one graphic show the English name as Brussels-Capital Region.) is a Communities, regions and language areas of Belgium#Regions, region of Belgium comprising #Municipalit ...
, a few months later. A student of his,
Georges Lemaître Georges Henri Joseph Édouard Lemaître ( ; ; 17 July 1894 – 20 June 1966) was a Belgian Catholic priest, theoretical physicist, and mathematician who made major contributions to cosmology and astrophysics. He was the first to argue that the ...
, was the first to propose the
Big Bang theory The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including the ...
of the formation of the
Universe The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...
.


Work

Although his first mathematical interests were in analysis, he became suddenly famous as he proved the
prime number theorem In mathematics, the prime number theorem (PNT) describes the asymptotic analysis, asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by p ...
independently of his coeval
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 ...
in 1896. Afterwards, he found interest in
approximation theory In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...
. He defined, for any
continuous function In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as '' discontinuities''. More preci ...
''f'' on the standard interval
1, 1 Onekama ( ) is a village in Manistee County in the U.S. state of Michigan. The population was 399 at the 2020 census. The village is located on the northeast shore of Portage Lake and is surrounded by Onekama Township. The town's name is deri ...
/math>, the sums : V_n=\frac , where : S_n=\fracc_0(f)+\sum_^n c_i(f) T_i and : c_i(f) \, are the vectors of the
dual basis In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimension of V), the dual set of B is a set B^* of vectors in the dual space V^* with the same index set I such that B and ...
with respect to the basis of
Chebyshev polynomials The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions: ...
(defined as : (T_0/2,T_1,\ldots,T_n). Note that the formula is also valid with S_n being the Fourier sum of a 2\pi-
periodic function A periodic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a ''cycle''. For example, the t ...
F such that : F(\theta)=f(\cos\theta). \, Finally, the de la Vallée Poussin sums can be evaluated in terms of the so-called Fejér sums (say F_n) :V_n=2F_-F_. \, The kernel is bounded (V_n \le 3) and obeys the property :f*V_n = f \,, if f(x)= \sum_^n a_j e^. \, Later, he worked on
potential theory In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that the two fundamental forces of nature known at the time, namely g ...
and
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 ...
. He also published a counterexample to
Alfred Kempe Sir Alfred Bray Kempe FRS (6 July 1849 – 21 April 1922) was a mathematician best known for his work on linkages and the four colour theorem. Biography Kempe was the son of the Rector of St James's Church, Piccadilly, the Rev. John Edwar ...
's false proof of the
four color theorem In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions shar ...
. The Poussin graph, the graph he used for this counterexample, is named after him.


''Cours d’analyse''

The textbooks of his mathematical analysis course have been a reference for a long time and had some international influence. The second edition (1909-1912) is remarkable for its introduction of the Lebesgue integral. It was in 1912, "the only textbook on analysis containing both Lebesgue integral and its application to Fourier series, and a general theory of approximation of functions by polynomials". The third edition (1914) introduced the now classical definition of
differentiability In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in ...
due to
Otto Stolz Otto Stolz (3 July 1842 – 23 November 1905) was an Austrian mathematician noted for his work on mathematical analysis and infinitesimals. Born in Hall in Tirol, he studied at the University of Innsbruck from 1860 and the University of Vienna fr ...
. The second volume of this third edition was burnt in the fire of Louvain during the German invasion. The further editions were much more conservative, returning essentially to the first edition. Starting from the eighth edition, Fernand Simonart took over the revision and the publication of the ''Cours d’analyse.''


Selected publications

*''Œuvres'', vol. 1 (Biography and number theory), 2000 (eds. Mawhin, Butzer, Vetro), vols. 2 to 4 planned *''Cours d´Analyse'', 2 vols., 1903, 1906 (7th edition 1938), Reprint of the 2nd edition 1912, 1914 by Jacques Gabay, (deals only with real analysis). Online:
''Cours d'analyse infinitésimale, Tome I''

''Cours d'analyse infinitésimale, Tome II''''Integrals de Lebesgue, fonctions d´ensemble, classes de Baire''
2nd edition 1934, Reprint by Jacques Gabay, *''Le potentiel logarithmique, balayage et representation conforme'', Paris, Löwen 1949 *''Recherches analytiques de la théorie des nombres premiers'', Annales de la Societe Scientifique de Bruxelles vol. 20 B, 1896, pp. 183–256, 281–362, 363–397, vol. 21 B, pp. 351–368 (prime number theorem) *''Sur la fonction Zeta de Riemann et le nombre des nombres premiers inferieur a une limite donnée'', Mémoires couronnés de l Academie de Belgique, vol.59, 1899, pp. 1–74
''Leçons sur l'approximation des fonctions d'une variable réelle''
Paris, Gauthier-Villars, 1919, 1952


See also

*
Poussin proof In number theory, a branch of mathematics, the Poussin proof is the proof of an identity related to the fractional part of a ratio. In 1838, Peter Gustav Lejeune Dirichlet proved an approximate formula for the average number of divisors of all the ...
*
Remez algorithm The Remez algorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a Chebyshev space that are the ...
* La Vallée-Poussin


Notes


External links

* * Biographie Universelle, by Didot. * {{DEFAULTSORT:La Vallee-Poussin, Charles-Jean De 1866 births 1962 deaths 19th-century Belgian mathematicians 20th-century Belgian mathematicians Number theorists Harvard University Department of Mathematics faculty Academic staff of the University of Paris Catholic University of Leuven (1834–1968) alumni Belgian barons Foreign associates of the National Academy of Sciences Scientists from Leuven