Charles Jean de la Vallée-Poussin
Encyclopedia
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is most well known for proving the Prime number theorem
Prime number theorem
In number theory, the prime number theorem describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are distributed amongst the positive integers....
.
The king of Belgium ennobled him with the title of baron.
Biography
He was born in LeuvenLeuven
Leuven is the capital of the province of Flemish Brabant in the Flemish Region, Belgium...
, Belgium
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
and spent most of his life there. He was taught mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the Catholic University of Leuven
Catholic University of Leuven
The Catholic University of Leuven, or of Louvain, was the largest, oldest and most prominent university in Belgium. The university was founded in 1425 as the University of Leuven by John IV, Duke of Brabant and approved by a Papal bull by Pope Martin V.During France's occupation of Belgium in the...
by Louis-Philippe Gilbert (who was his uncle), after he obtained his diploma in engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
he was encouraged to obtain a doctorate in the sciences of physics and mathematics, and from 1891 when he was 25 he was assistant professor in Mathematical Analysis. He became a teacher at the same university (just like his father, Charles-Louis-Joseph-Xavier de la Vallée-Poussin
Charles-Louis-Joseph-Xavier de la Vallée-Poussin
Charles-Louis-Joseph-Xavier de la Vallée-Poussin was a Belgian geologist and mineralogist. His son was the mathematician Charles Jean de la Vallée-Poussin.-Academic career:...
, who taught mineralogy
Mineralogy
Mineralogy is the study of chemistry, crystal structure, and physical properties of minerals. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, as well as their utilization.-History:Early writing...
and geology
Geology
Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...
) in 1892, obtaining Gilbert's chair at his death. While teaching he 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 to be awarded this prize a second time in 1924 for his work in the period 1914 to 1923. In 1898 he was nominated correspondent to the Royal Academy (at the age of 32) and a Member of the Academy in 1908. In 1923 he was President of the Division of Sciences. In 1914 he escaped from Leuven on its destruction by the invading Germans and was invited to teach at Harvard in the United States, this was followed by professorships in Paris at the Collège de France and at the Sorbonne in 1918. After the war he returned to Belgium, The International Union of Mathematicians was created and he was invited to become its President; he was to remain Honorary President. Between 1918 and 1925 he traveled extensively, teaching in Geneva, Strasbourg and Madrid and then in the United States where he gave lectures at the Universities of Chicago, Berkeley, Brown, Yale, Princeton, Columbia, Philadelphia and the Rice Institute. He was Doctor Honoris Causa of the Universities of Paris, Toronto, Strasbourg and Oslo, Associate of the Institute of France and Member of the Pontifical Academy of Nuovi Lincei, Nazionale dei Lincei, Madrid, Naples, Boston. He was awarded the title of Baron by King Albert 1 of the Belgians in 1928.
In 1961, he fractured his shoulder and this incident led him to death in Boitsfort
Watermael-Boitsfort
Watermael-Boitsfort or Watermaal-Bosvoorde is one of the nineteen municipalities located in the Brussels-Capital Region in Belgium....
(Watermaal-Bosvoorde), Brussels
Brussels
Brussels , officially the Brussels Region or Brussels-Capital Region , is the capital of Belgium and the de facto capital of the European Union...
a few months later.
A student of his, Georges Lemaître
Georges Lemaître
Monsignor Georges Henri Joseph Édouard Lemaître was a Belgian priest, astronomer and professor of physics at the Catholic University of Louvain. He was the first person to propose the theory of the expansion of the Universe, widely misattributed to Edwin Hubble...
, would later be the first to propose a Big Bang theory of the history of the Universe.
Work
Although his first mathematical interests were in analysis, he became suddenly famous as he proved the prime number theoremPrime number theorem
In number theory, the prime number theorem describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are distributed amongst the positive integers....
independently of his coeval Jacques Hadamard
Jacques Hadamard
Jacques Salomon Hadamard FRS was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.-Biography:...
in 1896.
Afterwards, he found interest in approximation theory
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby...
. He defined, for any continuous function
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
f on the standard interval
Interval (mathematics)
In mathematics, a interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers satisfying is an interval which contains and , as well as all numbers between them...
[−1,1], the sums
,where
and
are the vectors of the dual basis with respect to the basis
Polynomial basis
In mathematics, the polynomial basis is a basis for finite extensions of finite fields.Let α ∈ GF be the root of a primitive polynomial of degree m over GF...
of Chebyshev polynomials
Chebyshev polynomials
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively. One usually distinguishes between Chebyshev polynomials of the first kind which are denoted Tn and...
(defined as
.Note that the formula is also valid with
being the Fourier sum of a 
-periodic functionPeriodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...
'F' such that
.Finally, the de la Vallée-Poussin sums can be evaluated in terms of the so-called Fejér
Lipót Fejér
Lipót Fejér , was a Hungarian mathematician. Fejér was born Leopold Weiss, and changed to the Hungarian name Fejér around 1900....
sums (say
)
.The kernel is bounded (
) and obeys the property
, if 
Later, he worked on potential theory
Potential theory
In mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions.- Definition and comments :The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which...
and complex analysis
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 useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
.
External links
- Biographie Universelle, by DidotDidotDidot is the name of a family of French printers, punch-cutters and publishers. Through its achievements and advancements in printing, publishing and typography, the family has lent its name to typographic measurements developed by François-Ambroise Didot and the Didot typeface developed by Firmin...
. - Obituary