Théophile Lepage (24 March 1901 – 1 April 1991) 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, structure, space, models, and change.
History
On ...
.
Biography
Théophile Henri Joseph Lepage, better known as Théophile Lepage, was born in
Limburg
Limburg or Limbourg may refer to:
Regions
* Limburg (Belgium), a province since 1839 in the Flanders region of Belgium
* Limburg (Netherlands), a province since 1839 in the south of the Netherlands
* Diocese of Limburg, Roman Catholic Diocese in ...
on March 24, 1901. Together with
Alfred Errera
Alfred Errera (1886 – 1960) was a Belgian mathematician.
Errera studied at the Université libre de Bruxelles, where he received his Ph.D. in 1921 with dissertation ''Du coloriage des cartes et de quelques questions d'analysis situs''. In his d ...
he founded the seminar for mathematical analysis at the
ULB. This seminar played an important role in the flourishing of the department of mathematics at this university. He was professor of
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
at the
University of Liège
The University of Liège (french: Université de Liège), or ULiège, is a major public university of the French Community of Belgium based in Liège, Wallonia, Belgium. Its official language is French. As of 2020, ULiège is ranked in the 301 ...
from 1928 till 1930. He taught
differential and
integral calculus
In mathematics, an integral assigns numbers to Function (mathematics), functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding ...
at the ULB from 1931 till 1956 and higher analysis from 1956 till 1971.
For 43 years he was a member of the
. On June 5, 1948, he was nominated a corresponding member and on June 9, 1956 an effective member of the Académie. In 1963 he became president of the Académie and director of the Klasse Wetenschappen. He was also active in the Belgisch Wiskundig Genootschap.
He died in Verviers on April 1, 1991.
Mathematical work
At the ULB, the ideas and the enthusiasm of
Théophile de Donder
Théophile Ernest de Donder (; 19 August 1872 – 11 May 1957) was a Belgian mathematician and physicist famous for his work (published in 1923) in developing correlations between the Newtonian concept of chemical affinity and the Gibbsian concept ...
formed the foundation of a flourishing mathematical tradition. Thanks to student Théophile Lepage, external differential calculus acquired one of the most helpful methods introduced in mathematics during the 20th century, and one for which De Donder was a pioneer, presenting new applications in the resolution of a classical problem—the partial differential equation of
Monge-Ampère—and in the synthesis of the methods of Théophile de Donder,
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...
and
Constantin Carathéodory
Constantin Carathéodory ( el, Κωνσταντίνος Καραθεοδωρή, Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany. He made significant ...
into a
calculus of variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions
and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...
of multipal integrals.
Thanks to the use of
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
, it is possible to avoid long and boring calculations. The results of Lepage were named in reference works. His methods are still inspiring contemporary mathematicians: Boener and Sniatycki talked about the congruence of Lepage; not so long ago,
Demeter Krupka, introduced—beside the eulerian forms which correspond to the classical equations of the calculus of variations of Euler—the so-called lepagian forms
or equivalents of Lepage in equations of variations on
fiber spaces.
We also have Lepage to thank for interesting results concerning
linear representations of the
symplectic group
In mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted and for positive integer ''n'' and field F (usually C or R). The latter is called the compact symplectic grou ...
, and more specifically Lepage's dissolution of an outer potency of the product of an even number of duplicates of a
complex surface
Complex commonly refers to:
* Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe
** Complex system, a system composed of many components which may interact with each ...
.
References
External links
*
{{DEFAULTSORT:Lepage, Theophile
1901 births
1991 deaths
Belgian mathematicians
Differential geometers
People from Limbourg
Academic staff of the Free University of Brussels (1834–1969)
Academic staff of the University of Liège
Members of the Royal Academy of Belgium