Théophile Henri Joseph 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, mathematical structure, structure, space, Mathematica ...
.
Biography
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 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
University of Liège
The University of Liège (), or ULiège, is a major public university of the French Community of Belgium founded in 1817 and based in Liège, Wallonia, Belgium. Its official language is French (language), French.
History
The university was foun ...
from 1928 till 1930. He taught
differential and
integral calculus
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Int ...
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
Theophilus is a male given name with a range of alternative spellings. Its origin is the Greek word Θεόφιλος from θεός (''theós'', "God") and φιλία (''philía'', "love or affection") can be translated as "Love of God" or "Friend ...
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, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...
and
Constantin Carathéodory
Constantin Carathéodory (; 13 September 1873 – 2 February 1950) was a Greeks, Greek mathematician who spent most of his professional career in Germany. He made significant contributions to real and complex analysis, the calculus of variations, ...
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 Function (mathematics), functions
and functional (mathematics), functionals, to find maxima and minima of f ...
of multiple integrals.
Thanks to the use of
differential geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...
, 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 gr ...
, 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