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

Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique The Royal Academy of Science, Letters and Fine Arts of Belgium ( , sometimes referred to as ' ) is the independent learned society of science and arts of the French Community of Belgium. One of Belgium's numerous academies, it is the French-speak ...

. 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