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Person: De Rham, Georges

Georges de Rham was a Swiss mathematician, known for his contributions to differential topology and to algebraic topology.

Mathematical Profile (Excerpt):

• Georges attended primary school in Roche but attended the secondary school Collège d'Aigle from 1914 to 1919.
• Another came, who no doubt loved mathematics, but apparently he liked even more the "Aigle " - the Aigle wine has indeed a good reputation.
• What basic mathematics was studied at the school did not fill him with any enthusiasm and de Rham's interests turned more towards philosophy and literature.
• Benjamin Valloton asked me to give a talk on 'La Légende des siècles' Ⓣ(The Legend of centuries) by Victor Hugo.
• In August 1920, in the summer break between his two years at the Gymnase classique in Lausanne, de Rham ascended the Grand Combin, one of the highest peaks in the Alps, on a trip from Valsorey to Panossière.
• Having graduated from the Gymnasium, despite his newly discovered interest in philosophy and literature, de Rham entered the University of Lausanne in 1921 with the intention of studying chemistry, physics and biology.
• At this stage he didn't consider studying mathematics, mainly because the way the subject had been taught led him to believe that there was nothing new to be discovered.
• He began to study mathematics in an attempt to understand questions that arose in the physics he was studying.
• de Rham considered moral straightness, altruism and respect as the very reasons of Dumas' success in teaching.
• In 1925 de Rham was appointed as an assistant to Gustave Dumas.
• Encouraged by Dumas to undertake research in topology, he spent two periods, each of 7 months, in Paris between 1926 and 1928.
• He attended courses at the Sorbonne, enjoying those by Élie Cartan, Ernest Vessiot, Gaston Julia, Arnaud Denjoy, Émile Picard and others.
• He also attended courses at the Collège de France, being particularly impressed by those of Jacques Hadamard and Henri Lebesgue.
• It was Lebesgue who provided encouragement, advice and unfailing support throughout de Rham's work towards his doctorate.
• While in Paris, de Rham read all the topology books he could find and, importantly for the work he went on to do, he read James Alexander's paper Note on two three dimensional manifolds with the same group.
• Another important step in the progress of his research was during this period when he read Élie Cartan's paper Sur les nombres de Betti des espaces de groupes clos.
• On reading the paper he became very excited realising how he could solve many of the problems he was considering.
• In April 1930 his thesis was complete and he sent a copy of it to Lebesgue who helped him to publish it in Liouville's journal, the Journal de mathématiques pures et appliquées.
• He was awarded his doctorate in mathematical sciences from the Faculty of Science, University of Paris, in 1931 after defending his 87-page thesis Sur "l'Analysis situs" des variétés à "n" dimensions Ⓣ(On the 'Analysis situs' of varieties in n dimensions) on 20 June before a committee consisting of Élie Cartan (who was the president), Paul Montel and Gaston Julia.
• is divided into four chapters; the first gives a good summary with improvements of the theory of finite complexes and their homology; the second chapter discusses intersection theory of chains in a complex; the third chapter introduces the use of multiple integrals over chains in an nnn-dimensional variety using as integrands differential forms, and the fourth chapter gives several examples of complexes which have the same Betti numbers and the same torsion, but are not equivalent.
• The International Congress of Mathematicians was held in Zürich in September 1932 and de Rham attended giving a talk based on material from his thesis.
• In 1935 he attended the First International Congress of Topology in Moscow organized by Pavel Aleksandrov.
• Many of the leading topologists attended, including Heinz Hopf, Witold Hurewicz, Jacob Nielsen, André Weil and Hassler Whitney.
• De Rham spoke on Reidemeister torsion and lens spaces.
• However de Rham also held a position at the University of Geneva although he always lived in Lausanne.
• In addition to these permanent appointments de Rham held a number of visiting professorships.
• In those early days at Princeton he would easily mingle with the boisterous postdocs, his exquisite manners contrasting amusingly with our rude ways.
• De Rham visited the Institute for Advanced Study again in 1957-58.
• These are the natural extensions to manifolds of the distributions which had been introduced a few years earlier by Laurent Schwartz and of course it is only in this extended setting that both the de Rham theorem and the Hodge theory become especially complete.
• The original theorem of de Rham was most probably believed to be true by Poincaré and was certainly conjectured (and even used!) in 1928 by Élie Cartan.
• But in 1931 de Rham set out to give a rigorous proof.
• The technical problems were considerable at the time, as both the general theory of manifolds and the 'singular theory' were in their early formative stages.
• Of course de Rham produced much in the way of important mathematics in addition to the 'de Rham theorem'.
• He gave a reducibility theorem for Riemann spaces which is fundamental in the development of Riemannian geometry.
• He also worked on Reidemeister torsion and his work on this topic was the beginning of rapid developments.
• de Rham had a subtle charm which drew younger people to him immediately.
• In those early days at Princeton he would easily mingle with the boisterous postdocs, his exquisite manners contrasting amusingly with our rude ways.
• He was always lean and one could feel the steel in his sinews, but he never boasted of his mountaineering exploits and it was only at second hand that the daredevil in him became apparent...
• De Rham received many honours.
• He was secretary/treasurer of the Swiss Mathematical Society in 1940-42, vice-president in 1942-44, and president in 1944-45.
• He was President of the International Mathematical Union from 1963 to 1966 and, in this capacity, was president of the International Congress of Mathematicians held in Moscow in August 1966.
• He was elected a member of the Accademia dei Lincei (1962), the Göttingen Academy of Sciences (1974), and the Académie des Sciences of the Institute of France.
• He received honorary degrees from the universities of Strasbourg, Genoble, Lyon, and l'École Polytechnique Fédérale Zürich.
• An international colloquium was held in Geneva in March 1969 to honour de Rham.
• he did as much as any one man could do to bring mathematicians together, young and old, classical and modern, from the East and West.
• There are many different aspects of de Rham's career, combining his passion for mathematics and for mountaineering.
• He regarded proving a theorem, delivering a lecture or reaching the top of a mountain as a personal endeavour, requiring a full involvement of the deepest and most precious faculties of the individual, in the name of some kind of transcendental beauty.
• On the occasion of the centenary of de Rham's birth, his former doctoral student Oscar Burlet remembers that he once explained to him: "For alpinism is not only a physical exercise, but it also a task for the mind, and it allows one to create a marvellous harmony between nature, soul and body." Climbing higher to attain a larger view could be considered as a metaphor for de Rham's constant attempt to advance in abstraction, to gain generality by looking at single problems and objects from above.
• The development set off by his first proof of the theorem bearing his name moved exactly in the direction of embracing specific questions in a more and more general framework.

Born 10 September 1903, Roche, Canton Vaud, Switzerland. Died 9 October 1990, Lausanne, Switzerland.

View full biography at MacTutor

Tags relevant for this person:

Origin Switzerland, Topology

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@J-J-O'Connor

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive