Hirsch, Guy Charles (1915-1993)

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Mathematician and philosopher of science, born in London on 20 September 1915, and died in Jette on 3 August 1993.

Biography

Guy Hirsch was born in London on 20 September 1915 and returned with his parents to Brussels shortly after the armastice of the First World War. He received his primary education at the State School in Laeken and his secondary education at the Royal Atheneum of Brussels. In 1936, he obtained the degree of licentiate in mathematics at the ULB. A year later he was promoted to Doctor of Science, group mathematics. In 1948 he became an aggregate for higher education.
He won a series of travel grants which allowed him to work several years abroad (Switzerland, Germany, the Netherlands and France): first place in the travel grants-competition in 1937, together with the travel grants of the University Foundation and the Francqui Foundation.
Between 1941 and 1949, he held all positions at the NFWO, from aspirant to certified researcher.
His academic career started in 1949 when he taught mathematics at the Rijkslandbouwhogeschool (State Agricultural College) in Ghent. He taught at this institute until 1962.
In 1957 he was appointed extraordinary professor at ULB and after the ULB-VUB split in 1959 he continued to teach as an ordinary professor at these institutions until his retirement in 1985.
On 3 October 1973 he became corresponding member of the Royal Flemish Academy of Belgium for Science and the Arts (KVAB), working member on 10 May 1978 and honorary member in 1990. He was a member of the National Committee for Mathematics and of the National Committee for Logic, History and Philosophy of Science.
Guy Hirsch was the driving force behind the Belgian Mathematical Society, of which he became the adjunct-secretary in 1947. In 1953 he became secretary, a function he would hold until his death.
He passed away in Jette on 3 Augaust 1993.

Works

His scientific work dealt with two domains: algebraic topology and philosophy of science. As a student of Alfred Errera, Guy Hiersch managed to elevate the field of algebraic topology in Belgian to an international level. He was one of the first to experiment with algebraic models, he published a series of articles on this topic that appeared between 1948 and 1956. He specialised in fibre bundles, a specific mathematical space, and left an important mark on this part of mathematics. His influence can be found to this day in for example the Leray-Hirsch theorem, Hirsch-Koszul algebras, the Hirsch-Wu spectral row and the Hirsch formula for the Poincaré polynomial associated with the topology of certain homogeneous spaces. He discovered a sixteen-dimensional variety, namely the projective plane of the octaves, which is defined on the Cayley-Graves octaves, forming a non-associative algebra.
For his groundbreaking work in mathematics he received multiple awards: the Baron Louis Empain prize in 1938, the Prize of the Alumni of the University Foundation in 1950 and the François Deruyts prize in 1954. During the academic year 1956-1957 he held the Francqui Chair at the Catholic University of Leuven and in 1958 he was a visiting professor at the Massachusetts Institute of Technology (MIT).

Philosophy of science

Guy Hirsch's interest in mathematics was not limited to algebraic topology. He was interested in the foundations and philosophy of mathematics (especially probability theory) and in the history of science. In 1956, at a colloquium organised by the journal Mathematica & Paedagogia, he gave a presentation on his philosophical views entitled Quelques réflexions sur le caractère des mathématiques. Initially, he studied the logical foundations of probability theory and its application to statistics.
His philosophy is generally considered to be a new form of rationalism, despite its links to logical empiricism.
Van Orman Quine, a logician and philosopher of science, defended in the 1950s that mathematics should be placed on the same plane as the other sciences. Guy Hirsch analysed the work of this philosopher of science. After this analysis, he came to a divergence between informal mathematical reasoning and the reconstruction given to it in formal logic. He attached great importance to the study of structures and diagrams. He also closely examined Gödel's problem, which showed that the hypothesis of the continuous is compatible with the axioms of the theory of sets and which was challenged in 1962.
For his efforts in this field, he received an honorary doctorate from the University of Dijon in 1983. The Belgian Mathematical Society published a selection of his work.
Guy Hirsch himself wrote analyses of books in the Society's Bulletin; these were short monographs on the theme of the book being analysed.

History of science

He edited the chapter on algebraic topology in a publication edited by Jean Dieudonné.

Publications

• Short list with publications Ghent University consulted on 15/07/2010 at 15:40.
• For a list with publications see: "Selected works of Guy Hirsch", In: Bulletin of the Belgian mathematical society - Simon Stevin. Supplement, 1995

Bibliography

• Félix, Yves, "Hirsch, Guy Charles", in Nouvelle Biographie nationale, vol. 8, p. 196-197.
• Gochets, Paul, "Les contributions de Guy Hirsch à la philosophie des sciences", In:Bulletin de la Société mathématique de Belgique, tome XXXVIII, 1986, p. 9-32.
• Mawhin, Jean, De wiskunde, in: Robert Halleux, Geert Vanpaemel, Jan Vandersmissen en Andrée Despy-Meyer (red.), Geschiedenis van de wetenschappen in België 1815-2000, Brussel: Dexia/La Renaissance du livre, 2001, vol. 1, p. 76-77; 80.
• "Guy Hirsch", In: De Koninklijke Vlaamse Academie van België voor wetenschappen en kunsten en haar leden, Koninklijke Vlaamse Academie van België voor wetenschappen en kunsten, 2010, p. 126.
• Mertens, R.A. , "In memoriam Guy Hirsch", Jaarboek 1993-1996, Brussel: KVAB, p. 121-123.
• "History of topology", In: James, I.M, History of Topology, Elsevier, 1999, p. 760.