Hans Freudenthal

Hans Freudenthal 1983

Memorial plaque in Luckenwalde

Hans Freudenthal (born September 17, 1905 in Luckenwalde ; † October 13, 1990 in Utrecht ) was a Dutch mathematician and science teacher.

life and work

Freudenthal came from a Jewish family and attended grammar school in Luckenwalde before he began studying mathematics and physics at the University of Berlin in 1923 . In 1927 he studied a summer semester at the Sorbonne in Paris. In 1930 he received his doctorate from topologist Heinz Hopf in Berlin on the ends of topological spaces and groups . He accepted a position as an assistant at LEJ Brouwer , whom he had met in 1927 at a guest lecture in Berlin, and went to Amsterdam. Just one year later he received his habilitation from the University of Berlin with his thesis on quality and quantity in mathematics .

On July 20, 1932, he married the Germanist and pedagogue Suus Lutter in Amsterdam .

In 1937 he published his famous suspension theorems ( suspension theorems ) for topological spaces. He also worked on the topology of semi-simple real Lie groups in the 1930s.

In 1941 he was released from university service in Amsterdam by the German occupying forces. In 1943 he was deported to a labor camp near Havelte in the Netherlands . In 1944, with the support of his wife, he managed to escape from the camp and hid in Amsterdam.

After the liberation in 1945 he worked again as a private lecturer at the University of Amsterdam . From 1946 to 1975 he held a chair for mathematics at the University of Utrecht , where he was rector in 1963/64 . Under the influence of his wife, the founder of the Jena Plan in the Netherlands, Freudenthal also dealt with science didactics. In 1971 he founded the IOWO (Instituut voor de Ontwikkeling van het Wiskunde Onderwijs) in Utrecht, which he was director until 1976. In 1991 the IOWO was renamed "Freudenthal Institute".

Freudenthal was also interested in the history of mathematics. He wrote several articles for the Dictionary of Scientific Biography and dealt, among other things, with the history of the axiomatization of geometry by David Hilbert and Leibniz . He also published the collected works of LEJ Brouwer.

He wrote a book about the introduction of the calculus of probability, about mathematical logic and the construction of a language, Lincos , which is supposed to enable communication with aliens based entirely on mathematics (1957–1960). In mathematical logic, he also worked on intuitionist logic, the favorite child of his mathematical mentor Brouwer. In geometry he worked on the Riemann-Helmholtz spatial problem. Another topic Freudenthals was the group-theoretical structure of geometry, he also worked on the geometric role of the algebra of octonions ("Zur Ebenen Oktavengeometrie", Proc. Kon. Akad. Wet. Amsterdam A 56, 1953, pp. 195-200) and exceptional Jordan algebras.

He had a lasting influence on mathematics didactics , prevented the introduction of New Mathematics in the Netherlands and founded the school of realistic mathematical education . In 1972, Freudenthal initiated the establishment of the Geometriae Dedicata magazine, which was dedicated to geometry .

His doctoral students include Johannes Jisse Duistermaat , Arnoud van Rooij and Willem Titus van Est .

Honors

On December 1, 2006, the University of Utrecht founded the Freudenthal Institute for Science and Mathematics Education (FIsme).

His scientific legacy is in the Freudenthal Collection in the library of the University of Magdeburg .

On the occasion of his 85th birthday, the city of Luckenwalde made Hans Freudenthal an honorary citizen.

In 1983 he was invited speaker at the International Congress of Mathematicians in Warsaw ( The implicit philosophy of mathematics history and education ) and in 1962 in Stockholm ( Real types and real representations of semi-simple Lie algebras ).

The Hans Freudenthal Medal of the International Commission on Mathematical Instruction was named in his honor. Freudenthal was President of the ICMI from 1967 to 1970 and it was on his initiative that the first International Congress on Mathematical Education (ICME) took place in Lyon in 1969. In 1968 he was also one of the founders of the journal for mathematics didactics Educational Studies in Mathematics .

On August 4, 2001 the asteroid (9689) Freudenthal was named after him.

bibliography

The following writings deal with mathematics didactics (it can be assumed that German, Dutch, English, and perhaps also French editions were produced by himself, or at least edited and are therefore to be regarded as originals with equal rights, not as translations).

with Tatjana Ehrenfest-Afanassjewa : Kan het wiskundeonderwijs tot de opvoeding van het denkvermogen bijdragen? (1951)
Mathematics as an educational task (1973), German mathematics as an educational task, 2 vols. Klett (1973, 1977)
Weeding and sowing: preface to a science of mathematical education (1978), preface to a science of mathematics teaching Oldenbourg (1978)
Didactische fenomenologie van wiskundige grondbegrippen (1979)
Méthodes et méthodologie dans les recherches didactiques (1980)
Didactical phenomenology of mathematical structures (1983), Dutch Didactische fenomenologie van wiskundige structuren (1984)
Appels en peren / wiskunde en psychologie: bundelde opstellen (1984)
Revisiting mathematics education: China lectures (1991)

More comments:

Mathematics in Science and Everyday Life , Kindler University Library 1968
Probability and Mathematical Statistics , Oldenbourg, 4th ed., 1981
Spatial Theory , Scientific Book Society Darmstadt 1978
Introduction to the language of logic , 3rd edition, Oldenbourg 1975
Linear Lie groups 1969
Lincos - design of a language of cosmic intercourse , Amsterdam 1960
Contributions in Behnke, Fladt, Süssmann, Bachmann eds. Grundzüge der Mathematik 1960 (functions, geometry - a phenomenological discussion, group theory and geometry)

Mathematical work:

Over the ends of topological spaces and groups. Math. Z. 33 (1931), no. 1, 692-713.
Rebuilding the end theory. Ann. of Math. (2) 43, (1942). 261-279.
Over the ends of discrete rooms and groups. Comment. Math. Helv. 17, (1945).
Relations of E ₇ and E ₈ to the octave level. I, II Nederl. Akad. Wetensch. Proc. Ser. A. 57 = Indagationes Math. 16, (1954). 218-230, 363-368.
The topology in the foundation of the geometry. Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, vol. III, pp. 178-184. Erven P. Noordhoff NV, Groningen; North-Holland Publishing Co., Amsterdam, 1956.

literature

van Dalen Freudenthal and the foundations of mathematics , Nieuw Archief voor Wiskunde 1991, no.9

van Bos The bond with reality is cut: Freudenthal on the foundations of geometry around 1900 , Educational Studies in Mathematics, Vol. 25, 1993, pp. 51-58

ders. In memoriam Hans Freudenthal (1905-1990) , Historia Mathematica, Vol. 19, 1992, pp. 106-108

Veldkamp Freudenkamp and the octonions , Nieuw Archief voor Wiskunde 1991, no.9
ders. Freudenthal in honor of his 80th birthday , Geometriae Dedicata, Vol. 19, 1985, No. 1
ders., Strambach, Obituary for Freudenthal in Geometriae Dedicata, Vol. 37, 1991, No. 2

Web links

Individual evidence

↑ Hans Freudenthal in the Mathematics Genealogy Project (English)

personal data
SURNAME	Freudenthal, Hans
BRIEF DESCRIPTION	German mathematician
DATE OF BIRTH	17th September 1905
PLACE OF BIRTH	Luckenwalde
DATE OF DEATH	October 13, 1990
Place of death	Utrecht

[1] Hans Freudenthal in the Mathematics Genealogy Project (English)