# Hans Freudenthal

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

## Life and work

Freudenthal came from a Jewish family and attended high school in Luckenwalde, before 1923 a math and physics studies began at the University of Berlin. In 1927 he studied for a summer semester at the Sorbonne in Paris. In 1930 he received his doctorate at the topologist Heinz Hopf in Berlin About the ends of topological spaces and groups. He took a job as an assistant at LEJ Brouwer in which he had met in 1927 at a guest lecture in Berlin, and went to Amsterdam. A year later he was habilitated with his work on quality and quantity in mathematics from the University of Berlin.

On July 20, 1932, he married in Amsterdam the German studies and teacher Suu Lutter.

In 1937 he published his famous suspension theorems ( Einhängungstheoreme ) for topological spaces. He also worked in the 1930s about the topology of real semisimple Lie groups.

From the German occupying forces 1941, he was dismissed from the university service in Amsterdam. In 1943 he was deported to a labor camp in Havelte in the Netherlands. In 1944 he succeeded with the support of his wife's escape from the camp, and he hid in Amsterdam.

After the liberation in 1945, he again worked as a lecturer at the University of Amsterdam. From 1946 to 1975 he occupied a chair of mathematics at the University of Utrecht, where he served 1963/64, as rector. Under the influence of his wife, the founder of the Jena- plan in the Netherlands, Freudenthal was also involved in science teaching. In 1971 he founded the IOWO ( Instituut voor de Wiskunde Onderwijs Ontwikkeling van het ) in Utrecht, over which he presided as director until 1976. 1991 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 with Leibniz. He also was the collected works of L.E.J. Brouwer out.

He wrote a book on the introduction of probability theory, on mathematical logic and the construction of a language, Lincos that will enable entirely on mathematical basis based communication with " aliens " ( 1957-1960 ). In mathematical logic, he also worked on intuitionistic logic, the favorite child of his mathematical mentor Brouwer. In geometry, he worked on the Riemann - Helmholtz space problem. Another issue Freudenthal was the group-theoretical structure of geometry, he also worked on the geometric role of the algebra of octonions ( "On the flat octave geometry ", Proc. Kon. Akad Wet. Amsterdam A 56, 1953, pp. 195-200 ) and exceptional Jordan algebras.

He exercised a lasting influence on mathematics education from, prevented the introduction of new mathematics in the Netherlands and founded the school of realistic mathematics education.

## Honors

On 1 December 2006, the University of Utrecht founded the " Freudenthal Institute for science and mathematics education" ( FIsme ).

In the library of the University of Magdeburg his scientific estate is in the Freudenthal collection.

On the occasion of his 85th birthday appointed the town of Luckenwalde 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 Stockholm in 1962 (Real types and real representations of semi -simple Lie algebras ).

## Bibliography

From mathematics education act, the following fonts ( it is assumed that German, Dutch, English, maybe French editions made by himself, have been but at least processed and thus to be seen as equal originals, not as translations ).

- Mathematics as to educational task (1973 ), dt 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 )
- Méthode et dans les recherches méthodologie didactiques (1980 )
- Didactical phenomenology of mathematical structures (1983 ), holl Didactische fenomenologie van wiskundige Structuren (1984 )
- Appels en peren / wiskunde s psychology: gebundelde Opstellen (1984 )
- Revisiting mathematics education: China lectures (1991 )

More Articles:

- Mathematics in science and everyday life, Kindler University Library 1968
- Probability and mathematical statistics, Oldenbourg, 4th edition, 1981
- Space Theory, Darmstadt University Press 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
- Posts in Behnke, Fladt, sweet man, Bachmann ed. Broad Mathematics 1960 ( functions, geometry - a phenomenological discussion, group theory and geometry)

Mathematical work:

- About the ends of topological spaces and groups. Math Z. 33 (1931 ), no 1, 692-713.
- Rebuilding the end of theory. Ann. of Math ( 2) 43, (1942 ). 261-279.
- About the ends of discrete spaces and groups. Comment. Math Helv 17 (1945 ).
- Relations of E7 and E8 the octave level. I, II Nederl. Akad Wetensch. Proc. Ser. A. 57 = Indagationes Math 16, (1954). 218-230, 363-368.
- La topology dans les Fondements de la géometrie. Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, vol. III, pp. 178-184. Erven P. Noordhoff N.V., Groningen; North - Holland Publishing Co., Amsterdam, 1956.