# Hans Freudenthal: Selecta

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*Tonny A. Springer; Dirk van Dalen*

A publication of the European Mathematical Society

Hans Freudenthal (1905–1990) was a Dutch mathematician, born in
Luckenwalde, Germany. His scientific activities were of a rich variety.
Enrolling at the University of Berlin as a student in the 1920s, he followed in
the footsteps of his teachers and became a topologist, but with a lively
interest in group theory. After a long journey through the realm of
mathematics, working on almost all subjects that drew his interest, he turned
toward the practical and methodological issues of the didactics of
mathematics.

The present Selecta are devoted to Freudenthal's mathematical
oeuvre. They contain a selection of his major contributions, including
his fundamental contributions to topology such as the foundation of
the theory of ends (in the thesis of 1931) as well as the introduction
(in 1937) of the suspension and its use in stability results for
homotopy groups of spheres. In group theory there is work on
topological groups (of the 1930s) and on various aspects of the theory
of Lie groups, such as a paper on automorphisms of 1941. From the
later work of the 1950s and 1960s, papers on geometric aspects of Lie
theory (geometries associated to exceptional groups, space problems)
have been included.

Freudenthal's versatility is further demonstrated by selections from
his foundational and historical work: papers on intuitionistic logic
and topology, a paper on axiomatic geometry reappraising Hilbert's
Grundlagen, and a paper summarizing his development of Lincos, a
universal ("cosmic") language.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in Hans Freudenthal.