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Hans Freudenthal: Selecta
Edited by: Tonny A. Springer and Dirk van Dalen, Utrecht University, The Netherlands
A publication of the European Mathematical Society.
Heritage of European Mathematics
2009; 661 pp; hardcover
Volume: 3
ISBN-10: 3-03719-058-2
ISBN-13: 978-3-03719-058-6
List Price: US$188
Member Price: US$150.40
Order Code: EMSHEM/3
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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.


Graduate students and research mathematicians interested in Hans Freudenthal.

Table of Contents

  • Biographical note
  • Ph.D. students of Hans Freudenthal
  • Über die Enden topologischer Räume und Gruppen
  • Einige Sätze über topologische Gruppen
  • Topologische Gruppen mit genügend vielen fastperiodischen Funktionen
  • Teilweise geordnete Moduln
  • Über die Friedrichssche Fortsetzung halbbeschränkter Hermitescher Operatoren
  • Zum intuitionistischen Raumbegriff
  • Zur intuitionistischen Deutung logischer Formelnm
  • Entwicklungen von Räumen und Gruppen
  • Alexanderscher und Gordonscher Ring und ihre Isomorphie
  • Zum Hopfschen Umkehrhomomorphismus
  • Über die Klassen der Sphärenabbildungen. I. Große Dimensionen
  • Die Topologie der Lieschen Gruppen als algebraisches Phänomen
  • Simplizialzerlegungen von beschränkter Flachheit
  • Über die Enden diskreter Räume und Gruppen
  • Oktaven, Ausnahmegruppen und Oktavengeometrie
  • Sur le groupe exceptionnel \(E_7\)
  • Sur des invariants caractéristiques des groupes semi-simples
  • Sur le groupe exceptionnel \(E_8\)
  • Zur ebenen Oktavengeometrie
  • Beziehungen der \(E_7\) und \(E_8\) zur Oktavenebene I
  • Beziehungen der \(\mathfrak{E}_7\) und \(\mathfrak{E}_8\) zur Oktavenebene II-XI
  • Zur Berechnung der Charaktere der halbeinfachen Lieschen Gruppen I-III
  • Neuere Fassungen des Riemann-Helmholtz-Lieschen Raumproblems
  • Grundzüge eines Entwurfes einer kosmischen Verkehrssprache
  • Zur Geschichte der Grundlagen der Geometrie
  • Zur Klassifikation der einfachen Lie-Gruppen
  • Symplektische und metasymplektische Geometrien
  • Bericht über die Theorie der Rosenfeldschen elliptischen Ebenen
  • Das Helmholtz-Liesche Raumproblem bei indefiniter Metrik
  • Lie groups in the foundation of geometry
  • Comments
  • Acknowledgements
  • Bibliography
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