Hans Freudenthal

Lore & Background

Freudenthal was born in Luckenwalde, Brandenburg, the son of a Jewish teacher. He studied mathematics at the University of Berlin from 1923, met L. E. J. Brouwer in 1927, and completed his thesis under Heinz Hopf in 1930 on the ends of topological groups. He moved to Amsterdam as Brouwer's assistant, married Dutch teacher Suus Lutter, and was promoted to lecturer at the University of Amsterdam. During the Nazi occupation of the Netherlands, he was suspended from duties, sent to a labor camp in Havelte in 1943, escaped in 1944 with his wife's help, and went into hiding. In hiding, he won first prize under a false name in a novel-writing contest.

After the war, his position was restored, but in 1946 he became a chair in pure and applied mathematics and foundations of mathematics at Utrecht University, where he remained. He served as the 8th president of the International Commission on Mathematical Instruction from 1967 to 1970. In 1971 he founded the Institute for the Development of Mathematical Education (IOWO), later renamed the Freudenthal Institute. He founded the journal Geometriae Dedicata in 1972 and Educational Studies in Mathematics in 1968. He retired in 1975 and died in 1990 in Utrecht.

Reader's Guide

Freudenthal's significance lies in his dual impact on pure mathematics and mathematics education. In topology, his 1931 thesis introduced the concept of ends of a topological space, which remains fundamental in topological group theory and other areas. The Freudenthal suspension theorem (1937) shifted homotopy groups via suspension, forming a basis for stable homotopy theory. He also contributed the Freudenthal spectral theorem in Riesz spaces and the Freudenthal magic square in Lie algebra. In education, he founded the journal Educational Studies in Mathematics and developed Realistic Mathematics Education (RME), which emphasizes mathematizing real situations in meaningful contexts. His single-handed intervention prevented the Netherlands from adopting 'new math' in the 1970s. He also designed the Lincos language for extraterrestrial communication and published the Impossible Puzzle. His legacy includes the Hans Freudenthal Medal awarded by the International Commission on Mathematical Instruction and the asteroid 9689 Freudenthal named after him.

Did You Know?

• Freudenthal won first prize under a false name in a novel-writing contest while in hiding during World War II.
• He designed Lincos, a constructed language intended for communication with extraterrestrial intelligence.
• The Freudenthal Institute at Utrecht University was originally founded by him in 1971 as the Institute for the Development of Mathematical Education (IOWO).
• He prevented the Netherlands from following the worldwide trend of 'new math' in the 1970s.