Hans Freudenthal | |
|---|---|
 Portrait of prof. dr. H. Freudenthal, 1957 | |
| Born | (1905-03-17)17 March 1905 |
| Died | 13 October 1990(1990-10-13) (aged 85) |
| Alma mater | University of Berlin |
| Known for | Freudenthal algebra Freudenthal magic square Freudenthal spectral theorem Freudenthal suspension theorem Freudenthal's diagonalization theorem Freudenthal's formula Freudenthal-Hopf theorems End (topology) Geometriae Dedicata Lincos language Sum and Product Puzzle |
| Awards | ICM Speaker (1936, 1954, 1983) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Amsterdam |
| Doctoral advisor | Heinz Hopf |
Hans Freudenthal (17 September 1905 – 13 October 1990) was aJewish German-bornDutchmathematician. He made substantial contributions toalgebraic topology and also took an interest inliterature,philosophy,history andmathematics education.[1]
Freudenthal was born inLuckenwalde,Brandenburg, on 17 September 1905, the son of a Jewish teacher. He was interested in both mathematics and literature as a child, and studied mathematics at theUniversity of Berlin beginning in 1923.[2][3] He metL. E. J. Brouwer in 1927, when Brouwer came to Berlin to give a lecture, and in the same year Freudenthal also visited theUniversity of Paris.[3][4] He completed his thesis work withHeinz Hopf at Berlin, defended a thesis on theends oftopological groups in 1930, and was officially awarded a degree in October 1931.[2][3][5] After defending his thesis in 1930, he moved to Amsterdam to take up a position as assistant to Brouwer.[2][3] In this pre-war period in Amsterdam, he was promoted to lecturer at theUniversity of Amsterdam,[3][4] and married his wife, Suus Lutter, a Dutch teacher.[2]
Although he was a German Jew, Freudenthal's position in the Netherlands insulated him from theanti-Jewish laws that had been passed in Germany beginning with theNazi rise to power in 1933.[3] However, in 1940 the Germansinvaded the Netherlands, following which Freudenthal was suspended from duties at theUniversity of Amsterdam by the Nazis.[3][4] In 1943 Freudenthal was sent to a labor camp in the village ofHavelte in the Netherlands, but with the help of his wife (who, as a non-Jew, had not been deported) he escaped in 1944 and went into hiding with his family in occupied Amsterdam.[6] During this period Freudenthal occupied his time in literary pursuits, including winning first prize under a false name in a novel-writing contest.[3]
With the war over, Freudenthal's position at the University of Amsterdam was returned to him, but in 1946 he was given a chair in pure and applied mathematics andfoundations of mathematics atUtrecht University, where he remained for the rest of his career.[2][3] He served as the 8th president of theInternational Commission on Mathematical Instruction from 1967 to 1970.[7] In 1971 he founded the Institute for the Development of Mathematical Education (IOWO) at Utrecht University, which after his death was renamed theFreudenthal Institute.[3] In 1972 he founded and became editor-in-chief of the journalGeometriae Dedicata.[8] He retired from his professorship in 1975[3] and from his journal editorship in 1981.[8] He died inUtrecht in 1990, sitting on a bench in a park where he always took a morning walk.[2]
In his thesis work, published as a journal article in 1931, Freudenthal introduced the concept of anend of atopological space.[9] Ends are intended to capture the intuitive idea of a direction in which the space extends to infinity, but have a precise mathematical formulation in terms of covers of the space by nested sequences ofcompact sets. Ends remain of great importance intopological group theory, Freudenthal's motivating application,[10] and also in other areas of mathematics such as the study ofminimal surfaces.
In 1936, while working with Brouwer, Freudenthal proved theFreudenthal spectral theorem on the existence of uniform approximations bysimple functions inRiesz spaces.[11] In 1937 he proved theFreudenthal suspension theorem, showing that thesuspension operation on topological spaces shifts by one their low-dimensionalhomotopy groups; this result was important in understanding thehomotopy groups of spheres (since every sphere can be formed topologically as a suspension of a lower-dimensional sphere) and eventually formed the basis ofstable homotopy theory.[12] TheFreudenthal magic square is a construction inLie algebra developed by Freudenthal (and independently byJacques Tits) in the 1950s and 1960s, associating each Lie algebra to a pair ofdivision algebras.[13]
In 1968, Freudenthal founded the journal,Educational Studies in Mathematics (ESM). Becoming one of the top-rated journals in the field of mathematics education, ESM was focused on publishing research around finding better ways to teach mathematics.[14]
Later in his life, Freudenthal focused on elementarymathematics education. In the 1970s, his single-handed intervention prevented the Netherlands from following the worldwide trend of "new math".[2] He was also a fervent critic of one of the first international school achievement studies.[15] He interpreted mathematics as a human activity where students should open a scientific eye on the world around them, mathematizing real situations, in a context that makes sense for the students. This approach is calledRealistic Mathematics Education (RME).[16]
Freudenthal published theImpossible Puzzle, a mathematical puzzle that appears to lack sufficient information for a solution, in 1969.[17] He also designed aconstructed language,Lincos, to make possiblecommunication with extraterrestrial intelligence.[18][19]
In 1951, Freudenthal became a member of theRoyal Netherlands Academy of Arts and Sciences.[21] He was also an honorary member of theInternational Academy of the History of Science.[4]He was awarded theGouden Ganzenveer award in 1984.[22]
In 2000, theInternational Commission on Mathematical Instruction instituted an award named in honor of Freudenthal, the Hans Freudenthal Medal. It is given in odd-numbered years (beginning in 2003) for an "outstanding achievement in mathematics education research" in the form of "a major cumulative program of research". Recipients of the medal have includedCelia Hoyles, Paul Cobb,Anna Sfard,Yves Chevallard,Luis Radford,Frederick Leung andOle Skovsmose.[7][23]
Theasteroid9689 Freudenthal is named after him.[24]
