Freudenthal was born in
Luckenwalde,
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 the
University of Berlin beginning in 1923.[2][3] He met
L. E. J. Brouwer in 1927, when Brouwer came to Berlin to give a lecture, and in the same year Freudenthal also visited the
University of Paris.[3][4] He completed his thesis work with
Heinz Hopf at Berlin, defended a thesis on the
ends of
topological 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 the
University 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 the
anti-Jewish laws that had been passed in Germany beginning with the
Nazi rise to power in 1933.[3] However, in 1940 the Germans
invaded the Netherlands, following which Freudenthal was suspended from duties at the
University of Amsterdam by the Nazis.[3][4] In 1943 Freudenthal was sent to a labor camp in the village of
Havelte 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 and
foundations of mathematics at
Utrecht University, where he remained for the rest of his career.[2][3] He served as the 8th president of the
International 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 the
Freudenthal Institute.[3] In 1972 he founded and became editor-in-chief of the journal Geometriae Dedicata.[8] He retired from his professorship in 1975[3] and from his journal editorship in 1981.[8] He died in
Utrecht in 1990, sitting on a bench in a park where he always took a morning walk.[2]
Contributions
In his thesis work, published as a journal article in 1931, Freudenthal introduced the concept of an
end of a
topological 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 of
compact sets. Ends remain of great importance in
topological group theory, Freudenthal's motivating application,[10] and also in other areas of mathematics such as the study of
minimal surfaces.
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 elementary
mathematics 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 called Realistic Mathematics Education (RME).[16]
Freudenthal, Hans; de Vries, H. (1969), Linear Lie Groups, Pure and Applied Mathematics, vol. 35, New York: Academic Press,
MR0260926.
Freudenthal, Hans (1972), Mathematics as an Educational Task, Springer,
ISBN9789027702357.
Freudenthal, Hans (1986), Didactical Phenomenology of Mathematical Structures, Mathematics Education Library, vol. 1, Springer,
ISBN9789027722614.
Freudenthal, Hans (1991), Revisiting Mathematics Education: China Lectures, Kluwer Academic Publishers,
ISBN0-7923-1299-6.
Freudenthal, Hans; Freudenthal, Matías (2015), El viaje de Ofantito (in Spanish), Granada (Spain): Esdrújula Ediciones,
ISBN978-84-164850-9-3 [Children's story left unfinished in 1943, completed and translated into Spanish by his son Matijs (Matías)].[20]
^
abVeldkamp, F. D. (1985), "In honor of Hans Freudenthal on his eightieth birthday", Geometriae Dedicata, 19 (1): 3–5,
doi:
10.1007/BF00233100,
S2CID122234088.
^Pupils achievements internationally compared — the
IEA. Educational Studies in Mathematics 6, 127–186. According to PISA critic Joachim Wuttke, some of the points Freudenthal made still apply to the most recent international school studies: unequal enrollment rates, the unsolved translation problem, lacking curricular validity, reading items that contain deeper science than the science items, overinterpretation of numerical outcomes, Kafkaesk confusion in the documentation and in the underlying decisions, dogmatic rejection of criticism
[1].
^Freudenthal, Hans (1972), Mathematics as an Educational Task, Springer,
ISBN9789027702357
Howson, G. (1985), "Hans Freudenthal and the foundations of a discipline of mathematics education", Nieuwe Wiskrant, 5: 68–72.
Van Est, W. T. (1993), "Hans Freudenthal (17 September 1905–13 October 1990)", Educational Studies in Mathematics, 25 (1–2): 59–69,
doi:
10.1007/BF01274102,
S2CID144711501.
Strambach, Karl; Veldkamp, Ferdinand D. (1991), "In memoriam Hans Freudenthal", Geometriae Dedicata, 37 (2): 119,
doi:
10.1007/BF00147407,
S2CID122967603.