Hans Freudenthal was a German-born Dutch mathematician who made important contributions to algebraic topology. He also published works on history and mathematical education.

In the late 1950's Freudenthal published several articles on the history of geometry around 1900, in particular on Hilbert's innovative approach to the foundations of geometry. Especially his essay-review of the eighth edition of Hilbert's Grundlagen der Geometrie has become a standard reference in historical studies of geometry. In the present article I discuss Freudenthal's contribution to our understanding

This study provides a historical analysis of Freudenthal’s didactic ideas and his didactic career. It is partly biographical, but also contributes to the historiography of mathematics education and addresses closely related questions such as: what is mathematics and where does it start? Which role does mathematics play in society and what influence does it have on the prevailing views concerning its accompanying didactics?. Hans Freudenthal (1905–1990), professor in mathematics, scientist, literator, but above all mathematics-educator, was inextricably linked to the changes which took place in mathematics education and didactics during the second half of the last century. His diversity as a scientist and his inexhaustible efforts to establish the didactics of mathematics as a seriously pursued science, made Freudenthal's influence in this area considerable. He foresaw an essential, practical role for mathematics in everyone’s life, encouraging students to discover and create mathematics themselves, instead of imposing a ready-made mathematical system. The theory of mathematics education thus developed in the Netherlands would gain world fame in the following decades. Today, in the light of the discussions about mathematics education, in which the call for `genuine’ mathematics instead of the so-called 'kindergarten'-mathematics can be heard, Freudenthal's approach seems to be passé. However, the outcome of this study (which is mainly based on documents from Freudenthal’s vast personal archive) shows a more refined picture. The direct identification of 'kindergarten'-mathematics with Freudenthal’s view on mathematics education is not justified. 'Realistic mathematics' as advocated by Freudenthal includes more than just a practical introductory and should, among other things, always aim at teaching 'genuine' mathematics in the end.

Hans Freudenthal heeft een belangrijke invloed gehad op de ontwikkeling van het basiswiskundeonderwijs. Niet minder belangrijk was zijn activiteit als docent en onderzoeker gedurende tientallen jaren op het Mathematisch Instituut van de Universiteit Utrecht. Hoe waren toen zijn ideeën over onderwijs, hoe was hij als collega en hoe waren zijn colleges? Nellie Verhoef en Ferdinand Verhulst interviewden voormalige collega’s en studenten van Freudenthal.