Nieuw Archief Voor Wiskunde

This book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdös, B.L. van der Waerden, and Henry Baudet.

Significs is one of those (by no means exclusively) sign theoretically relevant movements which arose at the turn of the century. It established a philosophical tradition which, from its very inception, was interlaced with widely varying movements ranging, for example, from Breal's semantics to Carnap's and Neurath's logical empiricism. In this volume, an international group of well-known scholars from various disciplines undertakes a broad re-evaluation of significs and its development which promises also to yield a better knowledge of research approaches in linguistics, semiotics, philosophy, and psychology with which significs was related or vied for acceptance. Contributions deal with Lady Welby's biography and socio-cultural background, the intellectual context of the signific movement at the turn of the century and the relationships between Welby's semiotic and philosophical ideas on the one hand and those of her contemporaries (Breal, Peirce, Schiller, Vailati etc.) and followers (Ogden, Van Eeden, Mannoury etc.) on the other. Descriptions of the historiographically most important archive materials, a bibliography of publications on Lady Welby and her significs and an index of names conclude the volume.

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.