Abstracts of activities during the ESU 5 The ESU 5 activities are listed alphabetically below and include Plenary Lectures , Panels , 3-hour Workshops based on historical and epistemological material , 2-hour workshops based on didactical pedagogical material 30-minute oral presentations and 10-min short oral presentations All activities during the ESU 5 are related to one of its main themes: MAIN THEMES 1. History and Epistemology as tools for an interdisciplinary approach in the teaching and learning of Mathematics and the Sciences 2. Introducing a historical dimension in the teaching and learning of Mathematics 3. History and Epistemology in Mathematics teachers’ education 4. Cultures and Mathematics 5. History of Mathematics Education in Europe 6. Mathematics in Central Europe The abstracts are shown below: Plenary Lectures , Panels , 3-hour Workshops , 2-hour Workshops , Oral Presentations Short Presentations Plenary Lectures (Ordered alphabetically) Name Title Theme Language Country Corry Leo Axiomatics between Hilbert and R.L. Moore: Two Views on Mathematical Research and their Consequences on Education 1 English Israel Gispert Hélène, Schubring Gert The History of Mathematics Education and its contexts in 20th century France and Germany 5 English France, Germany Hyksova Magdalena Contribution of Czech Mathematicians to Probability Theory 6 English Czech Republic Puig Luis Researching the history of algebraic ideas from an educational point of view 2 English Spain Rebstock Ulrich Mathematics in the service of the Islamic community 4 English Germany Schweiger Fritz The implicit grammar of mathematical symbolism 3 English Austria Plenary Lectures ABSTRACTS (ordered by theme) Theme 1 AXIOMATICS BETWEEN HILBERT AND R.L. MOORE: TWO VIEWS ON MATHEMATICAL RESEARCH AND THEIR CONSEQUENCES ON EDUCATION Leo Corry University of Tel Aviv, Ramat Aviv 69978, Israel David Hilbert is widely acknowledged as the father of the modern axiomatic approach in mathematics. The methodology and point of view put forward in his epoch making Foundations of Geometry (1899) had lasting influences on research and education throughout the twentieth century. Still, his own conception of the role of axiomatic thinking in mathematics and in science in general was significantly different from the way in which it