By Jean A. Dieudonne

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Examples of Paradigmatic Shifts. The above mentioned trials and suggestion reflect the fact that "modern" societies-as they are contending to socio-economic prosperity and advancement-need numerate citizens, top mathematicians, authentic scientists and creative engineers and technologists. This implies compelling and imperative necessity to make paradigmatic shift in the course of mathematics education so as to tune it to the appropriate content, delivery systems and learning theories. In this context the following projects give examples of indigenous shifts, not just changes through addition and deletions.

A. A. -S. F. Obada © 2 0 0 1 World Scientific Publishing Co. (pp. 41-52) EINSTEIN'S THEORY OF SPACETIME AND GRAVITY J U R G E N EHLERS Max-Planck-Institut fiir Gravitationsphysik, Albert-Einstein-Institut, Am Muhlenberg 1, 1^16 Golm, Germany INTRODUCTION T h e general theory of relativity (GR), created almost single-handedly by Albert Einstein between 1907 and 1915, deals with both gravitation and spacetime structure. While in Newtonian physics and in special relativity theory the geometry of spacetime - its topological, affine and metric structure - is assumed to be independent of whatever physical processes are taking place, according to G R spacetime carries a dynamical metric which interacts with matter, and this leads to the phenomena of gravitation.

S. A. , Porta and Uhl, J. " A paper distributed at the Rosilde University Conference in 1997, Demark. (7) Ebeid, William (1999): "Current and Future Trends in Learning and Teaching Mathematics" ; MOE, Dubai, United Arab Emirates. (8) Ebeid, William (1999): "Socieetal Mathematics as a Futuristic Trend", International Conference on Mathematics Education into the 21 st Century". ) Cairo, Egypt, Nov. 1999. (9) Ebeid, William (1998): "Enrolment in Mathematics, Problems and Aspirations in Kuwait University", in Proceedings of Conference on Justification and Enrolment Problems Involving Mathematics or Physics", Roskilde University, Denmark.