Final Report

The Conference on Mathematics and the Century was held in Cairo-Egypt during the period 15-20 January 2000. The Conference was an event of the WMY2000 initiative launched by the International Mathematical Union. The Conference was hosted in the Tiba Rose hotel in Cairo where most of the foreign participants were lodged.

I. Scientific activities:

The Conference was opened at 10AM on January 15, 2000. The opening ceremony was, attended by H.E. Prof. Dr. Mofeed Shehab, Egyptian minister of scientific research. In addition, Prof. M. Yosry president of the Egyptian Academy for Science and Technology (ASRT), Prof. Jacob Palis, President of the International Mathematical Union (IMU), and also representing the Third World Academy of Science (TWAS), Prof. M. El-Deek, Head of the UNESU Regional Office for Science and Technology for the Arab States (ROSTAS) addressed the conference. A message of good wishes from Prof. M. Verasoro Director of Abdus Salam International Centre for Theoretical Physics was delivered by Prof. A. Ashour chairman of the conference. The opening session was followed by the Millenium lecture, delivered by Sir Michael Atiyah. The title of the lecture was " A Thousand Years of Mathematics"

The conference's sessions consisted of 11 plenary lectures and of 24 topical sessions. Some of the plenary lectures covered general fields are: Rewriting the history of mathematics, Education of mathematics, Relation between Mathematics and Sciences " Is Interdisciplinary Research Possible? ", Mathematical Aspects of Transportation. General reviews of the recent researches and standing problems were also delivered. In this aspect the following lectures are relevant: A global view of dynamical systems; Einstein's theory of space-time and gravitation; A geometrical theory for the unification of all fundamental forces; Transfer of energy from low frequency to high frequency modes; Stratification of algebras; Multivariate statistical distributions.

Each topical session comprised an invited 40-minute talk and 3-4 contributed papers. The invited topical lectures covered: Finite groups, Radical theory; Enumerative geometry; Moduli problems in geometry; Asymptotic behaviour of solutions of evolution equations; Instability of nonlinear evolution equations; Non-smooth dynamical systems; On approximations of functions; On a semi-analytic method for the solution of some elliptic B.V.P; On robust layer resolving methods for computing numerical approximations; Eigen values for fractal drums; Electrostatic models and orthogonal polynomials; On the developments on theory of functions of several complex variables; Invertibility preserving linear maps; Entire functions sections; Optical solitons; Non-classical properties of intermediate states; On the relativistic 2-body problem; Singularities in general relativity; Linear geometry of light cone; Advances and new results in prediction; and Theory of accelerated experiments.

The topical sessions were grouped in the following sections: Algebra (4), Applied mathematics (4), Computer Science, and Operational research, Analysis (4), Analysis and diff. eqn. Quantum theory (2), Statistics; Numerical analysis, Relativity(2) and geometry, Optimization and control , Topology. The plenary and invited topical lectures covered a broad spectrum of research in mathematics and its applications together with the history of Mathematics and Mathematics Education. Details of the program can be found in the web site http://wmy2000.math.jussieu.fr/Cairo/cairo2000.html

The Conference offered a unique opportunity for mathematicians from Egypt, and nearby countries to have an overview of the actual status of research in many areas of the mathematical sciences and to tighten connections with their colleagues in other countries. The Conference was attended by 132 participants, coming from 19 countries, including 11 invited plenary speakers and 24 invited topical speakers. For a complete list of participants and the distribution of participants by country see web site http://wmy2000.math.jussieu.fr/Cairo/cairo2000.html

In the closing ceremony at 5.00 PM on Jan 20,2000, Prof. Narasimhan the Director of Mathematics in ICTP gave a short speech and Prof. Ali H. Nayfeh of Virginia Polytech. USA spoke for the invited speakers and Prof. Ashour chairman of the conference gave some concluding remarks.