Fred Uhlman⁽¹⁾

A Colloquium on Mathematics and Art was hold in the French city of Maubeuge in September 2000. The scientific committee included Jacek Bochnak (Amsterdam), Ronald Brown (Bangor), Claude-Paul Bruter (Paris 12), Manuel Chaves (Porto), Michele Emmer (Roma), Tzee-Char Kuo (Sydney), Richard Palais (Brandeis) and Valentin Poenaru (Paris 11). We would like to warmly thank Francis Trincaretto and his team who arranged to have the meeting in such an agreable venue : the "Théâtre du Manège".

Placed at the transition of the second and the third millennium, this Colloquium presented original ideas related to the development of new forms of civilization based on the many recent and rapid technological advances in communication and computation. With the strong encouragement of the local organizer, Francis Trincaretto, the Colloquium was - unlike more formal mathematical conferences - videoed and could be attended on the web. The speakers were true artists and mathematicians of rather unusual standard : while the artists were partly inspired by advanced mathematics, or even were sometimes ahead of mathematics, the mathematicians intended to show the beauty of their work and to share their feeling with the greater part of the population. They used all the old and new means of static and dynamic visualizations. Their works may be understood as symbolic and iconic representations of our environment and as essential tools for the understanding of our world, and the development of mankind.

Indeed, this Colloquium can be related to a renewal in the ways of diffusion and of teaching of mathematics. While schools of plastic or musical art are beginning to ask for some mathematics, mathematicians are seriously thinking of setting forth the artistic qualities of their work to attract the mind, and to support and facilitate the learning of their discipline.

We hope that readers may find in these proceedings ideas, projects and realizations which can contribute towards the inspiration and promotion of new cultural developments in Society.

The order of the articles follows that of the talks. Pictures and images appear in grey in the articles. Some of the images appear also in colour both in the Appendix and in the CD-Rom attached with the book. Such an image is labelled [XY]k where XY are the main initials of the author, while k numbers the image.

To conclude, we would like to thank Mike Field who accepted to help the translations into English of most French written texts, Bill Mac Callum who did that work for the second part of my first contribution, and the Springer team who accepted to publish these Proceeedings, and provided their help to the editor.

⁽¹⁾(1901-1985) German advocate, then British painter and writer : his booklet "Reunion" is a true masterpiece.