By Noga Alon, Jean Bourgain, Alain Connes, Misha Gromov, Vitali D. Milman

"Visions in arithmetic - in the direction of 2000" was once some of the most notable mathematical conferences lately. It used to be held in Tel Aviv from August twenty fifth to September third, 1999, and united the various major mathematicians around the world. The objectives of the convention have been to debate the significance, the equipment, the prior and the way forward for arithmetic as we input the twenty first century and to think about the relationship among arithmetic and comparable components. The goals of the convention are mirrored within the current set of survey articles, documenting the country of paintings and destiny customers in lots of branches of arithmetic of present curiosity. this can be the second one a part of a two-volume set that might serve any learn mathematician or complicated scholar as an outline and guide in the course of the multifaceted physique of mathematical study within the current and close to destiny.

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