One way to deal with these questions is offered by realizability theory, where we build an entire mathematical universe on top of a computational model, for example RAM machines or a programming language. In such a custom-made mathematical world every mathematical construction is automatically equipped with an implementation in the underlying computational model. The development of a computation-sensitive mathematics can then proceed at an abstract and conceptual level, with a clear idea of what it means to correctly implement a given mathematical objects.

In the new world, not everything is the same as in classical mathematics. Not all classical axioms are valid anymore, and some classically invalid axioms are validated. These changes influence the properties of well known mathematical objects, such as the real numbers. A computationally minded person will admit, however, that the new world is better than the old one.

Speaker Bio:

Andrej Bauer joined the Institute of Mathematics, Physics and Mechanics at the University of Ljubljana, Slovenia, as a Research Fellow in July 2001. Prior to this appointment, he held a research fellowship at the Mittag-Leffler Institute, The Royal Swedish Academy of Sciences in Stockholm, Sweden. Dr. Bauer received his Ph.D. in Pure and Applied Logic from the School of Computer Science at Carnegie Mellon University in September 2000, where his thesis focussed on "The Realizability Approach to Computable Analysis and Topoology." He earned his International Baccalaureate from the United World College of the Adriatic Duino (Trieste), Italy, in 1990 and his B.S. in Mathematics from the Department of Mathematics and Physics at the University of Ljubljana in 1994.

Dr. Bauer is the co-winner of this year's prestigious School of Computer Science Doctoral DissertationAward, along with Rob O'Callahan, currently at the IBM T.J. Watson Research Center in New York.

<< Back