Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Computational Lists and Challenges in Mathematics

Speaker: **Jonathan Borwein**, Dalhousie University

Date: November 10, 2005 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

I aim to discuss Experimental Mathodology, its philosophy, history, current practice and proximate future, and using concrete accessible---entertaining I hope---examples, to explore implications for mathematics and for mathematical philosophy. Thereby, to persuade you both of the power of mathematical experiment and that the traditional accounting of mathematical learning and research is largely an ahistorical caricature.

I shall do so with a sample of material largely from the 2005 Clifford Lectures which I gave at Tulane University in New Orleans in April 2005.

*Plausible Reasoning in the 21st Century, I*is a general introduction to Experimental Mathematics, its Practice and its Philosophy. It reprises the `Experimental methodology' that David Bailey and I---among many others---have practiced over the past two decades.-
*Plausible Reasoning in the 21st Century, II*focusses on the differences between Determining Truths and Proving Theorems. It explores various of the tools available for deciding what to believe in mathematics, and using accessible examples---illustrates the rich experimental tool-box mathematicians can now have access to. *Ten Computational Challenge Problems*is a more advanced analysis of the themes developed in Lectures 1 and 2. It discusses examples including*Apery-Like Identities for zeta(n).*The final lecture comprises a research level case study of generating functions for zeta functions.