On 8 Mar 2010 Jonathan M. Borwein gave the First Plenary Lecture on “Exploratory Experimentation and Computation” (Lecture) at the 2010 German Mathematical Society meetings in Munich. An associated paper, co-authored with David H. Bailey, is here: PDF.
Abstract:
The mathematical research community is facing a great challenge to re-evaluate the role of proof in light of the growing power of current computer systems, of modern mathematical computing packages, and of the growing capacity to data-mine on the Internet. Add to that the enormous complexity of many modern capstone results such as the Poincaré conjecture, Fermat’s last theorem, and the Classification of finite simple groups. As the need and prospects for inductive mathematics blossom, the requirement to ensure the role of proof is properly founded remains undiminished. I shall look at the philosophical context with examples and then offer some of five bench-marking examples of the opportunities and challenges we face.