Experimental (Computational) Mathematicsâ€”and Philosophical Implications
by Prof. Jonathan Borwein
Abstract: Kurt GÃ¶del overturned the mathematical apple cart entirely deductively, but he could hold quite different ideas about legitimate forms of mathematical reasoning:
"If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied to mathematics just the same as in physics." (Collected Works Vol. III, 1951)
And Christopher Koch accurately captures a great scientific distaste for philosophizing:
"Whether we scientists are inspired, bored or infuriated by philosophy, all our theorizing and experimentation depends on particular philosophical background assumptions. This hidden influence is an acute embarrassment to many researchers, and it is therefore not often acknowledged." (Thinking About the Conscious Mind, 2004)
I aim to discuss Experimental Mathodology, its philosophy, history, current practice and proximate future, and using concrete accessibleâ€”entertaining I hopeâ€”examples, to explore implications for mathematics and for mathematical philosophy.
For More Information: Graham Keen, AMSI Ph. 8344-1772