Stumbling Around in the Dark: Lessons from Everyday Mathematics

The growing use of the internet for collaboration, and of numeric and symbolic software to perform calculations it is impossible to do by hand, not only augment the capabilities of mathematicians, but also afford new ways of observing what they do. In this essay we look at four case studies to see what we can learn about the everyday practice of mathematics: the polymath experiments for the collaborative production of mathematics, which tell us about mathematicians attitudes to working together in public; the minipolymath experiments in the same vein, from which we can examine in finer grained detail the kinds of activities that go on in developing a proof; the mathematical questions and answers in math overflow, which tell us about mathematical-research-in-the-small; and finally the role of computer algebra, in particular the GAP system, in the production of mathematics. We conclude with perspectives on the role of computational logic.