Ursula Martin

Online blogs, question answering systems and distributed proofs provide a
rich new resource for understanding what mathematicians do, and hence
devising better computer tools for supporting mathematical advance.
In this talk we discuss the first steps in such a research programme, looking at two examples through a sociological lens, to see what we can learn about mathematical practice, and whether the reality of mathematical practice supports the theories of philosophers of mathematics such as Polya and Lakatos, or the expectations of computer scientists devising software to do maths. Polymath provides structured way for a number of people to work on a proof simultaneously: we analyse polymath proofs of a math olympiad problem to see what kinds of techniques the participants use. Mathoverflow supports asking and answering research level mathematical questions: we look at a sample of questions about algebra, and provide a typology of the kinds of questions asked, and consider the features of the discussions and answers they generate. Finally we outline a programme of further work, and consider what our results tell us about opportunities for further computational support for proof and question answering. 