|Scheme:||Royal Society Research Professorship|
|Dates:||Oct 2009 - Sep 2014|
University of Cambridge
I am working with a colleague, Mohan Ganesalingam, on a computer program that can solve mathematical problems by itself, using the same kinds of methods that a human mathematician would use. That last qualification is important: unlike, say, the Deep Blue algorithm for playing chess, it does not do big searches. For the moment, the problems it can solve are all quite easy for an expert mathematician, though some of them would be found hard by some undergraduates. The proofs the program produces are written in a way that human mathematicians find hard to distinguish from the kinds of proofs that they themselves would write: this we know because we have tested it. The potential impact of this project is large. One benefit of a program that uses human methods to solve problems is that it can explain its thought processes in a comprehensible way. So one possibility amongst many is that our work could one day be used as part of an interactive mathematics educational program. There has been a great deal of talk about Massive Online Open Courses, but what is missing from those is the kind of interaction you get with a human teacher. A computer program that could understand how humans think, diagnose mistakes and misconceptions, and explain how to come up with mathematical ideas, could take MOOCs to another level. This would be a long-term project, but I firmly believe that it is feasible without the need for any major advances in artificial intelligence.