FACES OF MATHEMATICS

Frank Kelly's research is in applied probability, and his main interest is in the design and control of communication networks. Large-scale networks, such as the Internet, present mathematical and engineering challenges in which randomness is a key feature. Kelly's research embraces both theoretical work in probability, and considerations of its impact and application to the stability and control of modern communication networks.

"The mathematician's job is to work out, of all the kinds of problems that there are with current networks, which ones are really worth trying to abstract into a model to work on... If you get a group of mathematicians and engineers, they each have different skills, and the mathematicians' ability to abstract, to look for the simplest thing that captures the true difficulty, is a powerful cooperative thing with the engineer who wants to solve the problem.

"The language of mathematics is a powerful tool for describing things, but also the process of mathematics is a fine way to collect information for future users of the language. Once you have a model, once you have a description of the system and a theorem about it, that compresses for later people what is otherwise a lot of work for them to recreate. Those premises, that conclusion: I can collect all that together, as a building block for something else.

"This construction of building blocks, trying to get a theorem out: it's not easy. As well as the usual difficulties in mathematics of things being damn hard to prove, you've also got the problem that it is not absolutely clear what the right premises are. Maybe that's true throughout mathematics, to find the right premises or technical conditions for a theorem. But there's something else going on here too: what is the right abstraction? You've got this engineering problem, and what it is that's going to be useful, that's an issue too."