There is a $1,000,000 prize on offer for the first person to come up with a complete solution to the problem P versus NP. At its heart is the question "are there problems for which the answers can be checked by computers, but not found in a reasonable time?" If the answer to that is yes, then P does not equal NP. However, if all answers can be found easily as well as checked, if only we knew how, then P equals NP. Melvyn Bragg talks to Colva Roney-Dougal and Leslie Ann Goldberg.

First broadcast on In Our Time, 5 November 2015.