P v NP
Melvyn Bragg and guests discuss the problem of P versus NP, which has a bearing on online security. There is a $1,000,000 prize on offer from the Clay Mathematical Institute for the first person to come up with a complete solution. 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. The area has intrigued mathematicians and computer scientists since Alan Turing, in 1936, found that it's impossible to decide in general whether an algorithm will run forever on some problems. Resting on P versus NP is the security of all online transactions which are currently encrypted: if it transpires that P=NP, if answers could be found as easily as checked, computers could crack passwords in moments.
Reader in Pure Mathematics at the University of St Andrews
Royal Society Research Professor in Mathematics at the University of Cambridge
Leslie Ann Goldberg
Professor of Computer Science and Fellow of St Edmund Hall, University of Oxford
Producer: Simon Tillotson.
LINKS AND FURTHER READING
Scott Aaronson, Quantum Computing Since Democritus (Cambridge University Press, 2013)
William J. Cook, In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation (Princeton University Press, 2012)
Lance Fortnow, The Golden Ticket: P, NP, and the Search for the Impossible (Princeton University Press, 2013)
Dennis Shasha, Out of their Minds: The Lives and Discoveries of 15 Great Computer Scientists (first published 1995; Springer, 2008)
|Interviewed Guest||Colva Roney-Dougal|
|Interviewed Guest||Timothy Gowers|
|Interviewed Guest||Leslie Ann Goldberg|