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.
Guests
 Colva RoneyDougal
11 episodes
Reader in Pure Mathematics at the University of St Andrews  Timothy Gowers
4 episodes
Royal Society Research Professor in Mathematics at the University of Cambridge  Leslie Ann Goldberg
2 episodes
Professor of Computer Science and Fellow of St Edmund Hall, University of Oxford
Reading list

Quantum Computing Since Democritus
Scott Aaronson (Cambridge University Press, 2013) Google Books → 
In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation
William J. Cook (Princeton University Press, 2012) Google Books → 
The Golden Ticket: P, NP, and the Search for the Impossible
Lance Fortnow (Princeton University Press, 2013) Google Books → 
Out of their Minds: The Lives and Discoveries of 15 Great Computer Scientists
Dennis Shasha (Springer, 2008) Google Books →
Related episodes

The Poincaré Conjecture
2 Nov, 2006 510 Mathematics 
Mathematics’ Unintended Consequences
11 Feb, 2010 510 Mathematics 
Fermat’s Last Theorem
25 Oct, 2012 510 Mathematics 
Godel’s Incompleteness Theorems
9 Oct, 2008 510 Mathematics 
Prime Numbers
12 Jan, 2006 510 Mathematics 
Random and Pseudorandom
13 Jan, 2011 510 Mathematics 
Alan Turing
15 Oct, 2020 510 Mathematics 
Artificial Intelligence
8 Dec, 2005 000 Computer science, knowledge and systems 
Theories of Everything
25 Mar, 2004 530 Physics 
Consciousness
25 Nov, 1999 120 Epistemology
Programme ID: b06mtms8
Episode page: bbc.co.uk/programmes/b06mtms8
Autocategory: 510 (Mathematics)