P v NP

P v NP

Author: BBC Radio 4 November 5, 2015 Duration: 45:45

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.

With

Colva Roney-Dougal Reader in Pure Mathematics at the University of St Andrews

Timothy Gowers Royal Society Research Professor in Mathematics at the University of Cambridge

And

Leslie Ann Goldberg Professor of Computer Science and Fellow of St Edmund Hall, University of Oxford

Producer: Simon Tillotson.


Melvyn Bragg and a panel of academic experts gather each week to explore the vast history of scientific thought on In Our Time: Science. This BBC Radio 4 podcast delves far beyond simple explanations, instead tracing the long and often winding paths of discovery that shaped our understanding of the world. Each episode focuses on a single idea, from the concept of zero to the theory of plate tectonics, unpacking its origins, the controversies it sparked, and the key figures who championed or challenged it. You’ll hear lively, in-depth conversations that place science firmly within its human and historical context, revealing how principles we take for granted today were hard-won through centuries of debate, accident, and insight. The discussions are rigorous and accessible, designed for the curious mind eager to appreciate not just what we know, but how we came to know it. By treating science as a deeply historical endeavour, this series offers a richer appreciation of the discipline itself. Tune in for a thoughtful and engaging journey through the experiments, the arguments, and the brilliant flashes of imagination that have defined our quest for knowledge.
Author: Language: English Episodes: 100

In Our Time: Science
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