Kevin Buzzard explains one of the biggest unsolved problems in theoretical computer science - the P vs NP problem. Watch the Q&A here: https://youtu.be/A6J9p4iOr3A Subscribe for regular science videos: http://bit.ly/RiSubscRibe Today’s computers are lightning-fast. But sometimes we want to make sure that they can’t solve a particular task quickly (perhaps for security purposes). This issue lies at the heart of the P vs NP problem, one of the most famous conundrums in computer science, which Kevin Buzzard will explore in this Discourse. Can every problem whose solution is quickly verifiable by a computer, also be quickly solved by a computer? Kevin Buzzard is a British mathematician and currently a Professor of Pure Mathematics at Imperial College London. He specialises in algebraic number theory. The Ri is on Twitter: http://twitter.com/ri_science and Facebook: http://www.facebook.com/royalinstitution and Tumblr: http://ri-science.tumblr.com/ Our editorial policy: http://www.rigb.org/home/editorial-policy Subscribe for the latest science videos: http://bit.ly/RiNewsletter