Why are there chess Grandmasters, but not Grandmasters of noughts and crosses (otherwise known as tic-tac-toe)? It is because chess is “harder” – but what do we really mean by that? Answering that question leads us to develop the idea of mathematical complexity, which is a measure of how ‘big’ a game is. We’ll look at the complexity of popular games, and ask: what is the hardest game of all time? This lecture was recorded by Sarah Hart on 10 October 2023 at Barnard's Inn Hall, London Sarah is Gresham Professor of Geometry. She is also Professor Emerita of Mathematics at Birkbeck, University of London. https://www.gresham.ac.uk/speakers/professor-sarah-hart The transcript and downloadable versions of the lecture are available from the Gresham College website: https://www.gresham.ac.uk/watch-now/maths-games Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: https://gresham.ac.uk/support/ Website: https://gresham.ac.uk/ Twitter: https://twitter.com/greshamcollege Facebook: https://facebook.com/greshamcollege Instagram: https://instagram.com/greshamcollege