A recent paper by Kapustin and Witten synthesises ideas from pure mathematics and quantum field theory that have been developing independently for more than thirty years. Thus the Langlands programme, itself a unification scheme in mathematics, relates to electromagnetic duality and the topological twisting of supersymmetry. An attempt will be made to explain these ideas.

Annual General Meeting of the London Mathematical Society. See http://www.lms.ac.uk/meetings/AGM04.html for further details.