Professor Alex Simpson, Personal Chair in Foundations of Computer Science, delivered his inaugural lecture entitled "The Intertwined Foundations of Mathematics and Computer Science". Mathematics is commonly perceived as a subject in which there are absolute standards of truth and proof. This perception, however, is not entirely accurate. There are ways in which it is possible to shape mathematics to suit the applications to which it will be put. In this talk, which is aimed at a general audience, Prof Simpson discusses various ways in which mathematics can be reshaped to take account of concepts arising in computer science. He also briefly touches upon how such reshapings might even be of use within certain areas of mathematics itself. Recorded on Thursday 17 May at the Informatics Forum, The University of Edinburgh.