An annual series of three or four informal lectures, held during Trinity Term as a subseries of the Mathematical Institute’s History of Mathematics Seminar, with the goal of demonstrating some of the research on the history of mathematics currently being done in the UK, and of giving a sense of what it means to do research in the history of mathematics. Each lecture allows plenty of time for questions and discussion. No previous knowledge is required: the lectures are open to members of all departments, from undergraduates upwards, and to members of the public.