A Cambridge Element with the above title is due to be published in the autumn of 2023. In my talk I will give an outline of this Element and present some of its contents in detail. The Element begins by claiming that Imre Lakatos (1922-74) in his famous paper ‘Proofs and Refutations’ (1963-64) was the first to introduce the historical approach to philosophy of mathematics. Lakatos died at the age of only 51, and at the time of this death had plans to continue his work on philosophy of mathematics which were never carried out. However, Lakatos’ historical approach to philosophy of mathematics was taken up by other researchers in the field, and the second part of the Element gives an account of how they developed this approach. The final section of the Element gives an overview of what has been achieved so far by the historical approach to philosophy of mathematics and considers what its prospects for the future might be. Lakatos was my PhD supervisor, and in the talk I will give some reminiscences of him as a man and a teacher.
Donald Gillies is Emeritus Professor of Philosophy of Science and Mathematics at University College London. He read mathematics and history and philosophy of science at the University of Cambridge and received his PhD in Philosophy at London School of Economics. He is a past President of the British Society for the Philosophy of Science. From 1982 to 1985 he was an editor of The British Journal for the Philosophy of Science. He has extensively worked on philosophy of probability, philosophy of mathematics, philosophy of AI, philosophy of medicine, and history and philosophy of science. He has published 15 books and over 120 research papers in leading philosophy journals.