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. Section 2 gives a detailed analysis of Lakatos' ideas on the 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 Sections 3 and 4 of the Element give an account of how they developed this approach. Then Section 5 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.

1. Introduction; 2. Lakatos' contribution to the philosophy of mathematics; 3. Lakatos' legacy in the philosophy of mathematics I (1975¿1995); 4. Lakatos' legacy in the philosophy of mathematics II (1996¿2023); 5. Concluding remarks; References.