Lakatos's Proofs and Refutations is usually understood as an attempt to apply Popper's methodology of science to mathematics. This view has been challenged because despite appearances the methodology expounded in it deviates considerably from what would have been a straightforward application of Popperian maxims. I take a closer look at the Popperian roots of Lakatos's philosophy of mathematics, considered not as an application but as an extension of Popper's critical programme, and focus especially on the core ideas of this programme (...) as they appeared where Popper specifically addressed philosophical problems concerning mathematics. (shrink)