in 1976, one devoted to physical sciences and Lakatos's general programme for rewriting the history of science, with a concluding critique by his great friend Paul Feyerabend, and the other devoted to economics. Philosophical work Philosophy of mathematics Lakatos' philosophy of mathematics was inspired by both Hegel's and Marx's dialectic, by Karl Popper's theory of knowledge, and by the work of mathematician George Pólya. The 1976 book Proofs and Refutations is based on the first three chapters of his 1961 four-chapter doctoral thesis Essays in the Logic of Mathematical Discovery. But its first chapter is Lakatos' own revision of its chapter 1 that was first published as Proofs and Refutations in four parts in 1963–64 in the British Journal for the Philosophy of Science. It is largely taken up by a fictional dialogue set in a mathematics class. The students are attempting to prove the formula for the Euler characteristic in algebraic topology, which is a theorem about the properties of polyhedra, namely that for all polyhedra the number of their vertices V minus the number of their edges E plus the number of their faces F is 2 (). The dialogue is meant to represent the actual series of attempted proofs that mathematicians historically offered for the conjecture, only to be repeatedly refuted by counterexamples. Often the students paraphrase famous mathematicians such as Cauchy, as noted in Lakatos's extensive footnotes. Lakatos termed the polyhedral counterexamples to Euler's formula monsters and distinguished three ways of handling these objects: Firstly, monster-barring, by which means the theorem in question could not be applied to such objects. Secondly, monster-adjustment, whereby by making a re-appraisal of the monster it could be made to obey the proposed theorem. Thirdly, exception handling, a further distinct process. These distinct strategies have been taken up in qualitative physics, where the terminology of monsters has been applied to apparent counterexamples, and the techniques of monster-barring and monster-adjustment recognized as approaches to the refinement of the analysis of a physical issue. What Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that we should not think that a theorem is ultimately true, only that no counterexample has yet been found. Once a counterexample is found, we adjust the theorem, possibly extending the domain of its validity. This is a continuous way our knowledge accumulates, through the logic and process of proofs and