Imre Lakatos (UK: /ˈlækətɒs/,[6] US: /-toʊs/; Hungarian: Lakatos Imre [ˈlɒkɒtoʃ ˈimrɛ]; 9 November 1922 – 2 February 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its "methodology of proofs and refutations" in its pre-axiomatic stages of development, and also for introducing the concept of the "research programme" in his methodology of scientific research programmes.

In March 1944 the Germans invaded Hungary, and Lakatos along with Éva Révész, his then-girlfriend and subsequent wife, formed soon after that event a Marxist resistance group.

He also continued his education with a PhD at Debrecen University awarded in 1948 and also attended György Lukács's weekly Wednesday afternoon private seminars.

In fact, Lakatos was a hardline Stalinist and, despite his young age, had an important role between 1945 and 1950 (his own arrest and jailing) in building up the Communist rule, especially in cultural life and the academia, in Hungary.

Still nominally a communist, his political views had shifted markedly, and he was involved with at least one dissident student group in the lead-up to the 1956 Hungarian Revolution.

[11] It was Agassi who first introduced Lakatos to Popper under the rubric of his applying a fallibilist methodology of conjectures and refutations to mathematics in his Cambridge PhD thesis.

With co-editor Alan Musgrave, he edited the often cited Criticism and the Growth of Knowledge, the Proceedings of the International Colloquium in the Philosophy of Science, London, 1965.

Published in 1970, the 1965 Colloquium included well-known speakers delivering papers in response to Thomas Kuhn's The Structure of Scientific Revolutions.

These case studies in such as Einstein's relativity programme, Fresnel's wave theory of light and neoclassical economics, were published by Cambridge University Press in two separate volumes 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.

[15] Lakatos's 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.

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.

Lakatos, Worrall and Zahar use Poincaré (1893)[18] to answer one of the major problems perceived by critics, namely that the pattern of mathematical research depicted in Proofs and Refutations does not faithfully represent most of the actual activity of contemporary mathematicians.

Lakatos is critical of those who would see Cauchy's proof, with its failure to make explicit a suitable convergence hypothesis, merely as an inadequate approach to Weierstrassian analysis.

Lakatos's model of the research programme aims to combine Popper's adherence to empirical validity with Kuhn's appreciation for conventional consistency.

More modest and specific theories that are formulated in order to explain evidence that threatens the "hard core" are termed auxiliary hypotheses.

Auxiliary hypotheses are considered expendable by the adherents of the research programme—they may be altered or abandoned as empirical discoveries require in order to "protect" the "hard core".

The difference between a progressive and a degenerative research programme lies, for Lakatos, in whether the recent changes to its auxiliary hypotheses have achieved this greater explanatory/predictive power or whether they have been made simply out of the necessity of offering some response in the face of new and troublesome evidence.

Lakatos's primary example of a research programme that had been successful in its time and then progressively replaced is that founded by Isaac Newton, with his three laws of motion forming the "hard core".

[22] The continued adherence to a programme's "hard core", augmented with adaptable auxiliary hypotheses, reflects Lakatos's less strict standard of falsificationism.

[24] Lakatos claimed that not all changes of the auxiliary hypotheses of a research programme (which he calls "problem shifts") are equally productive or acceptable.

For Lakatos, it is essentially necessary to continue on with a theory that we basically know cannot be completely true, and it is even possible to make scientific progress in doing so, as long as we remain receptive to a better research programme that may eventually be conceived of.

As he put it: Lakatos's own key examples of pseudoscience were Ptolemaic astronomy, Immanuel Velikovsky's planetary cosmogony, Freudian psychoanalysis, 20th-century Soviet Marxism,[27] Lysenko's biology, Niels Bohr's quantum mechanics post-1924, astrology, psychiatry, and neoclassical economics.

Almost 20 years after Lakatos's 1973 challenge to the scientificity of Darwin, in her 1991 The Ant and the Peacock, LSE lecturer and ex-colleague of Lakatos, Helena Cronin, attempted to establish that Darwinian theory was empirically scientific in respect of at least being supported by evidence of likeness in the diversity of life forms in the world, explained by descent with modification.