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As a participant in the influential philosophy-of-science debates of the 1960s and 1970s, mostly surrounding Thomas Kuhn’s The Structure of Scientific Revolutions, Imre Lakatos (1922–1974) made pedagogy and critical method the dual focus of his historicist philosophy.

At Cambridge as a refuge from the 1956 Hungarian Revolution, Lakatos wrote the English language PhD thesis edited and published posthumously as Proofs and Refutations: The Logic of Mathematical Discovery. Influenced by his countryman, the mathematician and pedagogue George Pólya, Lakatos made mathematical heuristic—meaning informal methods of mathematical discovery, innovation, and proof—a central philosophical idea.

The book takes the form of a pedagogical dialogue between a teacher and 18 characters, named Alpha, Beta, and so forth, who debate and improve a theorem and proof of polyhedra by the 18th-century Swiss ...

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