Abstract
The aim of this lecture is to give an overview of several different notions of the concepts of truth and proof in mathematics. This includes the two main directions of ‘Platonic realism’ and ‘Formalism’, with some variants, and other views such as ‘Intuitionism’, empiricism and quasi-empiricism, Field’s fictionalism, and social constructivism and realism. The lecture concludes with remarks on the notion of proof, including very recent progress obtained by computer scientists for understanding the overall notion of complexity of proof checking, and finally with some personal reminiscences and remarks on the subject.
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