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.
The full text of this lecture has been published in: The shifting aspects of truth in mathematics, Enrico Bombieri, Euresis Journal, Volume 5, Summer 2013, 249–272.
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Bombieri, E. (2015). The Mathematical Truth1 . In: Zannier, U. (eds) Colloquium De Giorgi 2013 and 2014. Publications of the Scuola Normale Superiore, vol 5. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-515-8_1
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DOI: https://doi.org/10.1007/978-88-7642-515-8_1
Publisher Name: Edizioni della Normale, Pisa
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Online ISBN: 978-88-7642-515-8
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