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Abstract : This paper briefly reviews some epistemological perspectives on the foundation of mathematical concepts and proofs. It provides examples of axioms and proofs, from Euclid to recent "concrete incompleteness" theorems. In reference to basic cognitive phenomena, the paper focuses on order and symmetries as core "construction principles" for mathematical knowledge. A distinction is then made between these principles and the "proof principles" of modern Mathemaical Logic. The role of the blend of these different forms of founding principles will be stressed,
both for the purposes of proving and of understanding and communicating the proof
https://hal-ens.archives-ouvertes.fr/hal-03319485 Contributeur : UAR 3608 République des savoirsConnectez-vous pour contacter le contributeur Soumis le : jeudi 12 août 2021 - 13:54:07 Dernière modification le : jeudi 17 mars 2022 - 10:08:28 Archivage à long terme le : : samedi 13 novembre 2021 - 18:38:28
Giuseppe Longo. Theorems as Constructive Visions. Hanna, Gila; de Villiers, Michael. Proof and Proving in Mathematics Education. The 19th ICMI Study, Springer, pp.51-66, 2010, 978-94-007-2129-6. ⟨hal-03319485⟩