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Article ID: CBB686392053

On Conceptual changes in Computer Assisted Proofs (2023)

Favio Ezequiel Miranda Perea (Author)
Lourdes del Carmen González Huesca (Author)

Almagest
Volume: 14
Issue: 2
Pages: 222-245
Publication date: 2023
Language: English

DOI: 10.1484/J.ALMA.5.136768

URI: https://www.brepolsonline.net/doi/abs/10.1484/J.ALMA.5.136768

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Philosophy of mathematics Computers and computing Mathematics Proof 21st century 20th century, late

The concept of proof in mathematics has evolved through centuries from the intuitive notions of justification and validation. Many aspects around proofs and their acceptance have been part of philosophical and mathematical discussions since long time ago, but the insight of what counts or not as a valid mathematical proof has been changed since the advent of computers. Nowadays computer-assisted proofs and methodologies play a relevant role in many scientific areas and in the case of today mathematics some of those proofs can be put on a par with traditional paperand- pencil proofs. This raises the question whether they are just two incarnations of the same idea of proof or some kind of conceptual change is required to elucidate whether a computer-assisted proof can be considered as a valid demonstration in the mathematical practice. In this paper we give some initial remarks and arguments to explore the emergence of possible conceptual changes related to a specific kind of computer-assisted proofs, namely those developed by a human agent with the help of a modern interactive theorem prover or proof-assistant.

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Article Vincent Jullien; Carmen Martínez-Adame (2023) Foreward. Almagest (pp. 6-14). unapi

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