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Reshaping the metaphor of proof. / Vavilov, Nikolai.

в: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Том 377, № 2140, 20180279, 11.03.2019.

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Harvard

Vavilov, N 2019, 'Reshaping the metaphor of proof', Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Том. 377, № 2140, 20180279. https://doi.org/10.1098/rsta.2018.0279

APA

Vavilov, N. (2019). Reshaping the metaphor of proof. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377(2140), [20180279]. https://doi.org/10.1098/rsta.2018.0279

Vancouver

Vavilov N. Reshaping the metaphor of proof. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2019 Март 11;377(2140). 20180279. https://doi.org/10.1098/rsta.2018.0279

Author

Vavilov, Nikolai. / Reshaping the metaphor of proof. в: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2019 ; Том 377, № 2140.

BibTeX

@article{445f5bb6e1cc4c63b8ecda1f77d4b643,
title = "Reshaping the metaphor of proof",
abstract = "The simplistic view of Mathematics as a logical system of formal truths deduced from a limited set of axioms by a limited set of inference rules immediately shatters when confronted with the history of Mathematics, or current mathematical practice. To become useful, mathematical Philosophy should contemplate what Mathematics actually was, over centuries, and what it is now, rather than speculate what it should be according to the philosophical orthodoxy. The first dogma that must be completely revised is the idea of proof as a text, rather than what it is for mathematicians themselves: a process, a plethora of interwoven arguments, a multi-dimensional structure.This article is part of the theme issue 'The notion of 'simple proof' - Hilbert's 24th problem'.",
keywords = "Mathematics, traditional proofs, formal proofs, mathematical mistakes, reliability of mathematical results, математика, традиционное доказательство, формальное доказательство, математические ошибки, надежность математических результатов, философия математики, 24я проблема Гильберта, программа Воеводского",
author = "Nikolai Vavilov",
year = "2019",
month = mar,
day = "11",
doi = "10.1098/rsta.2018.0279",
language = "English",
volume = "377",
journal = "Philosophical transactions. Series A, Mathematical, physical, and engineering sciences",
issn = "0962-8428",
publisher = "Royal Society of London",
number = "2140",

}

RIS

TY - JOUR

T1 - Reshaping the metaphor of proof

AU - Vavilov, Nikolai

PY - 2019/3/11

Y1 - 2019/3/11

N2 - The simplistic view of Mathematics as a logical system of formal truths deduced from a limited set of axioms by a limited set of inference rules immediately shatters when confronted with the history of Mathematics, or current mathematical practice. To become useful, mathematical Philosophy should contemplate what Mathematics actually was, over centuries, and what it is now, rather than speculate what it should be according to the philosophical orthodoxy. The first dogma that must be completely revised is the idea of proof as a text, rather than what it is for mathematicians themselves: a process, a plethora of interwoven arguments, a multi-dimensional structure.This article is part of the theme issue 'The notion of 'simple proof' - Hilbert's 24th problem'.

AB - The simplistic view of Mathematics as a logical system of formal truths deduced from a limited set of axioms by a limited set of inference rules immediately shatters when confronted with the history of Mathematics, or current mathematical practice. To become useful, mathematical Philosophy should contemplate what Mathematics actually was, over centuries, and what it is now, rather than speculate what it should be according to the philosophical orthodoxy. The first dogma that must be completely revised is the idea of proof as a text, rather than what it is for mathematicians themselves: a process, a plethora of interwoven arguments, a multi-dimensional structure.This article is part of the theme issue 'The notion of 'simple proof' - Hilbert's 24th problem'.

KW - Mathematics

KW - traditional proofs

KW - formal proofs

KW - mathematical mistakes

KW - reliability of mathematical results

KW - математика

KW - традиционное доказательство

KW - формальное доказательство

KW - математические ошибки

KW - надежность математических результатов

KW - философия математики

KW - 24я проблема Гильберта

KW - программа Воеводского

U2 - 10.1098/rsta.2018.0279

DO - 10.1098/rsta.2018.0279

M3 - Article

VL - 377

JO - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

JF - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

SN - 0962-8428

IS - 2140

M1 - 20180279

ER -

ID: 51598920