Demonstração, Verdade e Entendimento no conhecimento matemático: um estudo de caso a partir do Teorema das Quatro Cores

Authors

  • Igor de Camargo e Souza Câmara Universidade de São Paulo

DOI:

https://doi.org/10.51359/2357-9986.2019.247940

Keywords:

mathematical knowledge, proof, validity, understanding

Abstract

In this paper, I argue that mathematical knowledge is not reduced to a collection of proved and verified (hence, true to all practical matters) theorems. I defend that the ideas of mathematical understanding and mathematical explanation are essential not only to mathematical practice and heuristics but also to the very foundations of the discipline. To accomplish that, I examine the classic Appel-Haken proof of the Four-Color Theorem and discuss it from a philosophical perspective, taking on account the rich literature on the topic. The Four-Color Theorem was one of the first original theorems to be proved with considerable help from computational machinery, employed for performing exhaustive case checking, and that was responsible for encouraging a relevant discussion on several topics of mathematical epistemology.

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Published

2020-08-19

Issue

Vol. 46 No. 1 (2019): Epistemologia Contemporânea - Primeira Parte: Questões de Epistemologia Analítica

Section

Dossiê de Epistemologia Contemporânea

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