TL;DR
This paper explores the nature of mathematical reasoning, emphasizing its exploratory and creative aspects over strict rigor, and discusses how mathematicians navigate the 'wilderness' of discovery.
Contribution
It offers a philosophical perspective on mathematical reasoning, highlighting its exploratory and heuristic qualities rather than solely focusing on formal rigor.
Findings
Mathematical reasoning is akin to exploration in a wilderness.
Rigor serves as a historical marker, not the essence of discovery.
The paper advocates for valuing intuition and creativity in mathematics.
Abstract
"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere." W.S. Anglin, the Mathematical Intelligencer, 4 (4), 1982.
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Taxonomy
TopicsHistory and Theory of Mathematics · Computability, Logic, AI Algorithms