Randomness in Arithmetic and The Decline and Fall of Reductionism in Pure Mathematics
G. J. Chaitin (IBM Research Division)
TL;DR
This paper discusses the role of randomness in arithmetic and argues against reductionist approaches in pure mathematics, highlighting philosophical and foundational implications.
Contribution
It presents a critique of reductionism in pure mathematics and explores the significance of randomness in arithmetic foundations.
Findings
Randomness plays a fundamental role in arithmetic.
Reductionism in pure mathematics faces philosophical challenges.
The lecture questions traditional deterministic views in mathematics.
Abstract
Lecture given Thursday 22 October 1992 at a Mathematics-Computer Science Colloquium at the University of New Mexico. The lecture was videotaped; this is an edited transcript.
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Taxonomy
TopicsComputability, Logic, AI Algorithms