Irreducible Complexity in Pure Mathematics

2004/11/04 by G. J. Chaitin, Gregory J. Chaitin, Chaitin, G. J. · 2 citations
Computer Science · Mathematics · #68Q30 #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Overview (math.HO) #math.HO #msc:68Q30

paper · pdf · doi:10.48550/arxiv.math/0411091

13 pages

arxiv created 2004/11/04 · openalex publication_date 2004/11/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using ideas on complexity and randomness originally suggested by the mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of algorithmic information is able to show that there can never be a "theory of everything" for all of mathematics.

Cited by

• The Importance of the Algorithmic Information Theory to Construct a Possible Example Where NP # P - II: An Irreducible Sentence
• Using Disentangled States and Algorithmic Information Theory to Construct a Not P Problem

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