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The Game of Life: A Six-Decade Chronicle of Engineering Innovation

2025-03-19

This article explores the nearly six decades of 'meta-engineering' development in Conway's Game of Life. The author traces the innovation arc from simple static structures to complex computational machines, analyzing the roles of 'invention' and 'discovery' (corresponding to manual construction and algorithmic search, respectively), and exploring concepts like modularity and computational irreducibility. By analyzing the evolution of various structures like oscillators, gliders, and glider guns, the article reveals patterns in Game of Life engineering innovation and compares it to biological evolution, offering a unique perspective on the nature of technological progress.

Can We Understand This Proof? A Glimpse into Formalized Mathematics

2025-01-10

Stephen Wolfram delves into a long-standing mathematical puzzle: the proof of a surprisingly simple axiom for Boolean algebra. Generated using automated theorem proving, the proof is incredibly complex and remains incomprehensible to humans. The article explores the proof's intricacies, dissecting its 'machine code' level operations, and poses a challenge: to humanize this proof. It discusses the potential of Large Language Models (LLMs) to understand and simplify the proof, and the implications for the future of mathematics. The conclusion suggests that some mathematical proofs may inherently be uninterpretable, hinting that mathematics will increasingly resemble an experimental science.