AI Reproduction of Lin's Busy Beaver Proof (nickdrozd.github.io)

In a notable advancement for the AI/ML community, ChatGPT has successfully reproduced Shen Lin's 1963 proof of the Busy Beaver problem for three states (BB(3)). This significant achievement highlights AI's growing capability to tackle complex mathematical proofs, which are traditionally labor-intensive and prone to human error. The Busy Beaver problem, defined as the longest a Turing machine with a certain number of states can run before halting, represents an uncomputable challenge in mathematics, with proof efforts becoming progressively more difficult as state numbers increase. Lin's proof of BB(3) involved careful enumeration of possible Turing machine states, a method bolstered by systematic pruning techniques to reduce computational complexity. The successful reproduction by ChatGPT not only underscores the AI's ability to follow complex algorithms encoded in natural language but also simplifies the replication of mathematical results, making advanced computational methods more accessible. ChatGPT's reproduction process involved generating a C program to run the proof, illustrating the potential for AI to automate detailed computation tasks, ultimately saving time and reducing human error. As AI systems continue to advance, they may serve as powerful tools to tackle long-standing challenges in mathematics and computer science.