Show HN: I solved a 12yr math problem using AI (formalized; awaiting review) [pdf] (raw.githubusercontent.com)

A mathematician named Kamil Braun has made a groundbreaking announcement on Hacker News, claiming to have solved a longstanding 12-year-old problem in theoretical computer science related to the bit pigeonhole principle (BPHP) using AI assistance from Claude and GPT models. His work demonstrates that resolving the BPHP for \(n+1\) pigeons and \(n=2^l\) holes necessitates superpolynomial-size resolutions in unrestricted proof systems over parities. This development is significant as it overturns previous assumptions about the complexity of resolutions in this domain, particularly by removing regularity and proof-depth limitations, thereby paving the way for deeper insights into complexity theory and related computational problems. The implications of Braun's findings extend beyond theoretical math; they contribute to the broader discourse on proof complexity and computational limitations within AI. The formalization of the proof framework in Lean, a proof assistant, ensures that the results are verifiable and opens up for collaborative research exploration. Key technical aspects include the introduction of DAG-like resolution over parities and matching moment extensions, which constructively illustrate the intricate relationships between algebraic structures and logical proofs. This breakthrough not only highlights the evolving intersection of AI and mathematics but also prompts further investigation into unresolved problems in proof complexity, potentially catalyzing innovations in algorithm design and optimization strategies within the AI/ML community.