Claude Mythos solves OpenAI's landmark Erdős problem with simple proof (the-decoder.com)

Anthropic's Claude Mythos has reportedly achieved a significant breakthrough by solving OpenAI's landmark Erdős problem with what has been described as a "cute, simple proof." This marks an important milestone for the AI/ML community, as the original Erdős unit-distance conjecture had remained unresolved since 1946. Anthropic engineer Sholto Douglas highlighted the accomplishment on social media, emphasizing the "serious overhang" that AI continues to demonstrate in advancing mathematical discoveries. The methodology employed by the Claude Mythos system involves a collaborative approach where isolated instances generate solution paths, with one instance responsible for summarizing and disseminating these findings. Notably, Mythos often utilized different strategies than OpenAI's models, leading to a diverse range of proofs. While mathematician Daniel Litt described Mythos's result as slightly inferior to OpenAI's, it still indicated that Mythos could replicate OpenAI's solution. This development, alongside Google DeepMind's recent success in addressing multiple Erdős problems using a formal proof language, showcases the growing impact of AI in solving complex mathematical issues, prompting discussions around the varying capabilities and approaches of AI systems in this domain.