Claude Mythos cracks OpenAI's landmark Erdős problem with a 'cute, simple proof'

Claude Mythos cracks OpenAI's landmark Erdős problem with a 'cute, simple proof'">

In a striking demonstration of artificial intelligence capabilities, Anthropic's Claude Mythos has reportedly solved the Erdős unit-distance conjecture, a problem that had stumped mathematicians since 1946. This achievement comes hot on the heels of OpenAI's recent disproof of the same conjecture, with Claude Mythos finding a solution 'over the weekend,' according to engineer Sholto Douglas. The Erdős unit-distance conjecture, posed by mathematician Paul Erdős in 1946, questioned whether it's possible to construct a set of points in a plane such that the distance between any two points is always an integer.

The problem has far-reaching implications in various areas of mathematics and computer science. Claude Mythos's ability to crack this longstanding problem has sparked excitement within the AI research community. Douglas described Claude Mythos's solution as arriving at a 'cute, simple proof,' which not only validates the model's capabilities but also hints at the potential for 'serious overhang' in AI-driven mathematical discoveries.

This implies that AI models may possess a significant untapped capacity for solving complex mathematical problems, which could be unlocked with further advancements in AI technology. The concurrent solutions by OpenAI and Claude Mythos underscore the rapid progress being made in AI-assisted mathematics. As these models continue to push the boundaries of what's possible, researchers are increasingly optimistic about the future of AI-driven mathematical discovery.

The intersection of AI and mathematics is yielding remarkable results, with Claude Mythos's solution to the Erdős unit-distance conjecture serving as a prime example. As the capabilities of AI models like Claude Mythos continue to expand, it's likely that we'll see even more groundbreaking mathematical discoveries in the near future.