Anthropic announced that an unreleased model made significant progress on the Riemann hypothesis, a long-standing unsolved problem in mathematics. The model increased the lower bound of solutions for which the hypothesis holds true, marking a notable advancement in the field. The progress was achieved through a process where a staff member without significant mathematical training prompted the model to tackle the problem, allowing it to operate autonomously for over 12 hours. The model tested 650 different ideas for solving the problem, coordinating across 60 subagents and spending 31 million output tokens in total.
The finding was confirmed by two of Anthropic’s in-house mathematicians and formalized using the open source proof assistant Lean. This development is part of a growing trend where large language models are contributing to mathematical breakthroughs, with several significant results achieved by AI models this year. The progress has sparked both excitement and concern among mathematicians, with some raising concerns about the attribution of mathematical proofs to specific authors. However, the field remains divided on how to approach these new research techniques.
The growing body of results has led to discussions about the role of AI in mathematics, with some suggesting that the influence of AI might change the field in a more complex and positive way. Source: techcrunch
