The Riemann hypothesis, one of the biggest problems in the world of mathematics that has remained unsolved for over 150 years, continues to hold its mystery, based on the distribution of prime numbers. The $1 million prize offered for a general proof of this hypothesis has yet to be claimed.

While current models cannot completely solve this problem, they are making more progress than expected in generating mathematical ideas. This situation brings back to the forefront the long-standing debate about the role of artificial intelligence in scientific discoveries.

AI Step in the Riemann Hypothesis

Anthropic has announced that one of its now-unreleased models has made significant progress on the Riemann hypothesis. The model has managed to significantly increase the lower limit of the analysis range in which the hypothesis is valid.

This development began with an Anthropic employee, who had no mathematical training, giving the model a simple command to prove the hypothesis. The model worked in coordination with 60 sub-agents for a day and a half, testing a total of 650 different solution ideas.

The model, which spent 31 million output tokens during the process, had its work validated by two mathematicians within Anthropic. The findings were formalized using the open-source proof assistant Lean.

The debate on artificial intelligence in the world of mathematics

The successes of large language models in mathematics are creating both excitement and anxiety in the field. Some leading mathematicians are concerned that artificial intelligence could weaken fundamental values, regarding the ownership and responsibility of proofs.

A declaration published in June emphasized that mathematical proofs should be attributed to legitimate authors. However, figures like Fields Medal winner Timothy Gowers argue that artificial intelligence could take mathematics in a more complex and positive direction.

Gowers states that the fact that mathematical theorems are no longer associated with specific individuals can be considered as natural as the naming conventions in the world of astronomy.

How do you think the active role of artificial intelligence in mathematical discoveries will change the future of science?