An Unreleased Anthropic Model Made Progress on One of Math's Biggest Unsolved Problems
Anthropic said the model tested 650 ideas with 60 subagents and formalized the result in Lean after two in-house mathematicians confirmed it.
- On Monday, Anthropic announced an unreleased model made significant progress on the Riemann hypothesis, increasing the lower bound of solutions for which the hypothesis holds true. This 150-year-old mystery concerns the distribution of prime numbers.
- Anthropic's model tested 650 ideas coordinating across 60 sub-agents while spending 31 million in total. A staff member prompted the system to "take a real stab" at the proof, then left it to work across the following day and a half.
- Formalized using Lean, the findings were confirmed by Anthropic's in-house mathematicians. OpenAI recently released ten major results proved by its internal Astra model, while Anthropic separately disproved the long-standing Jacobian conjecture.
- Fields Medal winner Timothy Gowers questioned whether AI might change mathematics positively, while prominent mathematicians raised concerns in June that proofs should remain attributable to specific authors. The field remains divided on how to approach these new techniques.
- Despite this breakthrough, the $1 million bounty for a general proof remains unclaimed. The results reopen long-standing questions about Large Language Models' ability to discover new scientific and mathematical ideas.
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17 Articles
A research version of Claude pushes the Riemann barrier from 41.6 to 67.2 percent. The AI model only doubted itself until an employee wrote "Faith to you." Real progress or stroke of luck?
I am not going to enter into the now worn out diatribe on the use of the word "intelligence" for the Large Language Model (LLM) as ChatGPT, Gemini, Claude and members. Honestly, the terminology issues have fed me up. Let's talk about facts, instead. There has been a huge progress in the use of these systems in a delicate context: mathematics. A result of the last [...] L'articolo The Ai systems have made progress in mathematics. But there is sti…
An unreleased Anthropic model made progress on one of math's biggest unsolved problems
For more than 150 years, the Riemann hypothesis has stood as one of the major unsolved problems in mathematics. Anthropic hasn't solved it — but the company's models made more progress than you might expect.
This is an almost absurd story, one of a machine that is asked to tackle the Everest of mathematics, and which, failing, discovers a new promising path at mid-slope.
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