AI success without an expert: Who owns the outcome

6 min read

“I’m certainly no mathematician. I dropped out of school at 16.” This man set the goal. 650 approaches failed before a research version of Claude raised a mathematical bound from 41.6 to 67.2 percent. For businesses, this raises a leadership question.

What is the Riemann hypothesis? The Riemann hypothesis is a fundamental unsolved problem in mathematics. It concerns the distribution of the zeros of the Riemann zeta function. It remains unproved. One measure of progress is proving that a larger proportion of certain zeros lies on a particular line.

Related:When AI replaces a job that was never advertised  /  Article 50 of the AI Act: What deployers must do from August 2026

A non-mathematician set the goal

The task came from Jarred Sumner, an Anthropic employee who describes himself as no mathematician. He says he is certainly no mathematician and dropped out of school at 16. Of the finished work, he adds that he contributed no mathematics. Sumner set the task and kept the process going. He did not do the mathematical work himself.

This division of responsibilities is the transferable lesson. The person asking the question need not be the person accountable for the result. Experts handled sign-off: Anthropic number theorists Levent Alpöge and Ralph Furman checked the work, as did external reviewers Brian Conrey and Dan Goldston. According to the paper, Furman and Alpöge take responsibility for correspondence.

Many businesses lack precisely this division of responsibilities when using AI. Either departments set goals and resist tools they do not understand. Or managers set goals and approve the results themselves, despite lacking the criteria to assess them. Both approaches produce weak results.

Persistence is a resource decision

The road to the result was long. Anthropic says Claude first generated and tested 650 ideas. None worked. In the decisive run, the model worked for around 37 minutes without intermediate output and downloaded 54 research papers. Each failed attempt consumed computing time and therefore money.

The appealing interpretation centres on encouragement. Sumner’s prompts consisted mostly of variations on “keep going” and “believe in yourself”. Anthropic describes their effect cautiously: they apparently helped Claude overcome its initial scepticism. No comparison run without encouragement has been published. This establishes the sequence of events, but no causal link.

A common alternative interpretation therefore treats the prompts as permission to spend more computing time. A 2023 paper by Cheng Li and Jindong Wang examines the effect of encouraging prompts. Automated tests showed an 8 percent improvement depending on the task category, with a much larger improvement in one test area. A study with 106 participants found an average improvement of 10.9 percent. That work measures neither research mathematics nor this particular case. For managers, the practical lesson remains: continuing is a resource decision and needs a named decision-maker.

A robust result has a clear verification process

The result is presented in a verifiable form. A machine-checkable version of the proof is publicly available, created in the Lean 4 proof assistant and checked with a verification tool. Four number theorists also reviewed the work. Two levels of verification are more than most business AI outputs ever receive.

The limits are also disclosed. Machine verification confirms the internal consistency of the formalised statement. It does not automatically confirm that the formalised statement addresses the intended question. This distinction applies directly to business: an AI output without a verification process remains a proposal. Before using AI, businesses should establish who will check the results, which tools they will use and what those checks will not cover.

The opposing view belongs alongside the result

James Maynard of the University of Oxford assessed the case in Scientific American on 12 August 2026. He recognises a real mathematical contribution but sees no path by which any of these approaches could get close to the Riemann hypothesis itself. One commentator described the work as applying existing research to an existing approach, without any invention of its own.

The strongest evidence against overstating the result comes from Anthropic itself: Anthropic does not expect Claude’s techniques to lead to a proof of the Riemann hypothesis. The manuscript is also hosted on an Anthropic-owned server. There is no evidence of peer review by an academic journal. Anyone sharing the story internally should include this context.

Three rules for business use

First, separate goal-setting from sign-off. Technical questions belong with experts; any manager who understands the problem can set the goal. Second, make persistence transparent. If a system needs hundreds of attempts, everyone must know who approves computing time and budget, and where the stopping point lies. Third, insist on a verification process. A result counts only once someone qualified has checked it and the limits of those checks are known.

Anthropic’s report describes a way of working that followed these rules. It used an unreleased research version. Customers cannot buy it. This remains a single case from basic research. Businesses can still adopt its division of responsibilities today.

Frequently asked questions

Image source: AI-generated (August 2026)

Translated from the German original using artificial intelligence. The German version is authoritative.