# Anthropic says unreleased Claude raised a Riemann-related lower bound > Source: > Published: 2026-08-10 17:55:43+00:00 Anthropic, co-founded by [Dario Amodei](https://darioamodei.com/?ref=runtimewire) and [Daniela Amodei](https://www.gsb.stanford.edu/insights/daniela-amodei-says-curiosity-underrated?ref=runtimewire), says an unreleased research version of Claude increased a lower bound related to the Riemann hypothesis. [Anthropic's post on the research](https://x.com/AnthropicAI/status/2086867246073401655?ref=runtimewire) Anthropic says Claude did not solve the hypothesis. The model instead worked on the fraction of nontrivial zeros of the Riemann zeta function that can be proved to lie on the critical line, where the real part equals 1/2. The date of the research run could not be established from the public materials reviewed for this article, and the date of the X post was not independently verified. The text of Anthropic's post available for this article ends immediately after the word "from," before giving either lower-bound figure. That excerpt does not establish whether Claude improved on a published result, reproduced known work or produced an argument that would survive specialist review. ### A mathematical claim needs a checkable proof The Riemann hypothesis states that every nontrivial zero of the zeta function lies on the critical line. Partial progress has come from proving that increasingly large proportions of those zeros lie on that line. A [paper by Kyle Pratt, Nicolas Robles, Alexandru Zaharescu and Dirk Zeindler](https://arxiv.org/abs/1802.10521?ref=runtimewire), published in 2020 after circulating on arXiv, established that more than five-twelfths of the zeros lie on the critical line. That is slightly above 41.67% and provides a public comparison for Anthropic's claim. The available excerpt does not establish that Claude surpassed that benchmark. A model-generated derivation becomes a mathematical advance after specialists can inspect its assumptions and proof, reproduce the reasoning and look for errors. Anthropic's post calls the system an "unreleased research version" of Claude. Anthropic did state plainly that Claude had not solved the Riemann hypothesis. The narrower lower-bound claim still requires the publication and review expected for work produced by human mathematicians. ### The Amodeis are building auditable research workflows Anthropic is a San Francisco-based public benefit corporation founded in 2021 by former OpenAI employees. Along with Dario and Daniela Amodei, its founding group included Jared Kaplan, Jack Clark, Chris Olah, Sam McCandlish and Tom Brown, according to Anthropic's [company materials](https://www.anthropic.com/company?ref=runtimewire). Dario Amodei came to AI through science. According to his [personal biography](https://darioamodei.com/?ref=runtimewire), he earned a PhD in biophysics from Princeton University as a Hertz Fellow, completed postdoctoral work at Stanford School of Medicine and later worked at Google Brain and OpenAI. Before Anthropic, he worked at Google Brain and OpenAI on neural-network research, language-model scaling and AI safety. Daniela Amodei, Anthropic's co-founder and president, managed technical teams at OpenAI before becoming its vice president of safety and policy. She has described herself as a generalist and discussed curiosity and "radical responsibility" in a [Stanford Graduate School of Business interview](https://www.gsb.stanford.edu/insights/daniela-amodei-says-curiosity-underrated?ref=runtimewire). Scientific research is also becoming a paid Claude workflow. On June 30, Anthropic launched [Claude Science](https://www.anthropic.com/news/claude-science-ai-workbench?ref=runtimewire), an AI workbench that connects Claude to research tools, databases and computing resources. Anthropic says the product retains the code, environment details and message history behind outputs so researchers can audit and reproduce them. A reviewer agent checks calculations and citations and flags figures that do not match their underlying code. Claude Science entered beta for Pro, Max, Team and Enterprise users. Anthropic did not provide separate Claude Science pricing, customer, revenue or usage figures in the materials reviewed for this article. The product's audit trail addresses a commercial obstacle in AI-assisted research: customers need to trace a result through its data, code and assumptions. ### Verification is becoming part of the competition Anthropic is competing with general AI labs and specialized mathematics companies that are building verification into research systems. In an [announcement](https://deepmind.google/blog/accelerating-mathematical-and-scientific-discovery-with-gemini-deep-think/?ref=runtimewire), Google DeepMind described Gemini Deep Think as a research system that uses verification under the direction of expert mathematicians and scientists. OpenAI has followed a related route in the life sciences. Its [GPT-Rosalind research preview](https://openai.com/index/introducing-gpt-rosalind/?ref=runtimewire) combines a specialized model with scientific databases and tools while restricting initial access to qualified organizations. Google has separately described a [multi-agent Co-Scientist system](https://deepmind.google/blog/co-scientist-a-multi-agent-ai-partner-to-accelerate-research/?ref=runtimewire) intended to assist researchers with scientific hypotheses and proposals. Specialized competitors are concentrating on mathematics. Harmonic is developing Aristotle, according to [Axios](https://www.axios.com/2026/01/15/nvidia-harmonic-ai-math-accuracy?ref=runtimewire). Axios also [reported](https://www.axios.com/2026/05/26/axiom-ai-math-journal?ref=runtimewire) that Axiom Math said its AxiomProver produces machine-checkable Lean proofs, with a separate checker verifying each step. According to Axios, Axiom said it raised $200 million at a $1.6 billion valuation in March 2026 and that its proofs had been accepted by five leading journals. The X post excerpt supports an Anthropic claim about an internal model rather than establishing an accepted mathematical advance. The lower-bound figures and a checkable derivation would allow mathematicians to determine whether Claude contributed an original result and whether it exceeded the published five-twelfths benchmark.