Models & Labs · United States

OpenAI dumps 372 AI-generated math proofs on GitHub, telling the academic world to keep up

Credited to The Decoder · the-decoder.com · 11h ago

OpenAI has released a large collection of mathematical results produced by an internal AI model. The proofs are published on GitHub rather than in academic journals, with formal verification intended to make review more practical.

OpenAI has published 372 new mathematical results generated by an internal frontier model. Each result is supposed to solve an open problem or make substantial progress toward one. The collection includes improvements to major computer algorithms and advances related to the Riemann hypothesis.

The company is hosting the results in a GitHub repository, complete with revision logs and citations. According to OpenAI, the same model already produced a solution to a Navier-Stokes problem that has been under formal review for weeks. Ad

Nearly every result came from a single prompt to a single AI agent, OpenAI says, though some took multiple attempts. That's a sharp contrast to the Navier-Stokes solution, which required a swarm of 10,000 agents and millions of dollars in compute. On average, each result consumed roughly three hours' worth of ChatGPT Pro Thinking compute. Ad

Formal verification could ease the review bottleneck

Many of the proofs come with formalizations in Lean, a programming language built for machine-checkable mathematical proofs. More formalizations are planned. The reason is practical: the sheer volume of AI-generated results could easily overwhelm the math community's capacity for manual review.

OpenAI also published details on its methodology, including summaries of the reasoning process, statistics on how many problems the model attempted, and estimates of compute costs. Ad

Traditional journals aren't built for this pace

OpenAI put its results on GitHub instead of peer-reviewed journals. It's a statement move, since it implies that the traditional process of doing science is too slow for this volume of potentially new knowledge.

OpenAI consulted with the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study and loosely followed their public recommendations, since the company didn't publish any prompts and only shared average compute costs rather than per-problem figures. The advisory group includes Fields Medal winner Timothy Gowers among other renowned mathematicians. Ad

The company also announced plans to fund workshops and conferences focused on understanding AI-produced results. OpenAI acknowledged it wants to improve the quality of its citations and presentation, and says it's working on a responsible release of the model to "directly empower scientists with state-of-the-art capabilities." Ad

OpenAI set one significant boundary for the advisory group beforehand, though: the mathematicians can advise on how results get communicated, but not on whether or how fast they're produced.

The math community is split on what mass-produced proofs actually mean

Lean formalizations can verify logical correctness, but they can't judge whether a result is mathematically relevant or original. OpenAI is betting that its results push the boundary of human knowledge. Whether the mathematical community agrees remains an open question. So far, reactions range from excitement to frustration.

In a recent open letter titled "A Severe Misalignment of AI in Mathematics," 25 Fields Medal winners warned of a deep disconnect between the AI industry's goals and those of mathematics. Problem-solving, they wrote, is merely a tool and proxy for the real goal of conceptual understanding and insight. Mass-producing true statements could destroy fertile ground rather than bring new ideas to life, they argued. The effect would spill over into other fields.

Gowers has warned that within one to two decades, mathematical literature could grow enormously while no human community remains that truly understands it. Fields Medal winner Terence Tao has added that training young mathematicians needs to emphasize the human side and tightly limit AI tool use so that genuine learning and understanding survive.

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Radisson Hotel Group brings hotel discovery into ChatGPT

Credited to OpenAI · openai.com13h ago

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Radisson partnered with Accenture to build a ChatGPT plugin using OpenAI technology, helping travelers find, compare, and book hotels while planning their trips.

Early plugin conversion versus organic search (Jul–Aug 2026)

Of recorded checkout and booking events attributed to ad views

Weeks to build and launch the ChatGPT plugin

“ AI is radically transforming how people search for and book hotel stays, and we are committed to being at the forefront of this shift. With Accenture and OpenAI, we are reimagining hotel discovery for the next generation of travelers, meeting guests in the planning moment with a branded experience that makes it easier to find, compare, and book Radisson Hotels properties. ”

“ We want guests to move naturally from a travel idea to a hotel they can book with confidence. Working with Accenture Song and OpenAI, we are bringing our branded app and sponsored advertising together in ChatGPT as part of one discovery strategy. Our focus is to connect those conversations to our direct booking experience, making the journey easier for guests and building a channel we can develop as travel planning evolves. ”

A new front door for hotel discovery

Radisson Hotel Group brings together ten distinctive hotel brands across EMEA and APAC, with more than 1,640 hotels in operation and under development. For the past seven years, Accenture has helped Radisson grow bookings through its direct digital channel, combining digital media strategy and execution with a transformation roadmap for its core digital capabilities. A stronger direct digital channel helps Radisson attract guests more efficiently and build relationships that encourage repeat stays. For hotel owners, this translates into stronger commercial performance and greater long-term value from their partnership with Radisson Hotel Group.

This work meant Accenture had a front-row seat to AI’s transformative impact on the travel industry. “Almost overnight, there was a new surface where prospects were getting inspired, comparing different alternatives, and almost making their decision before even reaching a hotel’s website,” explains Borja Lizarraga Rodríguez, Data & AI Lead at Accenture Song. “It was critical for us to ensure the visibility of Radisson across this new experience.”

Early results from the Radisson Hotels plugin in ChatGPT show a visit-to-booking conversion rate approximately 1.5 times Radisson’s organic search for July–August 2026. The plugin gives travelers a direct path from conversational hotel discovery to Radisson’s own booking channel.

A recent ChatGPT update means users no longer have to type @RadissonHotels before their query; if they have the plugin installed, ChatGPT will automatically show it whenever relevant. “If you’re planning a trip to Madrid, and there’s a new Radisson Hotel you might want to consider, now in ChatGPT it will just automatically work,” says Brittny Cantor, Agentic Commerce Lead at Accenture. “We’re really excited about that change to increase discoverability.”

Building for the next era of travel

The plugin gives Radisson a new way to reach travelers organically in ChatGPT. Radisson is also among the hospitality pioneers launching sponsored advertising campaigns in ChatGPT as part of an integrated discovery strategy. Since launching in July, its campaigns have expanded into additional markets across Europe and beyond. More than half of the campaign’s recorded checkout and booking events were attributed through view-through measurement, extending Radisson’s assessment of discovery beyond direct ad clicks.

Accenture designed the underlying infrastructure to support more than a single application. The MCP server and APIs that Accenture developed for the Radisson plugin are also powering the ads experience and will play a role in other new features to come.

Radisson is aware that with AI, the way users make decisions about travel has changed dramatically and will continue to evolve. They’re determined to be the first among their competitors to capitalize on these changes, becoming not only a hotel chain but an advisor on the entire travel experience. Its next priorities include encouraging plugin adoption and developing additional functionality within the ChatGPT experience.

“What stands out about Radisson is its ability to move quickly while keeping a clear focus on guests and hotel owners. Together, we are applying new technology where it can make a meaningful difference: helping travelers find the right hotel, strengthening direct guest relationships, and supporting more profitable growth,” Borja Lizarraga says.

“Great stays have always started with good advice. Today, more of that advice happens in conversation, and we moved quickly to be there. Initial results are encouraging, with our ChatGPT plugin converting at around 1.5 times organic search. This is just the start: wherever a journey begins, we want Radisson to be the advisor guests trust and the direct channel that delivers lasting value for our hotels and owners,” says Velit Dundar, Vice President, Global Ecommerce, Radisson Hotel Group.

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