Last Tuesday could come to be remembered as a turning point in the history of mathematics. On September 8, an artificial intelligence company announced that it had solved one of the best-known, most difficult and most important Millennium Prize problems: the Navier–Stokes problem.

The Navier–Stokes equations are roughly 200 years old and describe how fluids behave. OpenAI, based in San Francisco, California, says its solution shows that the equations can break down under certain conditions, making them unreliable for describing real-world fluids.

Questions surround OpenAI’s claimed mathematics breakthrough

However, the circumstances of the alleged breakthrough and the way it was presented in a press release have complicated the celebration. OpenAI said the work, which cost millions of US dollars, was verified using automated techniques that are becoming increasingly common in mathematical research.

At the same time, mathematicians are raising broader concerns about how AI models learn from user interactions and whether the companies and researchers developing and using them are properly crediting earlier work.

No information has been released to substantiate these concerns. Nevertheless, last week’s events should serve as a wake-up call for researchers and institutions. The integrity of science could be threatened if research produced both inside and outside technology companies fails to credit the people whose work helps make AI models more capable.

Did earlier AI-assisted research contribute?

Twelve hours before OpenAI’s announcement, New York University mathematician Tristan Buckmaster posted on social media on behalf of himself and Levent Arposis, a mathematician at San Francisco technology company Anthropic. They said they had developed a partial solution to the Navier–Stokes problem with the help of AI tools from OpenAI and Anthropic.

The post linked to a social-media statement and a statement by Buckmaster suggesting that the researchers’ interactions with OpenAI’s Codex, an agent designed to assist software engineers, might have been relevant to the company’s result. The statement is available at go.nature.com/46y3pgx. OpenAI denies this.

One challenge is that AI systems are already capturing and processing vast amounts of digitized human knowledge. The neural networks at the heart of these models are often described as “black boxes” because they do not necessarily record where or how they acquired the information they use.

As a result, it can be nearly impossible to establish where the starting point for a scientific breakthrough came from. Inspiration might arise from informal brainstorming between chatbots and human experts, but it is currently impossible to determine whether or how this occurs. Recording those paths is an important part of the scientific process.

Why AI companies should make data use more transparent

Technology companies must be transparent about whether, how and when they collect user data, and should warn users proactively. A good-faith starting point would be changing data-sharing policies from “opt-out” to “opt-in”. Under that approach, user interactions would not be used to train an AI model unless users explicitly gave permission.

Companies must also control unauthorized AI agents. Independent audits should assess whether internal data processes can prevent such behaviour and respond quickly when it occurs, keeping pace with the development of frontier models.

AI agents must not bypass safeguards or access private user data, whether that data is stored on a company’s own servers or on a competitor’s systems.

What researchers and universities should do

Academic institutions also have an important role. They should examine the fine print in contracts with technology companies and ensure that activity on digital platforms is not used for purposes beyond those agreed by both parties.

Researchers who use AI models should ensure that these agreements apply to the environments and applications in which the tools are being used. For example, they should not upload manuscripts under review to an AI chatbot. They should also avoid using personal accounts or search engines accessed through devices that are not covered by the relevant agreements.

Information provided to a chatbot, including the contents of a manuscript, could be used to train other AI products if it is shared through a personal account or an interaction outside the scope of an agreement. Researchers and institutions without such agreements should be especially cautious when using free-access versions of AI tools.

Finally, researchers in academia and industry should strengthen efforts to encourage AI companies to support the Leiden Declaration on the Responsible Use of AI in Mathematics, published earlier this year.

Signatories pledged that results produced with AI tools should be made publicly available for peer review in line with open-science principles. They also said that training data should be attributed and not used without consent.

AI’s progress must be matched by research transparency

OpenAI’s latest claims are striking evidence of the kinds of mathematics that frontier AI models may be becoming capable of solving. The pace of improvement in AI is breathtaking, even to some of the technology’s most optimistic proponents.

But independent verification, transparency about the research process and recognition of previous work remain cornerstones of scientific integrity.

Technology companies must work with the research community to develop reliable and transparent ways to assign credit and share discoveries in the age of AI. This is not a minor issue. It is essential to the spread of knowledge, collaboration and, ultimately, trust in science.