AI causes uproar in mathematics as experts warn against sharing research with LLMs after OpenAI shares 722 manuscripts and proofs

Last week, OpenAI shared over 400 results for longstanding mathematical formulas that have troubled humans for decades; now researchers say it could take years for humans to validate and prove all the AI-driven work. But while analysts try to check the work of the unnamed OpenAI internal frontier model that found these alleged solutions, mathematicians argue this kind of AI-powered research and release threatens the field itself.

There's even the claim that by leaping from a prompt to a solution without a clear working in between, there is little benefit to these solutions in the first place. Mathematicians and the field itself may not be able to build on the results, as they don't know how they were achieved, nor has the development of such solutions produced new fields of mathematical understanding.

To make matters worse, there are suggestions that the growing confluence of mathematical and cybersecurity capabilities of frontier AI could bring into question the sanctity of cryptography itself. Alongside raising serious concerns for national security and modern digital systems, it could also put trillions of dollars worth of cryptocurrency at imminent risk.

Over 722 manuscripts dropped

The official count for OpenAI's maths solution release was 722 manuscripts, but with only 300 of the results formalized — digitizing human-readable formulas so they can be computer-verified — it's very difficult to know what's legitimate research. Some of the researchers The Verge spoke to found nonsense explanations within the reports, formulas that don't make sense, and some research that has already been completed by others.

The burden of proving the veracity of OpenAI and its model's claims is very much on the mathematical community, too. OpenAI didn't release the name of the model it used to generate these results, nor the prompts that generated them — despite those recommendations from the Advisory Group on Mathematicians and Artificial Intelligence (AGMAI).

OpenAI has at least published changelogs for its GitHub repository of the results, making it clearer where mistakes were made. But with several retractions and corrections already, it seems clear that it didn't check over the results in any great detail before releasing them.

It's this brashness, the pace of releases, and OpenAI's seeming disinterest in remotely slowing down its progress in the field that have so many mathematicians up in arms.

A looming threat becomes immediate

Mathematics isn't the first field to suffer a major upheaval because of AI. Writers first felt the looming threat with the release of ChatGPT in 2022, and both visual and musical artists faced the same concerns shortly after. Artificial intelligence is impacting almost every industry in some way, but while there are some potential benefits for its use in the field of mathematics, researchers within the field are concerned about the impact this may have on the collaborative nature of the field and how it might discourage future mathematicians from exploring it.

Speaking to Business Insider, mathematics professor at NYU, Tristan Buckmaster, said that OpenAI's release had upended the world of many early-career mathematicians, suggesting it had wiped out their whole research programs. Alongside their own research being invalidated by some of OpenAI's solutions, he suggested that some were now fearful that, by using AI tools, researchers had inadvertently contributed to the results, raising the potential of them not using advanced tools in the future and being less likely to talk about their research publicly.

This could cause huge problems for mathematics as a whole, argued mathematics professor at Northwestern University, Bryna Kra. Highlighting how collaborative maths is, with researchers sharing ideas, research data, and formulas, she is now extremely concerned that OpenAI has made mathematicians more secretive, reducing their ability to work together towards solutions and build on each other's research.

Professor of mathematics at the University of California, Terence Tao said on Mastodon that "many fewer seminars, workshops, collaborations, or other activities are being generated from these results compared to traditional breakthroughs." He argued mathematics may need to pivot to value "progress more holistically," by elevating the role of community building over raw solutions.

Researchers have described an atmosphere of extreme anxiety, that whatever they're working on could be invalidated overnight. That can undermine job applications, grant proposals, and those building the early components of their academic careers. Understanding and developing core mathematical capabilities at a high level can take years. AI dumps eradicating years of effort in such a haphazard fashion risk making it seem a near-pointless endeavour.

With swirling rumors of yet more releases from OpenAI, and potentially companion releases from other AI labs chasing the same headlines, the morale in many mathematical fields is extremely low.

Cryptography

With how much mathematics underpins key components of our digital world, it's no surprise that major changes in the pace of its development could have a domino effect elsewhere. One proposed potential minefield is the fertile ground of cryptography.

Associate professor of computer science at Johns Hopkins Whiting School of Engineering, Matthew Green, said on social media that he believes the congruence of mathematical developments and cybersecurity capabilities could result in AI that can defeat encryption as we know it.

While that raises potential concerns for all manner of fields that rely on encryption to protect the security of sensitive data, it could open up the cryptocurrency industry to wholesale theft, potentially impacting trillions of dollars of digital tokens.

Not everyone agrees with Green that this is an inevitability. British cryptographer — and one of the few people accused of being Bitcoin developer Satoshi Nakamoto — Adam Back, described these claims as nonsense and that there was little suggestion that just because AI can do certain mathematics now, that they'll be able to defeat encryption at some unnamed date in the future.

Ethereum creator Vitalik Buterin urged calm too, stating on Twitter/X that nobody should rush to move their tokens to a new wallet or panic over wallet security. However, he did argue that AI had the potential to one day be a far more dangerous threat to the sanctity of cryptocurrency than quantum computing.

While it doesn't appear that cryptography is a field AI is set to invalidate just yet, it's clear that it poses a potential threat to mathematical researchers and the core underlying 'way of doing things.' Much like it has just about everywhere else.

Researchers are adjusting to it, but the dust isn't likely to settle anytime soon, and in the meantime, OpenAI and its contemporaries may just move on to a new field to focus on as it continues to chase relevance and profitability.