OpenAI's Mathematical Breakthroughs Spark Controversy Over Norms and Transparency

In a chaotic few months, OpenAI has demonstrated it can do two things with remarkable consistency: make impressive breakthroughs in mathematics, then colossally screw up announcing them. OpenAI is now trying to do better. Somehow, it has botched that too.

OpenAI’s latest attempt to repair fractured relations with a mathematical community it has repeatedly alienated is to consult a new independent advisory group of elite practitioners. But mathematicians speaking to The Verge, including one of the group’s members, describe a messy and confusing affair bearing many of the hallmarks of OpenAI’s previous rushed forays into mathematics, suggesting the company has learned little from its mistakes. And then there’s the daunting task the group has been handed first: helping coordinate the release of scores more results OpenAI says its unreleased model has produced, the prospect of which is already stirring dread among researchers over what this looming tidal wave of breakthroughs could do to their field.

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After turning a string of spectacular mathematical results into a reputational crisis, OpenAI is consulting human mathematicians to help it figure out a less disastrous path forward.

On Monday, the company announced a new independent panel of mathematicians tasked with advising it and other AI companies on their interactions with mathematical research and the wider mathematics community, including how new results are presented and released. Its abrupt arrival caught many mathematicians by surprise. Researchers told The Verge the group is a good first step, but many said they were left with basic questions about what it will actually do, how much influence it will have, and whether OpenAI will actually listen to it, as well as concerns over whether such a small group of prominent researchers can represent the wider mathematical community.

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OpenAI has spent the last few years planting flags across the increasingly difficult terrain in mathematics. This week, it claimed one of its biggest prizes yet: a solution to a legendary Millennium Prize problem. In normal circumstances, this would have been celebrated as a historic achievement.

Instead, many mathematicians have watched OpenAI’s relentless advance with growing unease. To them, the company appears less like an enthusiastic newcomer than an impossibly well-resourced interloper, charging into problems they have dedicated their lives to studying with little apparent regard for long-standing norms or the consequences for those left in its wake. At the heart of that unease is a sense that OpenAI is doing mathematics for different reasons. Mathematicians want to advance the field. OpenAI wants to win.

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Another researcher is challenging OpenAI about the data driving its increasingly impressive array of mathematical discoveries. Just days after a bitter row erupted over whether the company’s models benefited from unpublished work, a second mathematician has come forward accusing the AI giant of unethical and “dishonest” behavior and a lack of transparency about the origins of its training data.

In a series of posts on Mastodon, mathematician Andreas Thom raised concerns that interactions he and his colleagues had had with the ChatGPT chatbot before OpenAI’s triumphant announcement may have contributed to its success in the field. One of the 10 results OpenAI announced with great fanfare last month involved Thom’s area of expertise, so-called non-sofic groups, and OpenAI acknowledged that their result built heavily on previous work by Thom and fellow mathematician Gábor Kun.

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OpenAI’s announcement Tuesday that it has solved one of mathematics’ legendary Millennium Prize problems should have been a moment of triumph. The result is both an undeniable achievement and a striking demonstration of just how rapidly AI is transforming mathematics. But before it was even formally announced, the breakthrough had been complicated by the unusual circumstances that prompted OpenAI to pursue the problem: After hearing other researchers were making progress, it seems to have thrown its considerable resources into a last-minute effort to beat them to the punch. The ensuing controversy has surfaced allegations of scooping, spying, and flagrant violations of long-standing academic norms that researchers fear could have a chilling effect on the field.

As Abhishek Saha, a mathematics professor at Queen Mary University of London, explains it, OpenAI has engaged in the “kind of things that mathematicians will generally not do.”

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OpenAI says it found a solution to a major math problem that has remained unsolved for around 90 years, as reported earlier by The New York Times and Wired. In a blog post on Tuesday, OpenAI announced that it discovered a solution to the Navier-Stokes problem — which relates to the flow of liquid and gas — using an internal AI model more powerful than the newly released GPT-6 Astra alongside 10,000 concurrent agents. The Navier-Stokes problem is one of seven Millennium Prize Problems, each of which comes with a $1 million reward for solving.

OpenAI says it started training the internal AI model on August 28th, which has “exhibited unprecedented performance in our benchmarks, including mathematics.” The solution is a big breakthrough for the mathematics community, but it doesn’t come without controversy.

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Today on Decoder, I’m talking with Robert Hart, The Verge’s London-based AI reporter, about what AI is doing to the field of mathematics and the existential crisis many lead mathematicians are having about it.

OpenAI just published a set of solutions to longstanding problems in math that went off like a bombshell in the field. It caused a huge debate in the math community, and Rob spent some time talking to some of the most accomplished mathematicians of our time about it.

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Mathematician James Maynard has spent a lot of time this past year “soul searching.” A professor at the University of Oxford and winner of the prestigious Fields Medal, Maynard told The Verge he’s been grappling with the future of his field as the traditionally slow-moving discipline hurries to adapt to AI.

Days before we spoke, OpenAI revealed it had produced the solutions to 10 long-standing mathematics problems, some of which had confounded academics for decades. Like generative AI used to produce text and images or propose ideas in science and medicine, the technology learns patterns and connections from the vast amount of material it’s trained on and uses them to create something new. Applied to mathematics, that can mean combining known results, methods, and tools in new ways to attack a problem, sometimes drawing links between disparate fields or resurfacing concepts buried in academic literature.

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