
Mathematics and AI... something changed?
Welcome to News From The Future read to you by the AI Voice Clone of Dr Cath made by eleven labs. This is the start of a new thematic across my work, also known as “What in the AI?” Enjoy! OpenAI has recently announced a groundbreaking achievement in mathematics, claiming to have solved a long-standing problem related to the Navier-Stokes equations using artificial intelligence. This development has stirred excitement and controversy alike, with implications for both the fields of mathematics and AI research. Let’s break down the details of this story, from the technical feat itself to the debates it has sparked. The Navier-Stokes equations are a cornerstone of fluid dynamics, describing how fluids like water and air move. These equations are crucial for understanding turbulence, a phenomenon that remains poorly understood despite its significance in areas such as engineering, meteorology, and physics. For nearly 90 years, mathematicians have struggled to prove the “existence and smoothness” of solutions to these equations under specific conditions. This challenge is one of the seven Millennium Prize Problems identified by the Clay Mathematics Institute, with a $1 million reward promised for a verified solution. OpenAI, the company behind ChatGPT, revealed that it had employed an advanced AI model to tackle this problem. This new model, which has not yet been released publicly, was trained specifically for advanced mathematical reasoning. OpenAI’s approach involved deploying approximately 10,000 AI agents—autonomous bots capable of working on tasks independently. These bots collaborated intensively, exchanging nearly 3 million messages and generating a staggering 130 billion output tokens (lines of text or code) during their efforts. The result? In just 88 hours, OpenAI claims that its AI agents solved two out of the four statements required to prove the Navier-Stokes “existence and smoothness” problem. The company has described this as a “milestone” and a demonstration of the rapid progress being made in AI technology. However, OpenAI has stated that it does not intend to claim the $1 million Millennium Prize for this result, framing it instead as a showcase of AI’s potential in addressing complex problems. The computational effort that went into this achievement was immense. Based on OpenAI’s own pricing for its most advanced AI models, the cost of this single endeavor is estimated to have been around $10 million. This highlights not only the capabilities of AI but also the significant resources required to achieve such breakthroughs. While the achievement is impressive, it is not without its caveats. OpenAI’s solution has yet to be independently verified or formally accepted by the Clay Mathematics Institute. As with any mathematical proof, rigorous peer review is essential to ensure that the solution is correct and complete. Until this process is completed, OpenAI’s claim remains unconfirmed. The announcement has also sparked controversy, particularly concerning the ethical and competitive aspects of AI research. Tristan Buckmaster, a mathematics professor at New York University, has alleged that OpenAI’s work on the Navier-Stokes problem may have been influenced by information about his own research. Buckmaster, along with Levent Alpöge, a mathematician working for OpenAI rival Anthropic, had been independently working on the problem using OpenAI’s Codex tool. According to Buckmaster, he became aware on September 3 that information about his team’s progress had been shared with OpenAI. He claims that OpenAI began its work on the Navier-Stokes equations only after learning about his research. Buckmaster has provided email exchanges as evidence and has publicly questioned the timing and methods of OpenAI’s announcement. He stated that he felt compelled to go public with his concerns to ensure that the narrative around the achievement remains accurate. OpenAI, for its part, has denied these allegations. The company has stated that it did not access any user data from Buckmaster and Alpöge’s work. However, OpenAI did acknowledge that de-identified data derived from their usage of OpenAI products might have indirectly contributed to improving its models. OpenAI has also emphasized that its proofs differ significantly from those of Buckmaster and Alpöge, even in terms of the specific results achieved. In response to the controversy, OpenAI congratulated Buckmaster and Alpöge on their “remarkable” concurrent work. The company has attempted to frame the situation as a coincidence, stating that it had not seen any of their work through any means until it was publicly released. Despite these assurances, the allegations have raised important questions about transparency, ethics, and intellectual property in AI research. The broader implications of this story extend beyond the specifics of the Navier-Stokes problem. If validated, OpenAI’s achievement could have far-reaching consequences for fields that rely on fluid dynamics, such as climate modeling, aerospace engineering, and medicine. More generally, it demonstrates the potential of AI to accelerate scientific discovery in areas that have traditionally been the domain of human researchers. At the same time, the controversy highlights the challenges and responsibilities that come with the use of AI in research. As AI tools become more powerful and widely used, ensuring fairness, transparency, and respect for intellectual property will be critical. The ethical questions raised by Buckmaster’s allegations underscore the need for clear guidelines and safeguards in the use of AI for collaborative and competitive research. This development also underscores the immense computational power and resources required for such achievements. OpenAI’s use of 10,000 AI bots working collaboratively over 88 hours is a testament to the scale of modern AI research. However, it also raises questions about accessibility and equity. If only well-funded organizations can afford to undertake such efforts, how do we ensure that the benefits of AI are distributed broadly and fairly? As the mathematical community awaits independent verification of OpenAI’s solution, the story serves as a reminder of both the promise and the challenges of AI. The ability of AI to tackle complex, abstract problems is undoubtedly impressive, but it also comes with ethical and practical considerations that cannot be ignored. In conclusion, OpenAI’s claim to have solved a significant part of the Navier-Stokes problem using AI represents a remarkable achievement, if validated. It showcases the growing capabilities of AI in addressing some of the most challenging problems in science and mathematics. However, the controversy surrounding the announcement highlights the need for transparency, fairness, and rigorous verification in AI research. As this story continues to unfold, it will likely shape discussions about the role of AI in research and innovation for years to come. Thank you for listening to this podcast. Please support Dr Cath’s works by buying her books or becoming a paid subscriber to her substack. "News From The Future" with Dr Catherine Ball is a reader-supported publication. To receive new posts and support my work, consider becoming a free or paid subscriber. This is a public episode. 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