The New York Post wrote that OpenAI "stunned the mathematics world" last week when it announced its AI model "cracked a legendary math problem left unsolved for nearly a century in just 88 hours." But a New York University professor "has come forward alleging OpenAI may have copied his work after asking him to collaborate — with one of the company's scientists allegedly warning he might 'ruin his career' if he refused." [P]rofessor Tristan Buckmaster, a British-Australian researcher who trained in Germany... had been working with Long Island-raised math prodigy Levent Alpöge, a researcher with OpenAI rival Anthropic, on a different elusive fluid dynamics equation, known as the Euler problem, when he found a solution using AI tools from both Anthropic and ChatGPT. He said scientists from OpenAI approached him and tried to convince him to jointly announce the solution, claiming they had independently solved Navier-Stokes. Buckmaster questioned the timing of their finding the solution in a blog post, noting OpenAI had only done so "in the past few days" — after the company became aware of his work. He asked OpenAI experts whether its AI systems used to solve the equation had been "trained on, or had access to" his research, but said they declined to answer, prompting him to wonder how they had advanced toward the solution so quickly. The puzzle is "not the direction one arrives at in a few days," Buckmaster wrote incredulously... In OpenAI's post on its website sharing the Navier-Stokes proof, which it credited to Astra, the company's latest AI bot, the firm insisted no user data was incorporated into its model to solve the problem. However, it noted that it "cannot rule out" that anonymized data was used to "improve our models." "We congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work," OpenAI said in the announcement. Buckmaster shot back, "Is it ethical to use customer's data to try to scoop their customer?" Alpöge's affiliation with Anthropic "seems to have been a sore point for OpenAI," writes TechCrunch. Buckmaster's public statement says the OpenAI's Sebastien "twice asserted that he wanted Levent removed from authorship" and also said that "it was so annoying that Levent works at Anthropic" — but that Buckmaster still refused to remove the Anthropic mathematician's credit. I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, "Why would you ruin your career?" [OpenAI's Bubeck said later on X that he'd meant unfounded accusations could damage Buckmaster's career.] I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, "If you don't want me to be nice, then I don't have to be nice." Buckmaster later told Australia's public broadcaster ABC that the companies building AI "have zero respect for the scientific community. I mean, it's appalling, honestly." But he went on to say AI has made the race to publish mathematical breakthroughs pointless. "I think it's pointless. Like, I think the game is up...." Professor Buckmaster said he and Dr Alpöge had more research they could publish but questioned the point of racing ahead with it when AI could perform work that had previously occupied researchers for years. He said there needed to be a discussion about how mathematics should operate in this new environment. Professor Buckmaster said some mathematicians had stopped publicly sharing what they were working on to avoid tipping off AI companies about their plans. He has called on academics and people from OpenAI, Anthropic and DeepMind to discuss ground rules for how they worked together. He said the companies' power carried responsibilities that went beyond competing to solve problems before their rivals... Building on the work of mathematicians Diego Córdoba and Luis Martínez-Zoroa, the pair found a solution to the Euler problem, a stepping stone to the Navier-Stokes problem. Professor Buckmaster said he spent weeks checking and improving the "slop" proofs generated by AI... For now, Professor Buckmaster said he wanted to finish existing work and support his PhD students and postdoctoral researchers, rather than chase another Millennium Prize. "I think it's more important to re-evaluate what math is," he said. "The New York University professor also warned Australia about the centralisation of resources into the hands of a small number of privately owned foreign companies..."

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An anonymous reader quotes a report from The New York Times: OpenAIsaid on Tuesday that its newest artificial intelligence technology had solved one of the "Millennium Problems," a collection of important unanswered math questions meant to push the world's leading mathematicians to new heights. The announcement is an another clear sign that A.I. is fundamentally changing the upper reaches of mathematics, which have long been viewed as a pinnacle of human achievement. The change has excited some mathematicians, while stirring concern among others. Over the past year, A.I. systems successfully solved a wide range of problems that have bedeviled mathematicians for decades. But these problems were not as complex, nor as closely watched, as the one that OpenAI's technology has solved over the past several days. The Millennium Problems are among the most heavily researched in the field. "This is a spectacular culmination of the arc we have seen over the past twelve months," OpenAI researcher Sebastien Bubeck said of the company's new solution. The company announced that one of its latest models, which has not yet been released to the public, needed just 88 hours to solve what mathematicians call "the Navier-Stokes existence and smoothness problem." This problem involves a series of equations that are often used to predict the weather. The equations describe the movement of water and other fluids. The Navier-Stokes problem, which has no clear practical value, asks whether these equations completely break down in certain situations. OpenAI's proof claims to have defined just such a situation. This would imply, at least theoretically, that the laws of physics themselves would break down under certain conditions: that, for example, water could be made to spontaneously explode. But mathematicians and physicists do not believe that this mathematical breakdown could really lead to such an outcome in the physical world. The Navier-Stokes problem was one of seven "Millennium Problems" selected by the Clay Mathematics Institute in the year 2000 as a way of tracking the progress of mathematics in the new millennium. The institute, founded by an American businessman named Landon T. Clay, offered a million dollars for the first correct solution to each problem. Before OpenAI's announcement, only one of the problems had been solved. OpenAI says it managed to solve the Navier-Stokes problem by coordinating as many as 10,000 AI agents, an extremely expensive process that may have cost millions of dollars in computing power. For those curious about the findings, the company has released a paper (PDF) and formal Lean proof.

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