OpenAI Astra Solves 10 Longstanding Math Problems Including Non-Sofic Group Discovery
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OpenAI announces solutions to 10 longstanding maths problems | New Scientist
OpenAI has revealed solutions to 10 longstanding mathematical problems that were found by its prototype AI model Astra. The announcement is the latest in a string of mathematical discoveries made by AI that are threatening to change the field beyond recognition. In May, an OpenAI model cracked a
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OpenAI teases Astra, its next major AI model, after it solves 10 long-standing math problems
OpenAI has revealed Astra, an unreleased model designed to tackle complex, long-running tasks, after an internal version produced ten significant advances in mathematics and theoretical computer science. In a new research post, OpenAI described Astra as "our next major model" and said the problems
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OpenAI says its next model, Astra, has solved ten open problems in mathematics
OpenAI says its unreleased Astra model solved ten open maths problems, shipping Lean proofs on GitHub for roughly $2,000 in compute OpenAI says an internal version of its next major model, called Astra, has produced ten new results in mathematics and theoretical computer science. Each of the
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OpenAI Smuggled the Announcement of Astra, Its Next AI Model, Into a Blog Post About Math
OpenAI announced its next major AI model Saturday, and it did so in the third paragraph of a blog post called "Ten advances in mathematics and theoretical computer science." The math results the post is touting, OpenAI writes, "were achieved by an internal version of Astra, our next major model."
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OpenAI Astra: The mysterious new quantum math-solving model
Do you understand quantum parallel repetition? What about quantum complexity, lattice cryptography, or extremal combinatorics? The new OpenAI model Astra knows all about them. Recently, OpenAI confirmed the existence of Astra, calling it "our next major model." Over the weekend, the ChatGPT-maker
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OpenAI Astra model solves 10 open math problems for $2,000
OpenAI announced Saturday that Astra, its next major model still awaiting public release, had generated solutions to 10 longstanding problems across mathematics and theoretical computer science, each unsolved for ten or more years. Alongside the announcement, OpenAI released a 249-page manuscript
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OpenAI's Astra solves 10 long-open math problems and publishes the proofs
OpenAI Group PBC revealed Saturday that an internal version of Astra, the model family it calls its next major release, produced new results for 10 problems in mathematics and theoretical computer science that had been open for at least a decade, and it published machine-checkable proofs alongside
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OpenAI Astra: OpenAI's Astra solves 10 longstanding math problems, igniting new debate
Apart from praise, the news, published on August 1, also kickstarted a debate on social media over whether the achievement is Fields medal-worthy -- and what these honours mean in the artificial intelligence (AI) era. The Fields medal is awarded by the International Mathematical Union (IMU), and is
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OpenAI Astra Solves 10 Math Problems with Logical Accuracy
OpenAI's latest AI model, Astra, has gained attention for solving ten significant mathematical problems, including breakthroughs in sphere packing and geometric conjectures. These areas have traditionally required deep human expertise, making Astra's achievements noteworthy. According to The Stack,
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OpenAI Astra Solves 10 Unsolved Math and Computing Problems
OpenAI's Astra has achieved a significant milestone by solving ten previously unsolved problems in mathematics and theoretical computer science. This achievement highlights Astra's advanced reasoning capabilities, supported by its unique sub-agent architecture designed for tackling complex,
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OpenAI's 'Astra' AI Model Makes Breakthroughs in 10 Long-Standing Math Problems
OpenAI announced that its unreleased Astra model family made major progress on 10 long-standing mathematical problems. Independent verification would confirm a major evolution, positioning AI as a legitimate contributor to scientific discovery. According to OpenAI, the unreleased Astra model
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OpenAI unveils Astra: its next major model family for harder problems
Inside OpenAI, Astra is now the name attached to what appears to be the company's next big model family. The goal is to take on harder problems and stay with them much longer than today's chat-style tools can. It uses multiple agents that can work together for hours, even days. Think less one-shot
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OpenAI's Astra Model solved 10 open math problems: This is how we know it's true
OpenAI is known to drop research bombs with no great announcement, and the newest one requires a closer look than just the small paper where it is published. The internal version of Astra, the next big model to be released by OpenAI, has come up with solutions to ten mathematical problems and
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OpenAI revealed its unreleased Astra model solved ten longstanding maths problems for roughly $2,000 in compute costs, including the first-ever construction of a non-sofic group. The announcement positions Astra as OpenAI's next major AI model while raising questions about transparency, attribution, and the future role of AI in mathematical research.
OpenAI Astra Tackles Ten Open Problems in Mathematics
OpenAI has unveiled solutions to ten longstanding maths problems discovered by its prototype AI model Astra, which the company describes as "our next major model."
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These open problems in mathematics had seen no progress on their central results for at least a decade, spanning areas including high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, quantum complexity, lattice cryptography, and extremal combinatorics.2
The total compute cost for all ten solutions was roughly $2,000 at Sol API rates, according to OpenAI's announcement.2
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The company published a 249-page manuscript alongside machine-checkable Lean 4 proofs for every result on GitHub, addressing concerns about verification.3
Non-Sofic Group Discovery Marks Major Breakthrough
The headline achievement among these AI-driven mathematical discoveries is the first-ever explicit construction of a non-sofic group, resolving a central question in group theory that has stood since Mikhail Gromov introduced the concept of soficity in 1999.
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Until now, all known groups had this property, leading mathematicians to propose that all countable groups are sofic.1
OpenAI Astra discovered a single counterexample that disproves this claim, a finding that has sparked significant attention in mathematical circles.1
The other results span several fields, including disproving Connes's rigidity conjecture on von Neumann algebras, proving Ehrhart's volume conjecture, and resolving three Erdős conjecture problems from Paul Erdős's famous catalogue.3
Astra also produced the first improvement to the general upper bound on high-dimensional sphere-packing density since 1978 and established new lower bounds on circuit complexity of computing the permanent.3
Concerns Over Attribution and Transparency Surface
The announcement has raised questions about how AI companies acknowledge prior human work in theoretical computer science and mathematics. Francesco Fournier-Facio at the University of Cambridge, who has been studying the soficity problem since starting his PhD in 2020, believes OpenAI's solution relies heavily on papers by Andreas Thom and Gábor Kun from 2016 and 2019.
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"In very broad strokes, the solution takes these two works from 2016 and 2019, pushes them forward and then does some clever tricks," Fournier-Facio explained.1
He expressed concern that AI companies aren't being transparent about how their solutions build on prior human research. OpenAI's initial announcement claimed all ten solutions "have seen no progress on the main result for at least a decade," but the company changed its statement after Fournier-Facio complained this was incorrect.1
Mathematical Community Debates AI's Role in Research
The revelation lands against escalating tension between AI companies and the mathematics community. In June, mathematicians issued the Leiden Declaration, endorsed by the International Mathematical Union, warning that AI companies are using published research without consent, bypassing peer review, and threatening the integrity of proof and attribution.
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The Declaration specifically cited companies that announce results through press releases rather than peer-reviewed journals. Whether the broader mathematical community will accept results announced through a blog post rather than peer review remains an open question.3
Columbia professor Andrew Blumberg noted that while these accomplishments are impressive, they don't necessarily change his expectations about AI capabilities. "If you look at what these are, they're pretty short. They are either counterexamples or they are small, extremely clever constructions that build on known things," Blumberg explained.5
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Next Major AI Model Designed for Long-Running Tasks
OpenAI has not announced when Astra will be released publicly or whether it will launch as GPT-5.7, GPT-6, or under another name.
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According to reports, Astra is designed for long-running workloads and allows AI agents to collaborate on different parts of a larger problem.2
CEO Sam Altman was reportedly in Washington, D.C. over the past week, demoing the model to federal officials.4
Human researchers used the same model to prepare arguments as manuscripts, with Astra then formalizing every argument as a Lean certificate, allowing the proofs to be checked using the mathematical verification system.2
The company is also giving 100,000 academic researchers free access to its frontier models through 2027, deepening its ties to the scientific community.3
Limitations and Future Implications for AI in Mathematics
Experts point out that most AI mathematical discoveries focus on finding counterexamples, which can be easily and quickly checked, rather than developing new theory.
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"Until AI shows that it can develop theory independently, it's hard to believe that it could have come up with this independently," Fournier-Facio noted.1
Abhishek Saha at Queen Mary University of London acknowledged that while human mathematicians had made significant progress with high-dimensional sphere-packing, the release of these ten solutions remains the most impressive display of AI mathematical prowess to date.1
Saha remains optimistic, stating, "I would not be surprised if, in two or three years, they can actually build enough new theory to solve some of the deeper questions."1
Watch for whether OpenAI Astra can move beyond counterexamples to develop genuinely new mathematical theory, and how the research community responds to AI-generated proofs announced outside traditional peer review channels.References
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