SCIENCE & TECH
Somewhere inside OpenAI's server farms, a machine that almost nobody outside the company has ever touched just did something that sounds lifted from science fiction. It sat down with ten of the hairiest, most stubborn unsolved problems in mathematics and theoretical computer science — puzzles that had defeated humanity's sharpest minds for years, in some cases for decades — and cracked every single one. Then it published the proofs in a language computers can check line by line, so nobody could accuse it of bluffing.
The model is called Astra. OpenAI describes it, cryptically, as its “next major model family” — not officially GPT-6, but widely assumed by researchers to be a preview of exactly that. On August 1, the company dropped a 249-page manuscript on the open internet titled “Ten advances in mathematics and theoretical computer science,” alongside machine-verified proof certificates written in Lean 4, a formal proof language, posted to GitHub under an open license for anyone on Earth to inspect, poke at, and try to break.
Within days, the math world was in an uproar — half awestruck, half furious. And a week later, some of the very experts Astra was supposed to be impressing accused OpenAI of something far less flattering than genius: taking credit for other people's work.
Ten Problems, Zero Mercy
To understand why mathematicians lost their minds, you have to understand what was actually on Astra's to-do list. These weren't textbook exercises. They were the kind of problems that get a single paragraph in a survey article followed by the words “remains open.”
The headline result is the construction of the first known non-sofic group — a direct answer to a question that had sat unresolved since the mathematician Mikhail Gromov introduced the concept of soficity back in 1999. In plain English: a group (a basic structure in abstract algebra) is called “sofic” if its behavior can be approximated, as closely as you like, by finite systems of permutations. Virtually every group mathematicians actually use day to day — every amenable group, every residually finite group — fits this description. Whether every countable discrete group had to be sofic was one of the most stubborn open questions in group theory for 27 years. Astra built an explicit counterexample.
Then it went further and took a swing at the Connes Rigidity Conjecture, a problem posed by Fields Medalist Alain Connes in 1980. Connes's conjecture held that for a particular rigid class of groups, a related algebraic object works like a unique fingerprint — pin down the fingerprint, and you've pinned down the group. Astra disproved it, demonstrating that infinitely many pairwise non-isomorphic “property (T)” groups can share the exact same von Neumann algebra fingerprint.
On top of those two flagship results, Astra knocked out three problems from the famous catalogue left behind by the legendary Hungarian mathematician Paul Erdős, including a result on multicolor Ramsey numbers. It also produced new upper and lower bounds and hardness proofs touching sphere packing, coding theory, arithmetic circuit complexity, quantum complexity, and lattice-based cryptography — the exact branch of math that underpins next-generation, quantum-resistant encryption standards now being rolled out across banking and government systems worldwide.
Every one of the ten results was formalized in Lean, producing what mathematicians call machine-checkable certificates. According to OpenAI, the GitHub repository's “sorry” count — Lean's marker for an unproven gap — sits at zero. Every logical step, in other words, checks out.
The Price Tag That Stunned Silicon Valley
Here's the detail that turned heads even among people who don't know a von Neumann algebra from a Neumann coffee mug: OpenAI says the total compute cost of generating all ten results was roughly $2,000 in tokens, priced at the company's internal Sol API rates.
Two thousand dollars. For work that, under normal academic conditions, might represent multiple PhD theses and years of specialized human labor spread across several subfields of pure mathematics. Forbes contributor Jon Markman flagged the number as the real headline, arguing it signals something markets have not remotely priced in: that novel, publishable-grade research output may be about to get radically, absurdly cheap.
OpenAI's mathematics research lead, Sebastien Bubeck, called the results “beautiful.” The company has framed Astra's math run as proof that frontier AI is crossing a threshold — moving from systems that regurgitate known solutions dressed up in new language, to systems capable of generating original, independently verifiable research contributions from scratch.
Genius or Grave Robbery? The Backlash Begins
The applause didn't last long. On August 6, multiple outlets reported that a group of mathematicians had accused OpenAI of academic misconduct over the same 249-page manuscript.
The most serious charge came from Steven Miller, a mathematician at Yeshiva University, who says a core argument Astra presented as an original contribution to the sphere-packing result actually first appeared in his own 2016 paper — uncredited. Miller isn't calling it an oversight. “It seems completely systematic to me,” he said, describing the pattern as the team “running roughshod over the work of others who came before them in a deliberate way,” and adding bluntly that it “points to research misconduct.”
He's not alone. Critics also flagged that Astra's soficity breakthrough — the one closing a 27-year-old open question — appears to combine key steps lifted from two previously published papers, one from 2016 and one from 2019, without OpenAI properly citing either as a source. In other words: some of what OpenAI billed as Astra thinking its way to a totally new proof may actually be Astra stitching together existing human proofs and presenting the collage as an original result.
OpenAI's response has been measured but firm. A company spokesperson affirmed that OpenAI stands behind the correctness of the results and insists the work meets the standards expected of any human mathematician publishing in the field — standards that, notably, include proper citation. The company has since gone back and revised language in its original announcement to be more precise about which of the ten problems were genuinely unsolved versus partially anticipated by prior work.
What the Experts Are Actually Saying
The reactions from the math community span the full spectrum from starstruck to skeptical, sometimes within the same sentence.
Thomas Bloom, a mathematician at the University of Manchester, called the results “big news,” though he tempered the praise: “Maybe not bigger than a proof of unit distance would have been, but in terms of constructions, this is big.”
Henry Yuen, a theoretical computer scientist at Columbia University, captured the split-screen reaction best. He described the work as impressive — before, in the same breath, calling it worrying.
Mathematician Jared Duker Lichtman pushed back hard on the hype machine that immediately sprang up around the announcement, insisting the results are “far from the ‘most important day in the history of mathematics’ or similarly hyperbolic statements” that circulated on social media within hours of the release.
And looming over all of it is Miller's misconduct accusation, which has turned what should have been a straightforward celebration of machine reasoning into a genuinely uncomfortable referendum on what “original research” even means when the researcher is a large language model trained on essentially the entire published mathematical literature.
What This Means for You
You don't need to understand a von Neumann algebra to feel the aftershocks of this story. Three things matter for ordinary readers.
First, the encryption angle is not abstract. Astra's results touch lattice-based cryptography, the mathematical foundation being built into new “post-quantum” encryption standards meant to protect everything from your bank's servers to government communications once quantum computers become powerful enough to break today's codes. Progress — or vulnerabilities — discovered in that space by an AI model matters to anyone who has ever typed a password.
Second, this is a preview of a coming credibility crisis in AI-assisted science. If a model can generate a 249-page, formally verified mathematical manuscript for $2,000, expect a flood of AI-assisted papers across every discipline in the next few years — and a parallel flood of disputes over attribution, plagiarism, and what “original discovery” even means when a machine has read every paper ever published.
Third, watch what happens to the price and pace of research itself. If genuinely novel, expert-level scientific output can be produced for the cost of a laptop, the economics of who gets to do cutting-edge research — universities with huge grants, or anyone with an API key — could shift dramatically and quickly.
The Bottom Line
Astra's math marathon is either one of the most significant moments in the history of artificial intelligence or a very expensive game of academic Whac-A-Mole, depending on who you ask — and possibly both at once. What's undeniable is that a machine sat down with ten problems that had broken some of the smartest people alive, and walked away with verified answers to all of them. Whether it built those answers from scratch, or borrowed more than it let on, is now a question for the mathematicians, the lawyers, and eventually, probably, the history books.
OpenAI has not announced a public release date for Astra itself. For now, the model remains locked away inside the company's servers — leaving the rest of us with only the proofs it left behind, and an increasingly heated argument about whether they were entirely its own.
