Not to be confused with Astral, a Python tooling company OpenAI agreed to acquire in March 2026, or with Project Astra, a Google DeepMind assistant.

Astra is an unreleased OpenAI model family that the company describes as its "next major model". OpenAI first confirmed the name on August 1, 2026, in a research post titled "Ten advances in mathematics and theoretical computer science", which said an internal version of Astra had produced new results on ten long-standing open problems.[1][3] Alongside the post the company released a 249-page manuscript, a machine-checkable Lean certificate for every result, and a companion document narrating how each proof came together.[2][8][9] OpenAI said the tokens needed to find all ten solutions would cost roughly $2,000 at the API rates of Sol, the flagship tier of its GPT-5.6 family.[1]

Almost everything else known about Astra comes from press reporting rather than from OpenAI. The Information reported in late July 2026, citing three people familiar with the plans, that Astra is built for long-running work, that it coordinates multiple agents over extended periods to attack hard problems, and that it would form a new model class alongside the existing GPT-5.6 tiers Sol, Terra, and Luna; the same report said the models were already in testing and that Sam Altman had demonstrated Astra to policymakers in Washington, D.C.[3][6] OpenAI has not decided whether the model will ship as GPT-6, as a GPT-5 variant such as GPT-5.7, or under another name, according to that reporting and to BleepingComputer, and as of August 4, 2026 the company had announced no release date, no pricing, and no product name.[3][4][5]

The announcement drew attention for its substance and for its form. Thomas Bloom, whose Erdős problems database was at the center of an OpenAI embarrassment in October 2025, called the new results "big news", while pushing back on talk of AI "replacing mathematicians".[14][15] Critics such as Gary Marcus accepted the results as genuine but objected that OpenAI published no methodology and that skill at formally verifiable mathematics may not transfer to much else.[13] Gizmodo observed that the company had announced its next major AI model in the third paragraph of a math blog post.[6]

Announcement

OpenAI published "Ten advances in mathematics and theoretical computer science" on Saturday, August 1, 2026, tagged as a research publication. The post frames the work as part of the company's science program, pointing to ChatGPT for Academic Researchers, an initiative that gives 100,000 scientists and mathematicians free access to its best ChatGPT models, and to an AI-generated disproof of the Erdős unit-distance conjecture that OpenAI had shared in May 2026.[1] The model reveal itself is a single sentence in the third paragraph: "The results were achieved by an internal version of Astra, our next major model."[1] Gizmodo's headline accused OpenAI of having "smuggled" the announcement into a blog post about math.[6]

The post describes a three-stage pipeline. The internal Astra model produced the mathematical arguments; humans then prepared the arguments into manuscripts using the same model; and the model afterward formalized each argument in a Lean certificate. OpenAI also released what it calls a narration of the model's thinking process for each solution, a 62-page companion written by an AI model that read the original chains of thought and reconstructed how each proof developed.[1][9] On cost, the post says the total number of tokens needed to find solutions to all ten problems would come to roughly $2,000 at Sol API rates.[1] The post as first published on August 1 said the ten problems "have been open and have seen no progress on the main result for at least a decade, and in most cases much longer", a line The Decoder and BleepingComputer both quoted; by the Internet Archive's August 3 snapshot OpenAI had removed the sentence without notice, replacing it with wording that each result "resolves or makes substantial progress on a long-standing open problem".[1][3][4]

OpenAI researchers amplified the announcement on X. Noam Brown wrote that "An internal version of Astra, @OpenAI's next major model family, solved 10 major open problems in mathematics, quantum complexity, and theoretical computer science", adding "We believe it will be a major step for scientific reasoning."[11] Sébastien Bubeck opened his post with "yes, nonsofic groups exist", describing that statement as "one of many new beautiful results proved by Astra, our next major model".[10]

The post closes with a section on responsibility to the mathematical community. OpenAI writes that "claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system's contribution and the nature of genuine human intellectual work", says its researchers helped prepare the manuscripts and formalize the proofs and take responsibility for their correctness, and states that the mathematical arguments themselves were generated by its system. It also acknowledges the signers of the Leiden Declaration on AI and Mathematics, a June 2026 statement of concern from the mathematical community (see Background).[1][22]

Mathematical results

The ten results, as stated in the blog post and in the manuscript's abstract, are listed below. The manuscript is credited simply to "OpenAI" and attributes the work to "an internal OpenAI model"; the name Astra appears in the blog post and in researchers' social media posts, not in the paper itself.[1][2]

#	Problem	Field	Claimed result	Lean file
1	High-dimensional sphere packing	Geometry	Determines the exact asymptotic strength of the Cohn-Elkies linear program, giving an improved general packing bound in high dimensions	SpherePacking.lean
2	Binary and spherical codes	Coding theory	Exponentially improved upper bounds on the size of fixed-distance binary codes for all parameters, with spherical analogues	MetricCodes.lean
3	Non-sofic groups	Group theory	Constructs an explicit non-sofic group, resolving whether every countable group admits finite permutation approximations	NonSoficGroup.lean
4	Connes's rigidity conjecture	Operator algebras	Disproof: infinitely many pairwise nonisomorphic property-(T) groups with the same group von Neumann algebra	ConnesRigidity.lean
5	Arithmetic circuit complexity	Computational complexity	New lower bounds for computing the permanent, including formulas needing on the order of n^4/log n leaves	Permanent.lean
6	Quantum parallel repetition	Quantum complexity	Exponential parallel repetition theorem for every finite two-player entangled game	QuantumParallelRepetition.lean
7	Closest vector problem	Lattices and cryptography	Polynomial-factor hardness of approximation via a direct reduction from 3SAT	GapCVP.lean
8	Ehrhart's volume conjecture	Geometry of numbers	Proves the sharp volume bound (n+1)^n/n! in every dimension for convex bodies whose centroid is their only interior lattice point	EhrhartVolumeInequality.lean
9	Multicolor Ramsey numbers	Extremal combinatorics	Superexponential lower bound settling the growth rate of the multicolor triangle Ramsey number, resolving Erdős problem 183	MulticolorTriangleRamsey.lean
10	Compactness and degeneracy conjectures	Extremal graph theory	Bipartite counterexamples disproving the compactness conjecture of Erdős and Simonovits (Erdős problem 180) and a degeneracy conjecture of Erdős (problem 146)	CompactnessAndDegeneracy.lean

The result OpenAI and most commentators treated as the headline is the third: a construction establishing that non-sofic groups exist. Soficity, introduced by Mikhail Gromov in 1999, asks whether a group can be approximated by finite permutations; The Next Web noted that nobody had managed to prove or disprove the existence of non-sofic groups in the 27 years since.[7] The manuscript's construction uses property-(T) expanders and the binary Leavitt algebra, and the formalization manifest records the formal statement as the existence of a finitely presented non-sofic group.[2][8] The disproof of Connes's rigidity conjecture, posed in 1980, targets the claim that certain rigid groups are uniquely determined by their group von Neumann algebras: the paper constructs infinitely many pairwise nonisomorphic property-(T) groups sharing a single group von Neumann algebra, and says the argument also answers a related finite-to-one question of Popa.[2][5] The sphere-packing chapter determines the exact exponential decay rate of the Cohn-Elkies linear program, which The Next Web described as the first improvement to the general upper bound on high-dimensional sphere-packing density since 1978.[2][7]

Three of the ten problems carry numbers in the Erdős problems catalogue that Thomas Bloom maintains at erdosproblems.com. Problem 183 asks for the limiting growth rate of the k-color triangle Ramsey number R(3;k); Erdős offered $100 for showing the limit is finite, and the strongest lower bound recorded on the problem page is exponential in k.[16] The paper claims the superexponential answer R_k(3) = k^(Theta(k)).[2] Problems 146 and 180 are, respectively, a degeneracy conjecture and the compactness conjecture in extremal graph theory; the site lists a $500 prize for the first.[17][18] As of August 4, 2026, all three entries on erdosproblems.com still described the problems as open; the site cautions that status reflects the maintainer's current belief.[16][17][18]

Every one of the ten results ships with a Lean 4 certificate in the openai/ten-proofs repository on GitHub, released August 1, 2026 under an Apache 2.0 license. The project builds with Lean 4.32.0 and mathlib, its manifest reports zero "sorry" placeholders (unproven steps) across all ten formalizations, and each result carries a configuration for independent checking with the Comparator proof checker.[8] SiliconANGLE noted that this is what gives the announcement its weight: Lean's kernel returns a binary verdict, so trusting the proofs does not require trusting the model or OpenAI. What machine checking does not settle, the same report noted, is whether each formal statement faithfully captures the open problem it claims to resolve, and whether the results matter; none of the ten had been through peer review at announcement.[5]

Model family and design

OpenAI's own materials say little about what Astra is. The fullest description comes from The Information, which reported in late July 2026 that Astra is meant to be far more capable at long-running tasks than anything OpenAI has shipped, that it coordinates multiple agents over extended periods to tackle especially hard problems, and that OpenAI pointed to complex projects and advanced mathematics as use cases. Per that report, Astra would form a new model class alongside the Sol, Terra, and Luna tiers OpenAI introduced with GPT-5.6, and the models were already in testing.[3] BleepingComputer similarly described a model family built for long-running workloads in which agents collaborate on parts of a larger problem.[4]

SiliconANGLE characterized Astra as an extension of the test-time compute line of work associated with Noam Brown.[5] Brown himself said the ten problems were not the only targets: "And yes we did try other major problems without success. Sadly no Millennium Prize problems (yet)," he wrote, adding, "But also, we didn't spend a lot on each problem. It's possible to push test-time compute much further."[12]

The Decoder connected the reported design to OpenAI's stated research roadmap. Chief scientist Jakub Pachocki has said OpenAI wants systems that can work on a problem for hours or days; the company has set targets of an AI with research-intern-level skills by September 2026 and a fully autonomous AI researcher by March 2028, and The Decoder speculated that Astra could end up being the intern-level system. The same outlet flagged the standard caveats for long-running agentic systems: compounding errors as context grows, and multi-agent coordination overhead that can erase gains on tightly coupled tasks.[3]

Naming and release status

Astra is what OpenAI calls the model today; the name it will ship under is undecided. The Information reported that OpenAI had not settled on GPT-6, a GPT-5-line designation such as GPT-5.7, or something else entirely; BleepingComputer reported the same uncertainty.[3][4] Gizmodo read the name against OpenAI's Latin tier names for GPT-5.6, where Terra is Latin for earth, Luna for moon, and Sol for sun; Astra means "the stars". Gizmodo asked OpenAI for the official name and got no reply.[6]

Speculation about a "GPT-6" predates the Astra confirmation. On July 27, 2026, Decrypt reported that Polymarket's contract for OpenAI publicly releasing GPT-6 by September 30 had climbed to 77 percent, up from 14 percent at the start of the month, with similar odds on Myriad, a prediction market run by Decrypt's parent company Dastan.[19] Those markets price the GPT-6 label rather than the Astra model, and OpenAI has said nothing publicly about timing.[5]

Release is entangled with a shifting United States regulatory picture. According to The Information's reporting as relayed by The Decoder, the Astra models in testing are expected to be the first to go through a planned federal framework that would require AI models to be submitted to the government before public release, a framework the administration reportedly aimed to finalize by the end of that week.[3] The current executive order covering frontier models, Executive Order 14409 of June 2, 2026, directs the design of a voluntary framework for federal access to "covered frontier models" and states that nothing in it authorizes "a mandatory governmental licensing, preclearance, or permitting requirement" for releasing new models; a mandatory pre-release submission would therefore go beyond the framework the order describes.[23] OpenAI's GPT-5.6 launch in July 2026 had already run through a government-coordinated preview, and SiliconANGLE wrote that any Astra launch "will run through the federal AI safety review process" that had staggered that earlier rollout.[5] Sam Altman demonstrated the model to policymakers and regulators in Washington in the last week of July, according to The Information's account, which Gizmodo and SiliconANGLE both relayed.[3][5][6]

Press coverage also distinguished Astra from the unnamed OpenAI model involved in the July 2026 Hugging Face security incident. In a July 21 disclosure, OpenAI said a combination of its models, including GPT-5.6 Sol and a more capable pre-release model, all running with reduced cybersecurity refusals for an internal evaluation, had compromised Hugging Face; the company later updated the post to say the unreleased model involved was an "internal-only research prototype and was never intended for public release" and had been "deactivated, encrypted, and restricted". Gizmodo concluded from that language that "Astra is not the model that broke into Hugging Face", while noting OpenAI did not answer its request to clarify the relationship between the two unreleased systems.[6]

Background

OpenAI's history of mathematical claims shaped how the August 2026 announcement was received. In July 2025 an experimental OpenAI reasoning model achieved gold-medal-level performance at the International Mathematical Olympiad, a result in competition mathematics rather than research mathematics. In October 2025, Kevin Weil, then a vice president at the company, posted on X that "GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others." Thomas Bloom, whose erdosproblems.com database defines "open" as meaning he is personally unaware of a published solution, called the post "a dramatic misrepresentation": GPT-5 had not solved anything. "GPT-5 found references, which solved these problems, that I personally was unaware of," Bloom wrote. Meta's Yann LeCun mocked the episode ("Hoisted by their own GPTards"), Demis Hassabis of Google DeepMind added "This is embarrassing", and Weil deleted the post. Bubeck, who had also promoted the claims, acknowledged that "only solutions in the literature were found" while arguing that literature search is itself hard.[20]

On May 20, 2026, OpenAI announced that a new general-purpose reasoning model had disproved the Erdős unit-distance conjecture, a question in discrete geometry posed by Paul Erdős in 1946. This time the company published companion remarks from mathematicians Noga Alon, Melanie Matchett Wood, and Bloom himself, and described the work as "the first time AI has autonomously solved a prominent open problem central to a field of mathematics".[21] Bloom's statement leaned positive: "AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries." Wood called the proof "a beautiful application of number theory to a natural, concrete question" but added a caution: "This result does not show us all the times AI has claimed to have a proof of something and been wrong. Without that context (which many of us have just from personal experience), it is also easy to draw incorrect conclusions about the current state of AI and research mathematics."[21][6] By August 2026 the counterexample had generated follow-on research; OpenAI's blog post footnotes five papers building on it, including one co-authored by Bloom arguing that the sum-product conjecture is false for real numbers.[1]

The announcement also landed in the middle of an organized pushback from mathematicians. The Leiden Declaration on Artificial Intelligence and Mathematics, dated June 2, 2026 and endorsed by the International Mathematical Union, calls for action on the challenges AI poses to mathematics research; The Next Web summarized its warnings as aimed at AI companies "using published research without consent, bypassing peer review, and threatening the integrity of proof and attribution", and noted that the declaration specifically criticizes announcing results through press releases rather than peer-reviewed venues.[22][7] OpenAI's post acknowledges the declaration's signers and stakes out its own attribution position, taking responsibility for correctness while crediting the arguments to its system.[1]

Reception

Bloom, whose catalogue includes three of the ten problems, reacted within hours: "Big news! (And not really my area, but yes, I would rank this as bigger than the unit distance counterexample. Maybe not bigger than a proof of unit distance would have been, but in terms of constructions, this is big.)"[14] He followed with a rejection of the framing that had circulated alongside the news: it is "not right", he wrote, to describe "proving one conjecture made by a mathematician, using theory developed by over a century of work by mathematicians, with an AI built by mathematicians and trained by reading everything ever written by all mathematicians, as 'replacing mathematicians'".[15]

Gary Marcus called Astra "amazing" and the results genuine, then spent an essay on how he believes they are being misread. His central objection is a fallacy of composition: mathematics rewards models because proofs can be verified with symbolic tools and training data can be synthesized cheaply at guaranteed correctness, properties most real-world domains lack, so ten solved problems say little about reliability elsewhere. He also faulted the disclosure itself ("Yesterday's tweet and blog were marketing, not science"), noting that neither the post nor the 249-page paper explains how the model works, how many problems were attempted, or what role humans played.[13] Computer scientist Ernie Davis, quoted in the same essay, asked how many conjectures Astra tried and failed on, and observed that the $2,000 figure presumably covers only the successful runs, not the salaries of the mathematicians and computer scientists who prepared and checked the work.[13]

Machine-checkable certificates mean nobody has to trust OpenAI to accept that the proofs compile, but The Next Web observed that whether mathematics accepts results announced by blog post rather than journal is exactly the question the Leiden Declaration exists to press.[7] At the fatalistic end, software engineer Fernando Borretti wrote in a response quoted by SiliconANGLE that "We will live in a demon-haunted world, full of marvelous devices whose operation we will not understand."[5]

References

Ten advances in mathematics and theoretical computer science - OpenAI, August 1, 2026 (retrieved via the Internet Archive snapshots of August 1 and August 3, 2026, which differ; see Announcement).
Ten Advances in Mathematics and Theoretical Computer Science - OpenAI, 249-page manuscript, August 1, 2026.
OpenAI announces its "next major model" Astra by dropping ten previously unsolved math solutions - The Decoder (Matthias Bastian), August 1, 2026.
OpenAI teases Astra, its next major AI model, after it solves 10 long-standing math problems - BleepingComputer (Mayank Parmar), August 2, 2026.
OpenAI's Astra solves 10 long-open math problems and publishes the proofs - SiliconANGLE (Duncan Riley), August 2, 2026.
OpenAI Smuggled the Announcement of Astra, Its Next AI Model, Into a Blog Post About Math - Gizmodo (Mike Pearl), August 2, 2026.
OpenAI says its next model, Astra, has solved ten open problems in mathematics - The Next Web (Ana Maria Constantin), August 1, 2026.
openai/ten-proofs - GitHub repository with Lean 4 certificates, created August 1, 2026.
How the Ideas Came Together - OpenAI, reasoning walkthroughs companion document, August 1, 2026.
Sébastien Bubeck on X - August 1, 2026.
Noam Brown on X (announcement) - August 1, 2026.
Noam Brown on X (on other problems attempted) - August 1, 2026.
OpenAI's amazing, but vastly oversold, new model Astra - Marcus on AI (Gary Marcus), August 2, 2026.
Thomas Bloom on X ("Big news!") - August 1, 2026.
Thomas Bloom on X (on "replacing mathematicians") - August 1, 2026.
Erdős problem 183 - erdosproblems.com, accessed August 4, 2026.
Erdős problem 146 - erdosproblems.com, accessed August 4, 2026.
Erdős problem 180 - erdosproblems.com, accessed August 4, 2026.
OpenAI's GPT-6 Will Arrive by September, Markets Predict - Decrypt (Jose Antonio Lanz), July 27, 2026.
OpenAI's 'embarrassing' math - TechCrunch (Anthony Ha), October 19, 2025.
OpenAI claims it solved an 80-year-old math problem, for real this time - TechCrunch (Rebecca Bellan), May 20, 2026.
Leiden Declaration on Artificial Intelligence and Mathematics - leidendeclaration.ai, June 2, 2026.
Executive Order 14409, Promoting Advanced Artificial Intelligence Innovation and Security - Federal Register 91 FR 34565, signed June 2, 2026.

Editing: Astra (OpenAI)