--- title: Ten advances in mathematics and theoretical computer science description: OpenAI's internal version of Astra, its next major model, has produced results on ten long-standing open problems in mathematics and theoretical computer... canonical: https://daily.dev/posts/ten-advances-in-mathematics-and-theoretical-computer-science-ngbzjedvn twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Ten advances in mathematics and theoretical computer science | daily.dev og:description: OpenAI's internal version of Astra, its next major model, has produced results on ten long-standing open problems in mathematics and theoretical computer... og:url: https://daily.dev/posts/ten-advances-in-mathematics-and-theoretical-computer-science-ngbzjedvn og:image: https://api.daily.dev/og/posts/nGBZjeDvN.png og:image:alt: Ten advances in mathematics and theoretical computer science og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Ten advances in mathematics and theoretical computer science **[OpenAI](https://daily.dev/sources/openai)** · 4 min read · 1 upvotes · 0 comments ## Summary OpenAI's internal version of Astra, its next major model, has produced results on ten long-standing open problems in mathematics and theoretical computer science. The problems span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics — many unsolved for decades. Solutions cost roughly $2,000 in compute at API rates. Each result was formalized in Lean, and OpenAI is releasing the proofs alongside narrations of the model's reasoning process. The announcement raises questions about AI attribution in academic research, with OpenAI acknowledging the AI generated the mathematical arguments while humans prepared manuscripts and verified correctness. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Community take How the wider developer community reacted, aggregated from 1 discussion and 326 comments across hackernews (as of 2026-08-01). **TL;DR:** The HN community is genuinely impressed by the mathematical results but deeply skeptical of OpenAI's transparency around methodology, cost claims, and experimental setup, with lively side debates about AI authorship, the chess analogy, and what this means for professional mathematicians. **Sentiment:** 25% positive · 40% mixed · 35% skeptical **The case for** - The mathematical results themselves are considered significant and largely accepted as real advances, with some calling them among the most impactful mathematical publications in history. - Lean formalization provides a meaningful layer of verifiability for the proofs. - Third-party examples of similar AI-assisted math results are emerging, suggesting the capability is not unique to OpenAI. - The results are seen as bringing mathematics more mainstream and opening new research directions. **The pushback** - The $2000/problem cost claim is potentially misleading without disclosure of how many total problems were attempted and how many failed runs were discarded. - The model used (Astra) is internal and secret, making independent verification impossible. - OpenAI's marketing framing invites skepticism given their track record of presenting results in the most favorable light. - The chess analogy is widely criticized as inapt because mathematics is a paid profession, not a spectator sport. - Lack of transparency about the full experimental setup (number of attempts, harness costs, cluster access) undermines scientific credibility. - No clear methodology for how AI-assisted proofs should be published or credited has emerged. **By community** - hackernews (mixed): Commenters accept the mathematical results as real but are sharply critical of OpenAI's lack of methodological transparency, the $2000 cost framing, and the broader implications for professional mathematicians. **Hottest debate:** Whether the $2000-per-problem cost figure is meaningfully accurate or statistically misleading given unknown numbers of failed attempts that were never disclosed. **Open questions** - How many total problems were attempted and at what total cost before the 10 successes were achieved? - How many attempts per problem were allowed before giving up? - What was the full cost of the compute harness and orchestration infrastructure? - Should AI-assisted mathematical proofs require a new publication standard disclosing model type, inference settings, seeds, and full prompt history? - Will open-weight models eventually replicate these results, or will this capability remain gated behind proprietary systems? **Highlights** > My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what percent were left unsolved at what cost before giving up? 2. How many attempts did you give the model at solving these problems? 3. How expensive was the harness, e.g. did the model have access to a job cluster? > — [aabhay on hackernews · 6 comments](https://news.ycombinator.com/item?id=49132235) > Nobody is claiming the results are false. We're saying look critically at the claims for how it was done, that it only cost $2000, etc. it would be extremely easy to run 100 sessions that failed, each costing ~$2000, and then just publishing an article about the one that succeeded, for example. This goes double since it's an internal secret model (Astra) so nobody else can verify the results. > — [esperent on hackernews · 1 comments](https://news.ycombinator.com/item?id=49133660) > Sure, but I don't really understand what the argument is to _not_ be transparent about methodology, since if they are as powerful as claimed, then doing so would easily support that and put these concerns to rest. People are right to be skeptical given what is being claimed. I know it's more exciting to say "AI disproved a longstanding conjecture" vs to say "it did so AND it took several PhD specialists in the field this many attempts to even produce a prompt that got the model spitting out something useful under some configurations, and many iterations to optimize the configurations, and the prompt itself, and many trials with that configuration to solve the problem. All told we spent more than a typical math academic can hope make in their career." By not being transparent, they invite skepticism and cynical takes, like maybe it's just that tempered and qualified claims are an existential threat to companies that are fully subsidized by the hype train? I don't know. Either way, it seems like it would be easy to address these, so why should they not do it? I say this btw as someone who uses these things extensively, including to disprove an old conjecture my advisor and I were stuck on recently. I know they are powerful and that everything is different now because of them. Let's be sober when discussing them though > — [vector\_spaces on hackernews](https://news.ycombinator.com/item?id=49134730) > Every time someone makes a comparison to chess I die inside. Chess is a spectator sport primarily funded by a few eccentric billionaires. Players artificially constrain themselves in timed environments knowing that they will never be able to produce better moves than a smartphone because a select few people find it interesting. Only ~30 top professionals actually make enough money to have a full career playing chess, maybe a few hundred more can sustain a meager lifestyle with coaching gigs. I shudder to imagine what will happen to the tens of thousands of non-Fields medalist caliber mathematicians if math goes the way of chess. Perhaps Terence Tao and a few other famous mathematicians will be funded by Peter Thiel to report on how well humanity can keep up with the machines? How do you expect any mathematician to be optimistic about this comparison. > — [traes on hackernews · 4 comments](https://news.ycombinator.com/item?id=49132269) > I believe we're seeing a new kind of mathematics that will require completely new formats for publication, a bit similar to those used in experimental sciences. AI-powered mathematics should be fully reproducible, so it's the authors' responsibility to disclose the exact model type, inference settings/seeds and the full prompt history leading to the result. Of course that would ideally require open weights models. It's not just about requiring to disclose AI use. AI-powered mathematics is a completely valid discipline that doesn't need to be shy, but it should develop its own publication culture. > — [c7b on hackernews](https://news.ycombinator.com/item?id=49135851) **Source threads** - [hackernews](https://news.ycombinator.com/item?id=49132058) · 168 points · 326 comments ## Similar posts on daily.dev - [OpenAI Publishes 10 AI-Generated Mathematical Breakthroughs Using Its Internal Model Astra](https://daily.dev/posts/openai-publishes-10-ai-generated-mathematical-breakthroughs-using-its-internal-model-astra-v6xjxofws) · Medium · 1 upvotes · 0 comments - [OpenAI teases Astra, its next major AI model, after it solves 10 long-standing math problems](https://daily.dev/posts/openai-teases-astra-its-next-major-ai-model-after-it-solves-10-long-standing-math-problems-jifwxasvg) · BleepingComputer · 1 upvotes · 0 comments --- Tags: [#ai](https://daily.dev/tags/ai), [#openai](https://daily.dev/tags/openai), [#cryptography](https://daily.dev/tags/cryptography), [#math](https://daily.dev/tags/math) [View this post on daily.dev](https://daily.dev/posts/ten-advances-in-mathematics-and-theoretical-computer-science-ngbzjedvn) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Ten advances in mathematics and theoretical computer science","url":"https://daily.dev/posts/ten-advances-in-mathematics-and-theoretical-computer-science-ngbzjedvn","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/ten-advances-in-mathematics-and-theoretical-computer-science-ngbzjedvn"},"datePublished":"2026-08-01T07:35:24.202Z","dateModified":"2026-08-01T16:34:09.492Z","description":"OpenAI's internal version of Astra, its next major model, has produced results on ten long-standing open problems in mathematics and theoretical computer...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/8f9f0fad2721d03949a82b754f44d4fa?_a=AQAEuop","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/8f9f0fad2721d03949a82b754f44d4fa?_a=AQAEuop","isAccessibleForFree":true,"articleSection":"OpenAI","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"OpenAI","logo":"https://media.daily.dev/image/upload/t_logo,f_auto/v1/logos/984b3632316f4afaa3d5213d5c64fe65","url":"https://daily.dev/sources/openai"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/ten-advances-in-mathematics-and-theoretical-computer-science-ngbzjedvn","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":1},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"ai,openai,cryptography,math","timeRequired":"PT4M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"OpenAI","item":"https://daily.dev/sources/openai"},{"@type":"ListItem","position":3,"name":"Ten advances in mathematics and theoretical computer science"}]} ```