{"@context":"https://schema.org","@type":"NewsArticle","generatedAt":"2026-08-21T18:21:36.167Z","headline":"OpenAI 用 Astra 模型攻克 10 道数学难题，数学家既兴奋又担忧","description":"OpenAI 宣布其未发布的 Astra 模型解决了 10 道长期悬而未决的数学难题，涵盖球体堆积、纠错码、非 sofic 群存在性等领域，并发布超 250 页论文及 Lean 验证结果。 🔗 阅读原文 via AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","url":"https://www.aioga.com/news/cmsokd2b00viorofwaq9wrsv1/","mainEntityOfPage":"https://www.aioga.com/news/cmsokd2b00viorofwaq9wrsv1/","datePublished":"2026-08-11T11:00:00.000Z","dateModified":"2026-08-11T11:00:00.000Z","inLanguage":"zh-CN","publisher":{"@type":"NewsMediaOrganization","name":"Aioga","url":"https://www.aioga.com"},"citation":["https://www.theverge.com/ai-artificial-intelligence/977273/the-ai-takeover-of-mathematics-has-begun","https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1"],"canonicalUrl":"https://www.aioga.com/news/cmsokd2b00viorofwaq9wrsv1/","directAnswer":{"@type":"Answer","text":"OpenAI称，未发布的Astra模型解决或推进了10道长期数学难题，并公布超过250页论文及Lean验证结果。相关成果覆盖球体堆积、纠错码、非sofic群等领域，引发数学界对突破速度与贡献归属的讨论。","url":"https://www.aioga.com/news/cmsokd2b00viorofwaq9wrsv1/","dateCreated":"2026-08-11T11:00:00.000Z","author":{"@type":"Organization","@id":"https://www.aioga.com/authors/aioga-editorial/#editorial-team","name":"Aioga Editorial Team","url":"https://www.aioga.com/authors/aioga-editorial/"}},"evidence":[{"@type":"CreativeWork","name":"The Verge source article","url":"https://www.theverge.com/ai-artificial-intelligence/977273/the-ai-takeover-of-mathematics-has-begun","datePublished":"2026-08-11T11:00:00.000Z","provider":{"@type":"Organization","name":"The Verge","url":"https://www.theverge.com/ai-artificial-intelligence/977273/the-ai-takeover-of-mathematics-has-begun"}},{"@type":"CreativeWork","name":"AIHot archive record","url":"https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","datePublished":"2026-08-11T11:00:00.000Z","provider":{"@type":"Organization","name":"AIHot","url":"https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1"}}],"aggregationSource":"The Verge：AI（RSS）","originalPublisher":{"name":"The Verge","url":"https://www.theverge.com/ai-artificial-intelligence/977273/the-ai-takeover-of-mathematics-has-begun"},"geoDeepAnswer":null,"article":{"id":"cmsokd2b00viorofwaq9wrsv1","slug":"cmsokd2b00viorofwaq9wrsv1","url":"https://www.aioga.com/news/cmsokd2b00viorofwaq9wrsv1/","title":"OpenAI 用 Astra 模型攻克 10 道数学难题，数学家既兴奋又担忧","title_en":"","summary":"OpenAI 宣布其未发布的 Astra 模型解决了 10 道长期悬而未决的数学难题，涵盖球体堆积、纠错码、非 sofic 群存在性等领域，并发布超 250 页论文及 Lean 验证结果。 🔗 阅读原文 via AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","source":"The Verge：AI（RSS）","sourceUrl":"https://www.theverge.com/ai-artificial-intelligence/977273/the-ai-takeover-of-mathematics-has-begun","aiHotUrl":"https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","publishedAt":"2026-08-11T11:00:00.000Z","category":"行业动态","score":72,"selected":true,"articleBody":["Mathematician James Maynard has spent a lot of time this past year “soul searching.” A professor at the University of Oxford and winner of the prestigious Fields Medal, Maynard told The Verge he’s been grappling with the future of his field as the traditionally slow-moving discipline hurries to adapt to AI.","Days before we spoke, OpenAI revealed：https://openai.com/index/ten-advances-in-mathematics/ it had produced the solutions to 10 long-standing mathematics problems, some of which had confounded academics for decades. Like generative AI used to produce text and images or propose ideas in science：/2024/5/8/24152088/google-deepmind-ai-model-predict-molecular-structure-alphafold and medicine：/ai-artificial-intelligence/961311/anthropic-claude-science-ai-drug-development, the technology learns patterns and connections from the vast amount of material it’s trained on and uses them to create something new. Applied to mathematics, that can mean combining known results, methods, and tools in new ways to attack a problem, sometimes drawing links between disparate fields or resurfacing concepts buried in academic literature.","For Maynard and other mathematicians The Verge spoke to, the announcement has added to a complex swirl of emotions about where their field is headed. There is palpable excitement at the prospect of accelerating mathematical discovery — but also apprehension, and in some cases despair, about what this could mean for the people who have dedicated their lives to the pursuit, and for the generations of future mathematicians who will follow them. Few doubt that a profound upheaval is already underway.","Few doubt that a profound upheaval is already underway.","The problems OpenAI solved, using an advanced unreleased model known as Astra, spanned a wide range of mathematical fields, from the highly abstract to questions with practical implications. One breakthrough concerned how tightly spheres can be packed in more than three dimensions, a problem linked to how efficiently data can be encoded and transmitted. Another pushed the limits of error-correcting codes, which can help recover information from noisy signals. A third resolved two long-standing questions about how complex connected networks can become before structural patterns emerge. Other results on the list tackled problems in quantum game theory and the search for targets inside high-dimensional grids, with implications for techniques used in post-quantum：https://www.nature.com/articles/d41586-026-01054-1 cybersecurity.","One of the most attention-grabbing results concerned the existence of non-sofic groups, infinite mathematical structures that, roughly speaking, cannot be approximated by finite ones. Whether such structures existed at all had remained an open question for decades. It was attention-grabbing for another reason, too: a dispute over how much credit belonged to OpenAI’s AI, and how much to the human mathematicians whose recent work it built upon.","Francesco Fournier-Facio, a mathematician at the University of Cambridge, told The Verge he and others working in that area believed OpenAI’s original announcement minimized the contributions of researchers Andreas Thom and Gábor Kun, whose recent works helped lay the groundwork for the result.","When OpenAI first published：https://web.archive.org/web/20260802205906/https://openai.com/index/ten-advances-in-mathematics/ its announcement, it said it was sharing “results to problems that have been open and have seen no progress on the main result for at least a decade, and in most cases much longer.” It later changed：https://openai.com/index/ten-advances-in-mathematics/ this to say it was sharing “results, each of which resolves or makes substantial progress on a long-standing open problem.” The page contains no correction note or explanation for the change.","Kun, a researcher at the Alfréd Rényi Institute of Mathematics in Hungary, told The Verge OpenAI reached out to him by email shortly before publishing to share its findings. He found the sweeping language in the original announcement “rather comical,” particularly as the more detailed research paper attached “clearly said that it builds on my results from 2016 and 2019,” the latter coauthored with Thom. “It’s rather sloppy,” Kun said.","After publication, OpenAI contacted Kun again. He declined to share the email exchange in full but read The Verge what he said was an excerpt in which an OpenAI mathematician wrote that the language had been intended to refer to other results in the collection. “It was not intended to suggest that there had been no progress on this problem,” the email read, he said. “We certainly agree that the argument relies crucially on your work.” The mathematician added that they would ask for the wording of the announcement to be revised.","OpenAI spokesperson Laurance Fauconnet confirmed to The Verge that the post was subsequently updated. “We updated the language to better reflect the prior research these results build upon. Although the question of whether non-sofic groups exist had remained open for decades, our sofic group proof relies on important mathematical work published more recently, and we wanted to ensure those contributions were properly acknowledged.”","Kun said he wondered whether similar oversights might have been made in the other results, which were outside his areas of expertise.","Assessing OpenAI’s results more broadly is complicated. Mathematics has become so specialized that few researchers are fully equipped to scrutinize all of the fields Astra touched upon. The company released more than 250 pages of papers：https://cdn.openai.com/pdf/ten-proofs-oai.pdf laying out the solutions, along with 60 more pages describing：https://cdn.openai.com/pdf/reasoning-walkthroughs.pdf “how the ideas came together,” and certified each result with Lean：https://www.quantamagazine.org/lean-computer-program-confirms-peter-scholze-proof-20210728/, software for verifying mathematical proofs. While many of the mathematicians The Verge spoke to said they couldn’t personally evaluate some or even any of the solutions themselves, all said there is a broad consensus that there seems to be real weight behind OpenAI’s achievement.","The problems, which OpenAI claimed were solved by an internal version of its “next major model,” Astra, were not trivial. Maynard said they were the kind of questions mathematicians and computer scientists had spent serious time thinking about, and repeatedly failed to resolve.","“There’s a general feeling that [solving] one of these 10 problems would get you a job in academia,” said Yang-Hui He, a fellow at the London Institute for Mathematical Sciences. He had just returned from a four-week AI and mathematics research conference：https://symposia.kias.re.kr/AI-Math2026 in South Korea, where he said many felt there had been something of a “phase transition” over the past six months, with AI producing genuine and meaningful advances.","Many felt there had been something of a “phase transition” over the past six months, with AI producing genuine and meaningful advances.","In May, OpenAI stunned：https://go.skimresources.com/?id=1025X1701640&xs=1&url=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2527564-mathematicians-stunned-by-ais-biggest-breakthrough-in-mathematics-yet%2F mathematicians when it announced：https://openai.com/index/model-disproves-discrete-geometry-conjecture/ that an unnamed internal model had cracked a conjecture：https://www.quantamagazine.org/why-the-legendary-erdos-problems-are-falling-to-ai-20260803/ by Paul Erdős that had eluded mathematicians for the better part of a century. In July, Harvard mathematician Levent Alpöge tweeted：https://x.com/__alpoge__/status/2079028340955197566?s=46 that Anthropic’s Claude Fable 5 had disproved the fiendish Jacobian conjecture：https://go.skimresources.com/?id=1025X1701640&xs=1&url=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2580374-ais-solution-to-87-year-old-riddle-takes-mathematicians-by-surprise%2F with a tiny counterexample, overturning decades of efforts to prove it was true. They are among the latest examples of problems mathematicians seriously care about falling to AI.","Maynard recalled that, until recently, this was not always the case. With some notable exceptions, he said AI breakthroughs in mathematics generated a lot of publicity while involving problems that had often attracted little serious attention from researchers. The speed at which this is changing has caught many researchers off guard, leaving the field scrambling to work out how to respond, and some wondering whether it can continue to survive in anything like its current form.","Many of the mathematicians The Verge spoke to seemed to still be working out what they thought about it all, while expressing surprise, even shock, at the speed of change. There was plenty of excitement, but He said his impression from the conference in South Korea, and from the field more broadly, is that many in the field are downplaying the significance of recent advances in a bid to “keep calm” about how quickly things are moving.","Money is at the heart of many of these concerns. “It’s not quite clear whether our universities are going to be willing to pay that much for our theorems,” said Colva Roney-Dougal, a professor at the University of St Andrews in Scotland. “Maths is a cheap discipline typically,” she said, gesturing to a whiteboard covered in her work. “Most of the time I don’t even bother getting a research grant. I don’t need one. I just get on with my job.”","That system could break down even if costs are relatively modest by AI standards. OpenAI estimates that generating Astra’s 10 solutions would have cost around $2,000 in tokens at the current API prices for its Sol model. Researchers The Verge spoke to said the true cost was likely considerably higher, depending on how many problems and attempts preceded the successful ones. OpenAI did not elaborate when asked about how the final list was assembled. But for a field used to operating on a shoestring budget, even the advertised price could be too much. Roney-Dougal fears researchers at smaller and less wealthy institutions could be locked out of some research entirely.","There is also a broader unease about the growing intrusion of commercial interests into a field that has largely operated in the open. Even as mathematics has become more computational, many tools researchers rely on are open source and freely available. The most capable models from companies like OpenAI and Anthropic are proprietary and access is tightly controlled by the companies. While both have programs：https://openai.com/index/chatgpt-for-academic-researchers/ offering free：https://www.anthropic.com/news/ai-for-science-program access to academic researchers, that access is far from universal, and few of the researchers The Verge spoke to had been able to use the most sophisticated systems. Both Maynard and Roney-Dougal expressed hope that open-weight models：/ai-artificial-intelligence/971444/how-chinese-open-weight-ai-models-impact-us-companies could eventually close that gap, giving mathematicians access to tools without having to rely on a handful of big AI companies.","Access isn’t the only concern. Several researchers The Verge spoke with questioned whether the values of AI companies align with those of the mathematical community. With products to sell and enormous valuations for impending IPOs to justify, companies have every incentive to hype and exaggerate their contributions, they said, while underselling the human scholarship those results rely on.","“That’s the bit I’m most unhappy about at the moment,” Roney-Dougal said. “They’re treating our discipline as an advertising playground.”","“They’re treating our discipline as an advertising playground.”","Those concerns extend beyond the researchers The Verge spoke to. In June, mathematicians published the Leiden Declaration：https://leidendeclaration.ai/, a set of principles for the responsible use of AI in mathematics that has been endorsed by the International Mathematical Union and signed by more than 3,400 people. It urges policymakers, governments, the media, and other groups to not buy into “the hype” created by companies who “overstate the capabilities of their products.” The fear is that exaggerated claims will have real consequences for the field, convincing funders and governments that human mathematicians are less necessary than they actually are.","OpenAI has been accused of doing just that with its 10 Astra advances, not least through its glossing over the contributions of Kun and Thom. Kun said his “feelings are quite ambivalent.” It was gratifying to see his work prove useful in resolving a significant problem, even if he wished he had been the one to finish it, and it brought him attention he otherwise might never have received, along with plenty of congratulations. His joke to well-wishers: He will be a “very famous unemployed” person.","Fournier-Facio feels considerably less ambivalent. “Most people will just look at the OpenAI announcement and take it at face value,” he said. Few people, he argued, will have the time, expertise, or inclination to dig through hundreds of pages of technical papers to understand the human work behind the headline, particularly journalists or policymakers working quickly. “They’re just choosing the narrative that benefits them most,” he said. “It’s a lot more impressive to say that an AI system came up independently with something that humans have done nothing on for 10 years. It’s a lot less sexy to say that this is a kind of building on ideas from the past 10 years from humans and combining them in a clever way.”","“It’s a lot more impressive to say that an AI system came up independently with something that humans have done nothing on for 10 years. It’s a lot less sexy to say that this is a kind of building on ideas from the past 10 years from humans and combining them in a clever way.”","There is already an element of unfairness in how mathematics assigns credit, Fournier-Facio acknowledged. “The person that does the last step gets most of the credit, right?” He likened mathematical research to building a pyramid, with generations of work accumulated beneath the person who finally places the last stone. Maybe there wouldn’t have been this much insistence on making sure Kun and Thom were credited if it were a human solving this problem, he said. But with AI taking that final step, he worries that everyone else will wrongly “be seen as useless.”","Worse still: “In the case of humans, the human that puts the last stone in is not necessarily going to steal the job of all the people that built the pyramid.”","That fear is especially troubling when mathematicians consider how AI will impact the next generation of researchers. Many of the problems LLMs are beginning to solve are precisely the kind that graduate students “typically work on,” said Oxford professor Andras Juhasz. They are not always particularly flashy, but working through them is crucial for developing the skills, intuition, and habits needed to become successful researchers. They now risk being scooped by someone swooping in and solving it with AI, said ETH Zurich researcher Johannes Schmitt.","The effects are already beginning to be felt. Project work has “become a problematic form of assessment” for undergraduates as AI systems become more capable of completing it, Juhasz said. The tools may help students get answers quicker, but risk harming the overall mathematical understanding that comes through struggle. Maynard, meanwhile, is already worrying about how to futureproof research projects for students. “If the standard for a publishable paper is something that an AI can’t do, particularly when a PhD is typically four years, you’re not trying to come up with a problem that AI can’t do now. It’s AI in four years’ time.”","“Many of the people that I talked with are really, really scared.”","This uncertainty is already hardening into despondency, particularly among mathematicians early on in their careers. “Many of the people that I talked with are really, really scared,” said Fournier-Facio. He pointed The Verge to two despairing：https://kirwinhampshire.substack.com/p/the-dark-night-of-mathematics?utm_campaign=post&utm_medium=web&triedRedirect=true essays：https://tasmin.substack.com/p/mathematicians-need-to-act?utm_id=97757_v0_s00_e0_tv2_a1demoo3x4dwia&fbclid=IwY2xjawTetIhleHRuA2FlbQIxMABzcnRjBmFwcF9pZBAyMjIwMzkxNzg4MjAwODkyAAEe7HYDDRhtkI8fMAAWEpFcu0vE8CKkzJyR2M0ok3TEUvs2I9EU-d5vMjMEZdY_aem_HZDqwE7hyLd5XXJMtnlblA from graduate students circulating online questioning their futures in the field. Roney-Dougal said she had seen similar doubts spreading across social media, with comments along the lines of “I’m not sure what I should be doing now. I don’t know if there’s any point in me carrying on.” Roney-Dougal herself is less pessimistic: “I’m not that depressed about it,” she said. “But plenty of people are.”","“I’m not that depressed about it,” she said. “But plenty of people are.”","The issue goes beyond how many problems AI can solve. Mathematics does not progress by simply checking problems off a list. A solution can matter most for what comes next. The best results can open up entirely new questions, techniques, or even fields of research. It remains to be seen whether AI can do that. Conversely, it is too early to dismiss the problems falling to AI as simply low-hanging fruit. Fully understanding what these results contribute, and how important they ultimately prove to be, will take time.","So far, Schmitt is unconvinced. He said he has seen little evidence of major AI contributions opening up new areas of thought and inquiry like this, raising the unsettling prospect of an increasingly lopsided endeavor. “We might be heading for a somewhat imbalanced situation, where lots of good and interesting problems get mowed down by AI agents,” he said, without those solutions feeding back into the creation of fruitful new directions for researchers to pursue.","“We might be heading for a somewhat imbalanced situation, where lots of good and interesting problems get mowed down by AI agents.”","Not everyone is so unsettled. The London Institute’s He was strikingly optimistic about what comes next. He said some contraction in the number of people pursuing traditional academic mathematics could even be a “healthy direction,” pointing to an already brutal job market for mathematics graduates. Others saw the potential for AI to broaden who gets to participate in research, allowing undergraduates and researchers without access to expertise concentrated at elite institutions to develop their ideas and potentially produce publishable work that might previously have been beyond their reach. For established researchers, meanwhile, handing off more routine work to AI could free up time to focus on more creative and conceptual parts of mathematics.","For all the fears and hopes, nobody knows where this is going. AI is moving too fast, and the mathematics it is producing is still too fresh to judge what its impact may be. Several researchers worried that the field could be reshaped for the worse by claims about what AI could become before anyone has had time to understand what it actually means.","When asked whether he thought any of Astra’s results were worthy of a Fields Medal, one of mathematics’ highest honors and an award he himself received：https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/IMU_Fields22_Maynard_citation.pdf four years ago, Maynard said his initial impression was that they fell short.","“The ones that I’ve looked at, they have the flavor of being very impressive results,” he said, but not necessarily ones that elevate mathematics at a conceptual level. For now, he said he sees more evidence of existing techniques and methods being pushed further and connected in clever ways than of some profound new mathematical ideas.","“But I think it’s also too early to say,” he said. “Sometimes it takes time and perspective to realize, ‘Oh, here is really a fundamental new idea.’”","At the speed it is going, AI may not give mathematicians much time to figure it out."],"articleImages":[{"sourceUrl":"https://platform.theverge.com/wp-content/uploads/sites/2/2025/09/ROB_H_BLURPLE.jpg?quality=90&strip=all&crop=0%2C0%2C100%2C100&w=2400","alt":"Robert Hart","afterParagraph":44,"url":"/media/articles/cmsokd2b00viorofwaq9wrsv1/29538ba2ebf71277.webp"}],"mediaStatus":"ok","articleBodyZh":["数学家詹姆斯·梅纳德在过去一年里花了大量时间进行“灵魂探索”。梅纳德是牛津大学的教授，也是享有盛誉的菲尔兹奖获得者，他告诉The Verge，他一直在思考自己的领域的未来，因为这个传统上动作缓慢的学科正急速适应人工智能。","在我们交谈的前几天，OpenAI透露：https://openai.com/index/ten-advances-in-mathematics/ 它已经解决了10个长期未解的数学问题，其中一些问题困扰学术界数十年。就像用于生成文本和图像或提出科学与医学创意的生成式人工智能一样：/2024/5/8/24152088/google-deepmind-ai-model-predict-molecular-structure-alphafold 和 /ai-artificial-intelligence/961311/anthropic-claude-science-ai-drug-development，这项技术从其训练的大量材料中学习模式和联系，并利用这些知识创造出新的东西。应用于数学，这可能意味着以新的方式组合已知的结果、方法和工具来解决问题，有时会在不同领域之间建立联系，或者重新发现曾被学术文献掩埋的概念。","对于梅纳德和The Verge采访的其他数学家来说，这一公告让他们对自己领域的未来产生了复杂的情绪漩涡。加快数学发现的前景令人兴奋——但同时也让人感到担忧，有些情况下甚至感到绝望，因为这可能会影响那些献身于数学研究的人，以及将来跟随他们的下一代数学家。几乎没有人怀疑，一场深刻的变革已经在进行中。","几乎没有人怀疑，一场深刻的变革已经在进行中。","OpenAI 使用一种名为 Astra 的先进未发布模型解决的问题，涵盖了广泛的数学领域，从高度抽象的问题到具有实际意义的问题。其中一个突破涉及在三维以上空间中球体的最紧密堆积问题，这与数据编码和传输的效率相关。另一个突破推动了纠错码的极限，这类代码可以帮助从噪声信号中恢复信息。第三个突破解决了两个长期存在的问题，即复杂连接网络在出现结构模式之前能达到的复杂程度。名单上的其他结果涉及量子博弈理论的问题以及在高维网格中搜索目标的问题，这对后量子网络安全技术有重要意义：https://www.nature.com/articles/d41586-026-01054-1。","最引人注目的结果之一涉及非 Sofic 群的存在问题，这是一种无限的数学结构，大致来说无法被有限结构近似。这样的结构是否存在，几十年来一直是一个未解之问。它之所以引人注目，还有另一个原因：关于应归功于 OpenAI 的人工智能多少，以及应归功于人类数学家多少的争议，这些数学家最近的工作为成果提供了基础。","剑桥大学的数学家 Francesco Fournier-Facio 告诉 The Verge，他和该领域的其他研究人员认为，OpenAI 最初的公告低估了研究人员 Andreas Thom 和 Gábor Kun 的贡献，他们最近的工作为该成果奠定了基础。","当 OpenAI 首次发布公告时：https://web.archive.org/web/20260802205906/https://openai.com/index/ten-advances-in-mathematics/，它表示正分享“对一些长期未解且在主要结果上至少十年没有进展的问题的解决结果，在大多数情况下时间更长。”之后，它将公告更改为：https://openai.com/index/ten-advances-in-mathematics/ 表示正在分享“结果，每一项都解决或在长期未解问题上取得实质性进展。”该页面没有包含更正说明或对更改的解释。","匈牙利阿尔弗雷德·雷尼数学研究所的研究员Kun告诉The Verge，OpenAI在发表前不久通过电子邮件联系了他，分享其研究成果。他觉得原公告中的夸张语言“相当滑稽”，尤其是因为附上的更详细的研究论文“明确说明它建立在我2016年和2019年的成果之上”，后者是与Thom合著的。“这相当马虎，”Kun说道。","发表后，OpenAI再次联系Kun。他拒绝全文分享邮件交流，但向The Verge读出了他所说的一段摘录，其中一名OpenAI数学家写道，这些措辞原本是指引用集合中的其他成果。“并非意在暗示在这个问题上没有进展，”邮件中写道，他说。“我们当然同意，这一论证关键依赖于你的工作。”该数学家补充说，他们会要求修改公告的措辞。","OpenAI发言人Laurance Fauconnet向The Verge证实，该帖随后已更新。“我们更新了措辞，以更好地反映这些成果所建立的先前研究。尽管非sofic群是否存在的问题几十年来一直没有解决，我们的sofic群证明依赖于最近发表的重要数学工作，我们希望确保这些贡献得到适当承认。”","Kun表示，他怀疑其他成果中是否也存在类似疏漏，而那些成果超出了他的专业领域。","更广泛地评估 OpenAI 的成果是复杂的。数学已经变得如此专业化，以至于很少有研究人员能够全面审查 Astra 涉及的所有领域。该公司发布了超过 250 页的论文：https://cdn.openai.com/pdf/ten-proofs-oai.pdf，阐述了解决方案，同时还有 60 页更多内容描述：https://cdn.openai.com/pdf/reasoning-walkthroughs.pdf “这些想法是如何结合在一起的”，并使用 Lean 软件：https://www.quantamagazine.org/lean-computer-program-confirms-peter-scholze-proof-20210728/ 对每个结果进行了认证，该软件用于验证数学证明。虽然《The Verge》采访的许多数学家表示，他们个人无法评估其中一些甚至任何解决方案，但所有人都表示，普遍共识认为 OpenAI 的成就似乎具有实际分量。","OpenAI 宣称由其内部版本的“下一代重大模型” Astra 解决的问题并非简单。Maynard 表示，这些问题是数学家和计算机科学家们曾认真思考过，并多次未能解决的那类问题。","“普遍的感觉是，解决这 10 个问题中的一个就能让你在学术界找到工作，”伦敦数学科学研究所的研究员杨惠赫说。他刚刚从韩国参加了为期四周的 AI 与数学研究会议：https://symposia.kias.re.kr/AI-Math2026，他表示许多人感觉在过去六个月里，AI 有一种“相变”，产生了真正有意义的进展。","许多人感觉在过去六个月里，AI 有一种“相变”，产生了真正有意义的进展。","在五月，OpenAI 让数学家们震惊：https://go.skimresources.com/?id=1025X1701640&xs=1&url=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2527564-mathematicians-stunned-by-ais-biggest-breakthrough-in-mathematics-yet%2F，当时它宣布：https://openai.com/index/model-disproves-discrete-geometry-conjecture/ 一个未具名的内部模型破解了 Paul Erdős 提出的一条数学猜想：https://www.quantamagazine.org/why-the-legendary-erdos-problems-are-falling-to-ai-20260803/，这一猜想已经困扰数学家们近一个世纪。七月，哈佛数学家 Levent Alpöge 在推特上发文：https://x.com/__alpoge__/status/2079028340955197566?s=46 称 Anthropic 的 Claude Fable 5 通过一个微小的反例推翻了棘手的雅可比猜想：https://go.skimresources.com/?id=1025X1701640&xs=1&url=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2580374-ais-solution-to-87-year-old-riddle-takes-mathematicians-by-surprise%2F，从而推翻了几十年来数学家们试图证明其为真的努力。它们是数学家们真正关心的问题被 AI 克服的最新例子之一。","梅纳德回忆说，直到最近情况并非总是如此。他说，除了个别显著例外，AI 在数学领域的突破往往引起了大量关注，而这些问题通常并未受到研究者的认真关注。变化的速度让许多研究者措手不及，使该领域不得不努力寻找应对之策，同时有人怀疑它是否能够以当前的形式继续存续。","许多 The Verge 采访到的数学家似乎仍在思考他们对此事的真实看法，同时对变化的速度表示惊讶，甚至震惊。整体上充满兴奋，但他表示，从在韩国的会议以及更广泛的领域来看，许多学者正在淡化近期进展的重要性，以“保持冷静”应对事态发展的速度。","金钱是许多这些问题的核心。“我们不太清楚我们的大学是否愿意为我们的定理支付那么多钱，”苏格兰圣安德鲁斯大学教授科尔瓦·罗尼-杜格尔说。“数学通常是一门成本低廉的学科，”她说着，指向一块写满她研究成果的白板。“大多数时候，我甚至不去申请科研经费。我不需要。我只管做我的工作。”","即使按人工智能标准成本相对适中，这一体系也可能崩溃。OpenAI估计，以其Sol模型的当前API价格，生成Astra的10个解决方案大约需要2000美元的代币成本。《The Verge》采访的研究人员表示，实际成本可能高得多，这取决于在成功解决问题之前尝试了多少问题和方法。被问及最终名单是如何生成的时，OpenAI没有详细说明。但对于一个习惯于拮据预算运作的领域，即使是公布的价格也可能过高。罗尼-杜格尔担心较小、资金较少的机构的研究人员可能完全无法参与某些研究。","对于商业利益在这一长期开放运作的领域中日益渗入，也存在更广泛的不安。即使数学变得更具计算性，许多研究人员依赖的工具仍是开源且可以自由使用的。来自OpenAI和Anthropic等公司的最强大模型是专有的，其访问权限受到公司严格控制。虽然两家公司都有项目：https://openai.com/index/chatgpt-for-academic-researchers/ 提供免费：https://www.anthropic.com/news/ai-for-science-program 访问学术研究人员，但这一访问远非普遍，《The Verge》采访的研究人员中很少人能够使用最复杂的系统。梅纳德和罗尼-杜格尔都表达了希望，开源权重模型：/ai-artificial-intelligence/971444/how-chinese-open-weight-ai-models-impact-us-companies 最终能够弥合这一差距，使数学家能够使用这些工具，而不必依赖少数大型人工智能公司。","访问并不是唯一的担忧。《The Verge》采访的几位研究人员质疑人工智能公司的价值观是否与数学界的价值观一致。他们表示，公司有产品要销售，并且为了即将到来的首次公开募股（IPO）高估市值，公司有充分的动机去炒作和夸大自己的贡献，同时低估这些成果所依赖的人类学术研究。","“这是我目前最不满意的部分，”Roney-Dougal说。“他们把我们的学科当作广告游乐场。”","“他们把我们的学科当作广告游乐场。”","这些担忧不仅限于《The Verge》采访到的研究人员。今年六月，数学家们发布了莱顿宣言：https://leidendeclaration.ai/，这是一套关于在数学中负责任使用人工智能的原则，得到了国际数学联盟的支持，并有超过3400人签署。宣言敦促政策制定者、政府、媒体及其他团体不要轻信“公司夸大其产品能力”制造的“炒作”。人们担心，夸大的声明会对该领域造成实际影响，说服资助者和政府认为人类数学家的必要性低于实际情况。","OpenAI就其10项Astra进展被指控正是如此，尤其是通过掩盖Kun和Thom的贡献。Kun表示他的“感受相当矛盾”。看到他的工作在解决重大问题上发挥作用令人欣慰，即便他希望自己是完成它的人，这也让他获得了原本可能不会得到的关注和大量的祝贺。他对祝贺者开玩笑说：他将会成为“非常有名的失业者”。","Fournier-Facio的态度明显不那么矛盾。“大多数人只会看OpenAI的公告并按字面理解，”他说。他认为，很少有人会有时间、专业知识或兴趣去翻阅几百页的技术论文，以理解标题背后的人类工作，尤其是工作节奏快的记者或政策制定者。“他们只是选择最有利于自己的叙事，”他说。“说一个AI系统独立提出了人类十年来没有做过的东西，会更令人印象深刻。相比之下，说这是基于过去十年人类的想法并以巧妙方式组合起来的，就没那么吸引人了。”","“说一个AI系统独立提出了人类十年来没有做过的东西，会更令人印象深刻。相比之下，说这是基于过去十年人类的想法并以巧妙方式组合起来的，就没那么吸引人了。”","Fournier-Facio承认，在数学领域，信任授予的方式已经存在一定的不公平性。“最后一步的人会得到大部分的荣誉，对吧？” 他把数学研究比作建造金字塔，最后放置最后一块石头的人之下，是几代人的工作积累。他说，如果解决这个问题的是人类，可能就不会如此强调确保Kun和Thom获得认可。但随着AI迈出最后一步，他担心其他人会被错误地“看作无用”。","更糟的是：“在人的情况下，放置最后一块石头的人不一定会抢走建造整个金字塔人的功劳。”","当数学家考虑AI将如何影响下一代研究人员时，这种担忧尤为突出。牛津大学教授Andras Juhasz说，LLMs开始解决的许多问题正是研究生“通常会研究”的问题。它们并不总是特别引人注目，但解决它们对于培养成为成功研究者所需的技能、直觉和习惯至关重要。苏黎世联邦理工学院研究员Johannes Schmitt表示，他们现在面临被某些人用AI迅速解决问题而抢先的风险。","随着人工智能系统在完成项目工作方面能力的提升，其影响已经开始显现。朱哈斯（Juhasz）说，项目工作“已经成为本科生评估中的一个问题形式”。这些工具可能帮助学生更快地得到答案，但也有可能损害通过努力学会的整体数学理解。与此同时，梅纳德（Maynard）已经开始担心如何为学生的研究项目做好未来的规划。“如果可发表论文的标准是人工智能无法完成的任务，尤其是博士通常需要四年时间，那么你现在并不是在想一个人工智能现在做不到的问题，而是四年后人工智能能不能做到的问题。”","“我交谈过的许多人真的，非常害怕。”","这种不确定性已经在逐渐演变为沮丧，特别是在职业早期的数学家中。“我交谈过的许多人真的，非常害怕，”福尼耶-法西奥（Fournier-Facio）说。他向《The Verge》指出了两篇研究生在网上流传的绝望文章，质疑自己在该领域的未来：https://kirwinhampshire.substack.com/p/the-dark-night-of-mathematics?utm_campaign=post&utm_medium=web&triedRedirect=true 和 https://tasmin.substack.com/p/mathematicians-need-to-act?utm_id=97757_v0_s00_e0_tv2_a1demoo3x4dwia&fbclid=IwY2xjawTetIhleHRuA2FlbQIxMABzcnRjBmFwcF9pZBAyMjIwMzkxNzg4MjAwODkyAAEe7HYDDRhtkI8fMAAWEpFcu0vE8CKkzJyR2M0ok3TEUvs2I9EU-d5vMjMEZdY_aem_HZDqwE7hyLd5XXJMtnlblA。罗尼-杜加尔（Roney-Dougal）说，她也看到类似的疑虑在社交媒体上传播，评论大致是“我现在不知道该做什么。我不知道继续下去是否还有意义。”罗尼-杜加尔本人则不那么悲观：“我并没有那么沮丧，”她说，“但很多人都是。”","“我并没有那么沮丧，”她说，“但很多人都是。”","问题不仅仅在于人工智能能解决多少问题。数学的进展并不是简单地把问题逐一勾选完成。一个解答的重要性往往在于它之后能引发什么。最好的成果可能会打开全新的问题、技术，甚至研究领域。人工智能是否能够做到这一点还有待观察。相反，现在就将人工智能解决的问题轻描淡写地认为只是“低悬的果实”也为时过早。全面理解这些成果的贡献以及它们最终的重要性，需要时间。","到目前为止，施密特并不信服。他表示，他几乎没有看到人工智能在开辟新的思考和探索领域方面做出重大贡献的证据，这提出了一个令人不安的前景，即这一事业可能越来越偏向一方。“我们或许正面临一种有些不平衡的局面：大量优秀而有趣的问题被人工智能消解，”他说，而这些解决方案并未反过来推动研究者创造有成效的新方向。","“我们或许正面临一种有些不平衡的局面：大量优秀而有趣的问题被人工智能消解。”","并非所有人都对此感到不安。伦敦学院的赫对未来的发展持非常乐观的态度。他表示，从事传统学术数学的人数出现某种收缩，甚至可以被视为一种“健康的方向”，并指出数学专业毕业生的就业市场早已非常严酷。其他人则看到了人工智能扩大研究参与范围的潜力，这允许本科生和无法获得精英机构集中专业知识的研究者发展自己的想法，并可能产生以往无法涉及的可发表成果。对于资深研究者来说，将更多常规工作交给人工智能处理，则可以腾出时间专注于数学中更具创造性和概念性的部分。","尽管存在种种担忧与希望，没有人能预测其走向。人工智能发展太快，而其产生的数学成果仍然过于新鲜，尚无法判断其影响。一些研究者担心，由于有关人工智能潜力的夸大宣传，该领域可能在大家尚未理解其实际意义之前，被重塑为更糟糕的方向。","当被问及他是否认为阿斯特拉的某些成果值得获得数学界最高荣誉之一的菲尔兹奖，而他本人四年前也获得过这一奖项：https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/IMU_Fields22_Maynard_citation.pdf 时，梅纳德表示，他最初的印象是这些成果还不够资格。","“我看过的那些成果，给人的感觉是非常令人印象深刻，”他说，但不一定是能够在概念层面提升数学的成果。他目前看到的更多是现有技术和方法被进一步推进，并以巧妙的方式连接起来，而不是一些深刻的新数学思想。","“但我认为现在下结论也为时过早，”他说。“有时候需要时间和视角才能意识到，‘哦，这里确实有一个根本性的全新想法。’”","以目前的发展速度，人工智能可能不会给数学家留下太多时间去弄清楚这个问题。"],"translationStatus":"translated","bodyOrigin":"source-page","editorial":{"summary":"OpenAI称，未发布的Astra模型解决或推进了10道长期数学难题，并公布超过250页论文及Lean验证结果。相关成果覆盖球体堆积、纠错码、非sofic群等领域，引发数学界对突破速度与贡献归属的讨论。","background":"材料显示，Astra处理的问题横跨高度抽象的数学领域及具有潜在应用价值的方向，包括数据编码、噪声信号恢复、量子博弈和后量子网络安全。非sofic群结果还涉及OpenAI与相关人类研究者之间的贡献争议。","viewpoint":"Aioga判断，这一事件的核心不只是模型能否提出新结果，也在于数学界如何核验证明、界定研究基础与分配贡献。OpenAI后来调整成果表述但未提供更改说明，值得关注其披露透明度。","implications":"如果论文和Lean验证能够经受独立审查，AI可能加快部分数学问题的探索，并改变研究者组织文献、组合方法和验证结果的方式。但材料尚不足以证明这些成果会立即转化为实际技术或全面替代数学家。","nextStep":"值得关注后续数学家对论文、证明细节和Lean形式化结果的独立复核，也应核对每项成果所依赖的既有研究及贡献说明。只有在这些信息更充分后，才能判断Astra的原创性与实际影响。","evidenceRefs":["title","summary","articleBody","source"],"status":"published","aiGenerated":true,"autoApproved":true,"generatedBy":"aioga-editorial:gpt-5.6-sol","reviewedBy":"aioga-editorial-review:gpt-5.6-sol","generatedAt":"2026-08-11T19:30:09.382Z","sourceHash":"eef3e87f9009a895","review":{"approved":true,"groundedness":96,"clarity":94,"duplicationRisk":8,"blockingIssues":[],"notes":["“Aioga判断”属于候选内容自身的观点标注，不是来源事实；建议确认该署名是否符合编辑规范。","“后量子网络安全”可进一步明确为相关数学结果对后量子密码技术的潜在关联，以避免被理解为已产生实际安全应用。"]},"validation":{"passed":true,"mode":"ai-auto","revisions":0,"checks":["schema","length","source-attribution","low-source-overlap","no-html","independent-ai-review"]}},"tags":["行业动态","The Verge：AI（RSS）"],"translations":{"zh-CN":{"title":"OpenAI 用 Astra 模型攻克 10 道数学难题，数学家既兴奋又担忧","summary":"OpenAI 宣布其未发布的 Astra 模型解决了 10 道长期悬而未决的数学难题，涵盖球体堆积、纠错码、非 sofic 群存在性等领域，并发布超 250 页论文及 Lean 验证结果。 🔗 阅读原文 via AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI 用 Astra 模型攻克 10 道数学难题，数学家既兴奋又担忧 - Aioga AI资讯","description":"OpenAI 宣布其未发布的 Astra 模型解决了 10 道长期悬而未决的数学难题，涵盖球体堆积、纠错码、非 sofic 群存在性等领域，并发布超 250 页论文及 Lean 验证结果。 🔗 阅读原文 via AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","url":"https://www.aioga.com/news/cmsokd2b00viorofwaq9wrsv1/","articleBody":["数学家詹姆斯·梅纳德在过去一年里花了大量时间进行“灵魂探索”。梅纳德是牛津大学的教授，也是享有盛誉的菲尔兹奖获得者，他告诉The Verge，他一直在思考自己的领域的未来，因为这个传统上动作缓慢的学科正急速适应人工智能。","在我们交谈的前几天，OpenAI透露：https://openai.com/index/ten-advances-in-mathematics/ 它已经解决了10个长期未解的数学问题，其中一些问题困扰学术界数十年。就像用于生成文本和图像或提出科学与医学创意的生成式人工智能一样：/2024/5/8/24152088/google-deepmind-ai-model-predict-molecular-structure-alphafold 和 /ai-artificial-intelligence/961311/anthropic-claude-science-ai-drug-development，这项技术从其训练的大量材料中学习模式和联系，并利用这些知识创造出新的东西。应用于数学，这可能意味着以新的方式组合已知的结果、方法和工具来解决问题，有时会在不同领域之间建立联系，或者重新发现曾被学术文献掩埋的概念。","对于梅纳德和The Verge采访的其他数学家来说，这一公告让他们对自己领域的未来产生了复杂的情绪漩涡。加快数学发现的前景令人兴奋——但同时也让人感到担忧，有些情况下甚至感到绝望，因为这可能会影响那些献身于数学研究的人，以及将来跟随他们的下一代数学家。几乎没有人怀疑，一场深刻的变革已经在进行中。","几乎没有人怀疑，一场深刻的变革已经在进行中。","OpenAI 使用一种名为 Astra 的先进未发布模型解决的问题，涵盖了广泛的数学领域，从高度抽象的问题到具有实际意义的问题。其中一个突破涉及在三维以上空间中球体的最紧密堆积问题，这与数据编码和传输的效率相关。另一个突破推动了纠错码的极限，这类代码可以帮助从噪声信号中恢复信息。第三个突破解决了两个长期存在的问题，即复杂连接网络在出现结构模式之前能达到的复杂程度。名单上的其他结果涉及量子博弈理论的问题以及在高维网格中搜索目标的问题，这对后量子网络安全技术有重要意义：https://www.nature.com/articles/d41586-026-01054-1。","最引人注目的结果之一涉及非 Sofic 群的存在问题，这是一种无限的数学结构，大致来说无法被有限结构近似。这样的结构是否存在，几十年来一直是一个未解之问。它之所以引人注目，还有另一个原因：关于应归功于 OpenAI 的人工智能多少，以及应归功于人类数学家多少的争议，这些数学家最近的工作为成果提供了基础。","剑桥大学的数学家 Francesco Fournier-Facio 告诉 The Verge，他和该领域的其他研究人员认为，OpenAI 最初的公告低估了研究人员 Andreas Thom 和 Gábor Kun 的贡献，他们最近的工作为该成果奠定了基础。","当 OpenAI 首次发布公告时：https://web.archive.org/web/20260802205906/https://openai.com/index/ten-advances-in-mathematics/，它表示正分享“对一些长期未解且在主要结果上至少十年没有进展的问题的解决结果，在大多数情况下时间更长。”之后，它将公告更改为：https://openai.com/index/ten-advances-in-mathematics/ 表示正在分享“结果，每一项都解决或在长期未解问题上取得实质性进展。”该页面没有包含更正说明或对更改的解释。","匈牙利阿尔弗雷德·雷尼数学研究所的研究员Kun告诉The Verge，OpenAI在发表前不久通过电子邮件联系了他，分享其研究成果。他觉得原公告中的夸张语言“相当滑稽”，尤其是因为附上的更详细的研究论文“明确说明它建立在我2016年和2019年的成果之上”，后者是与Thom合著的。“这相当马虎，”Kun说道。","发表后，OpenAI再次联系Kun。他拒绝全文分享邮件交流，但向The Verge读出了他所说的一段摘录，其中一名OpenAI数学家写道，这些措辞原本是指引用集合中的其他成果。“并非意在暗示在这个问题上没有进展，”邮件中写道，他说。“我们当然同意，这一论证关键依赖于你的工作。”该数学家补充说，他们会要求修改公告的措辞。","OpenAI发言人Laurance Fauconnet向The Verge证实，该帖随后已更新。“我们更新了措辞，以更好地反映这些成果所建立的先前研究。尽管非sofic群是否存在的问题几十年来一直没有解决，我们的sofic群证明依赖于最近发表的重要数学工作，我们希望确保这些贡献得到适当承认。”","Kun表示，他怀疑其他成果中是否也存在类似疏漏，而那些成果超出了他的专业领域。","更广泛地评估 OpenAI 的成果是复杂的。数学已经变得如此专业化，以至于很少有研究人员能够全面审查 Astra 涉及的所有领域。该公司发布了超过 250 页的论文：https://cdn.openai.com/pdf/ten-proofs-oai.pdf，阐述了解决方案，同时还有 60 页更多内容描述：https://cdn.openai.com/pdf/reasoning-walkthroughs.pdf “这些想法是如何结合在一起的”，并使用 Lean 软件：https://www.quantamagazine.org/lean-computer-program-confirms-peter-scholze-proof-20210728/ 对每个结果进行了认证，该软件用于验证数学证明。虽然《The Verge》采访的许多数学家表示，他们个人无法评估其中一些甚至任何解决方案，但所有人都表示，普遍共识认为 OpenAI 的成就似乎具有实际分量。","OpenAI 宣称由其内部版本的“下一代重大模型” Astra 解决的问题并非简单。Maynard 表示，这些问题是数学家和计算机科学家们曾认真思考过，并多次未能解决的那类问题。","“普遍的感觉是，解决这 10 个问题中的一个就能让你在学术界找到工作，”伦敦数学科学研究所的研究员杨惠赫说。他刚刚从韩国参加了为期四周的 AI 与数学研究会议：https://symposia.kias.re.kr/AI-Math2026，他表示许多人感觉在过去六个月里，AI 有一种“相变”，产生了真正有意义的进展。","许多人感觉在过去六个月里，AI 有一种“相变”，产生了真正有意义的进展。","在五月，OpenAI 让数学家们震惊：https://go.skimresources.com/?id=1025X1701640&xs=1&url=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2527564-mathematicians-stunned-by-ais-biggest-breakthrough-in-mathematics-yet%2F，当时它宣布：https://openai.com/index/model-disproves-discrete-geometry-conjecture/ 一个未具名的内部模型破解了 Paul Erdős 提出的一条数学猜想：https://www.quantamagazine.org/why-the-legendary-erdos-problems-are-falling-to-ai-20260803/，这一猜想已经困扰数学家们近一个世纪。七月，哈佛数学家 Levent Alpöge 在推特上发文：https://x.com/__alpoge__/status/2079028340955197566?s=46 称 Anthropic 的 Claude Fable 5 通过一个微小的反例推翻了棘手的雅可比猜想：https://go.skimresources.com/?id=1025X1701640&xs=1&url=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2580374-ais-solution-to-87-year-old-riddle-takes-mathematicians-by-surprise%2F，从而推翻了几十年来数学家们试图证明其为真的努力。它们是数学家们真正关心的问题被 AI 克服的最新例子之一。","梅纳德回忆说，直到最近情况并非总是如此。他说，除了个别显著例外，AI 在数学领域的突破往往引起了大量关注，而这些问题通常并未受到研究者的认真关注。变化的速度让许多研究者措手不及，使该领域不得不努力寻找应对之策，同时有人怀疑它是否能够以当前的形式继续存续。","许多 The Verge 采访到的数学家似乎仍在思考他们对此事的真实看法，同时对变化的速度表示惊讶，甚至震惊。整体上充满兴奋，但他表示，从在韩国的会议以及更广泛的领域来看，许多学者正在淡化近期进展的重要性，以“保持冷静”应对事态发展的速度。","金钱是许多这些问题的核心。“我们不太清楚我们的大学是否愿意为我们的定理支付那么多钱，”苏格兰圣安德鲁斯大学教授科尔瓦·罗尼-杜格尔说。“数学通常是一门成本低廉的学科，”她说着，指向一块写满她研究成果的白板。“大多数时候，我甚至不去申请科研经费。我不需要。我只管做我的工作。”","即使按人工智能标准成本相对适中，这一体系也可能崩溃。OpenAI估计，以其Sol模型的当前API价格，生成Astra的10个解决方案大约需要2000美元的代币成本。《The Verge》采访的研究人员表示，实际成本可能高得多，这取决于在成功解决问题之前尝试了多少问题和方法。被问及最终名单是如何生成的时，OpenAI没有详细说明。但对于一个习惯于拮据预算运作的领域，即使是公布的价格也可能过高。罗尼-杜格尔担心较小、资金较少的机构的研究人员可能完全无法参与某些研究。","对于商业利益在这一长期开放运作的领域中日益渗入，也存在更广泛的不安。即使数学变得更具计算性，许多研究人员依赖的工具仍是开源且可以自由使用的。来自OpenAI和Anthropic等公司的最强大模型是专有的，其访问权限受到公司严格控制。虽然两家公司都有项目：https://openai.com/index/chatgpt-for-academic-researchers/ 提供免费：https://www.anthropic.com/news/ai-for-science-program 访问学术研究人员，但这一访问远非普遍，《The Verge》采访的研究人员中很少人能够使用最复杂的系统。梅纳德和罗尼-杜格尔都表达了希望，开源权重模型：/ai-artificial-intelligence/971444/how-chinese-open-weight-ai-models-impact-us-companies 最终能够弥合这一差距，使数学家能够使用这些工具，而不必依赖少数大型人工智能公司。","访问并不是唯一的担忧。《The Verge》采访的几位研究人员质疑人工智能公司的价值观是否与数学界的价值观一致。他们表示，公司有产品要销售，并且为了即将到来的首次公开募股（IPO）高估市值，公司有充分的动机去炒作和夸大自己的贡献，同时低估这些成果所依赖的人类学术研究。","“这是我目前最不满意的部分，”Roney-Dougal说。“他们把我们的学科当作广告游乐场。”","“他们把我们的学科当作广告游乐场。”","这些担忧不仅限于《The Verge》采访到的研究人员。今年六月，数学家们发布了莱顿宣言：https://leidendeclaration.ai/，这是一套关于在数学中负责任使用人工智能的原则，得到了国际数学联盟的支持，并有超过3400人签署。宣言敦促政策制定者、政府、媒体及其他团体不要轻信“公司夸大其产品能力”制造的“炒作”。人们担心，夸大的声明会对该领域造成实际影响，说服资助者和政府认为人类数学家的必要性低于实际情况。","OpenAI就其10项Astra进展被指控正是如此，尤其是通过掩盖Kun和Thom的贡献。Kun表示他的“感受相当矛盾”。看到他的工作在解决重大问题上发挥作用令人欣慰，即便他希望自己是完成它的人，这也让他获得了原本可能不会得到的关注和大量的祝贺。他对祝贺者开玩笑说：他将会成为“非常有名的失业者”。","Fournier-Facio的态度明显不那么矛盾。“大多数人只会看OpenAI的公告并按字面理解，”他说。他认为，很少有人会有时间、专业知识或兴趣去翻阅几百页的技术论文，以理解标题背后的人类工作，尤其是工作节奏快的记者或政策制定者。“他们只是选择最有利于自己的叙事，”他说。“说一个AI系统独立提出了人类十年来没有做过的东西，会更令人印象深刻。相比之下，说这是基于过去十年人类的想法并以巧妙方式组合起来的，就没那么吸引人了。”","“说一个AI系统独立提出了人类十年来没有做过的东西，会更令人印象深刻。相比之下，说这是基于过去十年人类的想法并以巧妙方式组合起来的，就没那么吸引人了。”","Fournier-Facio承认，在数学领域，信任授予的方式已经存在一定的不公平性。“最后一步的人会得到大部分的荣誉，对吧？” 他把数学研究比作建造金字塔，最后放置最后一块石头的人之下，是几代人的工作积累。他说，如果解决这个问题的是人类，可能就不会如此强调确保Kun和Thom获得认可。但随着AI迈出最后一步，他担心其他人会被错误地“看作无用”。","更糟的是：“在人的情况下，放置最后一块石头的人不一定会抢走建造整个金字塔人的功劳。”","当数学家考虑AI将如何影响下一代研究人员时，这种担忧尤为突出。牛津大学教授Andras Juhasz说，LLMs开始解决的许多问题正是研究生“通常会研究”的问题。它们并不总是特别引人注目，但解决它们对于培养成为成功研究者所需的技能、直觉和习惯至关重要。苏黎世联邦理工学院研究员Johannes Schmitt表示，他们现在面临被某些人用AI迅速解决问题而抢先的风险。","随着人工智能系统在完成项目工作方面能力的提升，其影响已经开始显现。朱哈斯（Juhasz）说，项目工作“已经成为本科生评估中的一个问题形式”。这些工具可能帮助学生更快地得到答案，但也有可能损害通过努力学会的整体数学理解。与此同时，梅纳德（Maynard）已经开始担心如何为学生的研究项目做好未来的规划。“如果可发表论文的标准是人工智能无法完成的任务，尤其是博士通常需要四年时间，那么你现在并不是在想一个人工智能现在做不到的问题，而是四年后人工智能能不能做到的问题。”","“我交谈过的许多人真的，非常害怕。”","这种不确定性已经在逐渐演变为沮丧，特别是在职业早期的数学家中。“我交谈过的许多人真的，非常害怕，”福尼耶-法西奥（Fournier-Facio）说。他向《The Verge》指出了两篇研究生在网上流传的绝望文章，质疑自己在该领域的未来：https://kirwinhampshire.substack.com/p/the-dark-night-of-mathematics?utm_campaign=post&utm_medium=web&triedRedirect=true 和 https://tasmin.substack.com/p/mathematicians-need-to-act?utm_id=97757_v0_s00_e0_tv2_a1demoo3x4dwia&fbclid=IwY2xjawTetIhleHRuA2FlbQIxMABzcnRjBmFwcF9pZBAyMjIwMzkxNzg4MjAwODkyAAEe7HYDDRhtkI8fMAAWEpFcu0vE8CKkzJyR2M0ok3TEUvs2I9EU-d5vMjMEZdY_aem_HZDqwE7hyLd5XXJMtnlblA。罗尼-杜加尔（Roney-Dougal）说，她也看到类似的疑虑在社交媒体上传播，评论大致是“我现在不知道该做什么。我不知道继续下去是否还有意义。”罗尼-杜加尔本人则不那么悲观：“我并没有那么沮丧，”她说，“但很多人都是。”","“我并没有那么沮丧，”她说，“但很多人都是。”","问题不仅仅在于人工智能能解决多少问题。数学的进展并不是简单地把问题逐一勾选完成。一个解答的重要性往往在于它之后能引发什么。最好的成果可能会打开全新的问题、技术，甚至研究领域。人工智能是否能够做到这一点还有待观察。相反，现在就将人工智能解决的问题轻描淡写地认为只是“低悬的果实”也为时过早。全面理解这些成果的贡献以及它们最终的重要性，需要时间。","到目前为止，施密特并不信服。他表示，他几乎没有看到人工智能在开辟新的思考和探索领域方面做出重大贡献的证据，这提出了一个令人不安的前景，即这一事业可能越来越偏向一方。“我们或许正面临一种有些不平衡的局面：大量优秀而有趣的问题被人工智能消解，”他说，而这些解决方案并未反过来推动研究者创造有成效的新方向。","“我们或许正面临一种有些不平衡的局面：大量优秀而有趣的问题被人工智能消解。”","并非所有人都对此感到不安。伦敦学院的赫对未来的发展持非常乐观的态度。他表示，从事传统学术数学的人数出现某种收缩，甚至可以被视为一种“健康的方向”，并指出数学专业毕业生的就业市场早已非常严酷。其他人则看到了人工智能扩大研究参与范围的潜力，这允许本科生和无法获得精英机构集中专业知识的研究者发展自己的想法，并可能产生以往无法涉及的可发表成果。对于资深研究者来说，将更多常规工作交给人工智能处理，则可以腾出时间专注于数学中更具创造性和概念性的部分。","尽管存在种种担忧与希望，没有人能预测其走向。人工智能发展太快，而其产生的数学成果仍然过于新鲜，尚无法判断其影响。一些研究者担心，由于有关人工智能潜力的夸大宣传，该领域可能在大家尚未理解其实际意义之前，被重塑为更糟糕的方向。","当被问及他是否认为阿斯特拉的某些成果值得获得数学界最高荣誉之一的菲尔兹奖，而他本人四年前也获得过这一奖项：https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/IMU_Fields22_Maynard_citation.pdf 时，梅纳德表示，他最初的印象是这些成果还不够资格。","“我看过的那些成果，给人的感觉是非常令人印象深刻，”他说，但不一定是能够在概念层面提升数学的成果。他目前看到的更多是现有技术和方法被进一步推进，并以巧妙的方式连接起来，而不是一些深刻的新数学思想。","“但我认为现在下结论也为时过早，”他说。“有时候需要时间和视角才能意识到，‘哦，这里确实有一个根本性的全新想法。’”","以目前的发展速度，人工智能可能不会给数学家留下太多时间去弄清楚这个问题。"]},"en":{"title":"OpenAI has solved 10 mathematical puzzles with the Astra model, leaving mathematicians both excited and worried","summary":"OpenAI announced that its unpublished Astra model solved 10 long-standing mathematical problems, covering sphere stacking, error correction codes, non-sofic group existence, and more, and published over 250 pages of papers and Lean validation results. 🔗 Read the original article via AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"Industry","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI has solved 10 mathematical puzzles with the Astra model, leaving mathematicians both excited and worried - Aioga AI News","description":"OpenAI announced that its unpublished Astra model solved 10 long-standing mathematical problems, covering sphere stacking, error correction codes, non-sofic group existence, and mo...","url":"https://www.aioga.com/en/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:06.861Z"},"ja":{"title":"OpenAIはAstraモデルで10の数学パズルを解き、数学者たちを興奮と不安の両方にさせています","summary":"OpenAIは、未発表のAstraモデルが球積み重ね、誤り訂正コード、非ソフィック群存在などを含む10の長年の数学的問題を解決し、250ページ以上の論文とリーン検証結果を発表したと発表しました。 🔗 原文記事はAIHOTより読むことができます。 https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"業界動向","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAIはAstraモデルで10の数学パズルを解き、数学者たちを興奮と不安の両方にさせています - Aioga AIニュース","description":"OpenAIは、未発表のAstraモデルが球積み重ね、誤り訂正コード、非ソフィック群存在などを含む10の長年の数学的問題を解決し、250ページ以上の論文とリーン検証結果を発表したと発表しました。 🔗 原文記事はAIHOTより読むことができます。 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https://aihot.virxact.com/items/cmsokd2...","url":"https://www.aioga.com/ko/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:15.808Z"},"es":{"title":"OpenAI ha resuelto 10 acertijos matemáticos con el modelo Astra, dejando a los matemáticos tanto emocionados como preocupados","summary":"OpenAI anunció que su modelo Astra no publicado resolvió 10 problemas matemáticos de larga data, que cubren el apilamiento de esferas, códigos de corrección de errores, existencia de grupos no sóficos y más, y publicó más de 250 páginas de artículos y resultados de validación Lean. 🔗 Lee el artículo original a través de AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"Industria","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI ha resuelto 10 acertijos matemáticos con el modelo Astra, dejando a los matemáticos tanto emocionados como preocupados - Aioga Noticias de IA","description":"OpenAI anunció que su modelo Astra no publicado resolvió 10 problemas matemáticos de larga data, que cubren el apilamiento de esferas, códigos de corrección de errores, existencia...","url":"https://www.aioga.com/es/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:15.851Z"},"fr":{"title":"OpenAI a résolu 10 casse-têtes mathématiques avec le modèle Astra, laissant les mathématiciens à la fois enthousiastes et inquiets","summary":"OpenAI a annoncé que son modèle Astra non publié a résolu 10 problèmes mathématiques de longue date, couvrant l’empilement de sphères, les codes de correction d’erreurs, l’existence de groupes non sofiques, et plus encore, et a publié plus de 250 pages d’articles et de résultats de validation Lean. 🔗 Lisez l’article original via AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"Industrie","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI a résolu 10 casse-têtes mathématiques avec le modèle Astra, laissant les mathématiciens à la fois enthousiastes et inquiets - Aioga Actualités IA","description":"OpenAI a annoncé que son modèle Astra non publié a résolu 10 problèmes mathématiques de longue date, couvrant l’empilement de sphères, les codes de correction d’erreurs, l’existenc...","url":"https://www.aioga.com/fr/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:24.546Z"},"de":{"title":"OpenAI hat mit dem Astra-Modell zehn mathematische Rätsel gelöst, was Mathematiker sowohl begeistert als auch beunruhigt zurücklässt","summary":"OpenAI gab bekannt, dass sein unveröffentlichtes Astra-Modell zehn langjährige mathematische Probleme gelöst hat, darunter Sphärenstapelung, Fehlerkorrekturcodes, nicht-sofische Gruppenexistenz und mehr, und über 250 Seiten mit Artikeln und Lean-Validierungsergebnissen veröffentlicht hat. 🔗 Lesen Sie den Originalartikel über AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI hat mit dem Astra-Modell zehn mathematische Rätsel gelöst, was Mathematiker sowohl begeistert als auch beunruhigt zurücklässt - Aioga KI-News","description":"OpenAI gab bekannt, dass sein unveröffentlichtes Astra-Modell zehn langjährige mathematische Probleme gelöst hat, darunter Sphärenstapelung, Fehlerkorrekturcodes, nicht-sofische Gr...","url":"https://www.aioga.com/de/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:23.763Z"},"pt-BR":{"title":"A OpenAI resolveu 10 quebra-cabeças matemáticos com o modelo Astra, deixando matemáticos tanto animados quanto preocupados","summary":"A OpenAI anunciou que seu modelo Astra não publicado resolveu 10 problemas matemáticos de longa data, abrangendo empilhamento de esferas, códigos de correção de erros, existência de grupos não sóficos e mais, e publicou mais de 250 páginas de artigos e resultados de validação Lean. 🔗 Leia o artigo original via AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"A OpenAI resolveu 10 quebra-cabeças matemáticos com o modelo Astra, deixando matemáticos tanto animados quanto preocupados - Aioga Notícias de IA","description":"A OpenAI anunciou que seu modelo Astra não publicado resolveu 10 problemas matemáticos de longa data, abrangendo empilhamento de esferas, códigos de correção de erros, existência d...","url":"https://www.aioga.com/pt-BR/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:33.214Z"},"ru":{"title":"OpenAI решил 10 математических головоломок с помощью модели Astra, оставив математиков одновременно в восторге и тревоге","summary":"OpenAI объявила, что её неопубликованная модель Astra решила 10 давних математических задач, охватывающих сферное стекирование, коды коррекции ошибок, существование не-sofic групп и многое другое, а также опубликовала более 250 страниц статей и результатов Lean-валидации. 🔗 Прочитайте оригинальную статью на сайте AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI решил 10 математических головоломок с помощью модели Astra, оставив математиков одновременно в восторге и тревоге - Aioga Новости ИИ","description":"OpenAI объявила, что её неопубликованная модель Astra решила 10 давних математических задач, охватывающих сферное стекирование, коды коррекции ошибок, существование не-sofic групп...","url":"https://www.aioga.com/ru/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:33.345Z"},"ar":{"title":"حلت OpenAI عشرة ألغاز رياضية باستخدام نموذج أسترا، مما ترك علماء الرياضيات متحمسين وقلقين في آن واحد.","summary":"أعلنت OpenAI أن نموذج Astra غير المنشور الخاص بها حل 10 مشاكل رياضية طويلة الأمد، تشمل تكديس الكرات، ورموز تصحيح الأخطاء، ووجود مجموعات غير SOFI، وأكثر من ذلك، ونشر أكثر من 250 صفحة من الأوراق ونتائج التحقق من صحة Lean. 🔗 اقرأ المقال الأصلي عبر AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"حلت OpenAI عشرة ألغاز رياضية باستخدام نموذج أسترا، مما ترك علماء الرياضيات متحمسين وقلقين في آن واحد. - Aioga أخبار الذكاء الاصطناعي","description":"أعلنت OpenAI أن نموذج Astra غير المنشور الخاص بها حل 10 مشاكل رياضية طويلة الأمد، تشمل تكديس الكرات، ورموز تصحيح الأخطاء، ووجود مجموعات غير SOFI، وأكثر من ذلك، ونشر أكثر من 250 صفح...","url":"https://www.aioga.com/ar/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:42.127Z"},"hi":{"title":"OpenAI ने एस्ट्रा मॉडल के साथ 10 गणितीय पहेलियों को हल किया है, जिससे गणितज्ञ उत्साहित और चिंतित दोनों हो गए हैं","summary":"OpenAI ने घोषणा की कि उसके अप्रकाशित एस्ट्रा मॉडल ने 10 लंबे समय से चली आ रही गणितीय समस्याओं को हल किया, जिसमें क्षेत्र स्टैकिंग, त्रुटि सुधार कोड, गैर-सोफिक समूह अस्तित्व, और बहुत कुछ शामिल है, और 250 से अधिक पृष्ठों के कागजात और लीन सत्यापन परिणाम प्रकाशित किए गए हैं। 🔗 AIHOT के माध्यम से मूल लेख पढ़ें · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI ने एस्ट्रा मॉडल के साथ 10 गणितीय पहेलियों को हल किया है, जिससे गणितज्ञ उत्साहित और चिंतित दोनों हो गए हैं - Aioga AI समाचार","description":"OpenAI ने घोषणा की कि उसके अप्रकाशित एस्ट्रा मॉडल ने 10 लंबे समय से चली आ रही गणितीय समस्याओं को हल किया, जिसमें क्षेत्र स्टैकिंग, त्रुटि सुधार कोड, गैर-सोफिक समूह अस्तित्व, और बहु...","url":"https://www.aioga.com/hi/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:42.256Z"},"it":{"title":"OpenAI ha risolto 10 enigmi matematici con il modello Astra, lasciando i matematici sia entusiasti che preoccupati","summary":"OpenAI ha annunciato che il suo modello Astra non pubblicato ha risolto 10 problemi matematici di lunga data, che coprono lo stacking delle sfere, i codici di correzione degli errori, l'esistenza di gruppi non sofici e altro ancora, e ha pubblicato oltre 250 pagine di articoli e risultati di validazione Lean. 🔗 Leggi l'articolo originale su AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI ha risolto 10 enigmi matematici con il modello Astra, lasciando i matematici sia entusiasti che preoccupati - Aioga Notizie IA","description":"OpenAI ha annunciato che il suo modello Astra non pubblicato ha risolto 10 problemi matematici di lunga data, che coprono lo stacking delle sfere, i codici di correzione degli erro...","url":"https://www.aioga.com/it/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:50.969Z"},"nl":{"title":"OpenAI heeft 10 wiskundige puzzels opgelost met het Astra-model, waardoor wiskundigen zowel enthousiast als bezorgd zijn","summary":"OpenAI kondigde aan dat het ongepubliceerde Astra-model 10 lang bestaande wiskundige problemen oploste, waaronder sphere stacking, foutcorrectiecodes, het bestaan van niet-sofische groepen en meer, en publiceerde meer dan 250 pagina's aan artikelen en Lean-validatieresultaten. 🔗 Lees het originele artikel via AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI heeft 10 wiskundige puzzels opgelost met het Astra-model, waardoor wiskundigen zowel enthousiast als bezorgd zijn - Aioga AI-nieuws","description":"OpenAI kondigde aan dat het ongepubliceerde Astra-model 10 lang bestaande wiskundige problemen oploste, waaronder sphere stacking, foutcorrectiecodes, het bestaan van niet-sofische...","url":"https://www.aioga.com/nl/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:50.352Z"},"tr":{"title":"OpenAI, Astra modeli ile 10 matematik problemini çözdü, matematikçiler hem heyecanlı hem de endişeli","summary":"OpenAI, yayımlanmamış Astra modelinin uzun süredir çözülemeyen 10 matematik problemini çözdüğünü, küre paketleme, hata düzeltme kodları, non-sofic grup varlığı gibi alanları kapsadığını ve 250 sayfadan fazla makale ile Lean doğrulama sonuçlarını yayınladığını duyurdu. 🔗 Orijinal metni okuyun via AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI, Astra modeli ile 10 matematik problemini çözdü, matematikçiler hem heyecanlı hem de endişeli - Aioga AI Haberleri","description":"OpenAI, yayımlanmamış Astra modelinin uzun süredir çözülemeyen 10 matematik problemini çözdüğünü, küre paketleme, hata düzeltme kodları, non-sofic grup varlığı gibi alanları kapsad...","url":"https://www.aioga.com/tr/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:32:26.759Z"},"vi":{"title":"OpenAI đã giải 10 câu đố toán học với mô hình Astra, khiến các nhà toán học vừa hào hứng vừa lo lắng","summary":"OpenAI thông báo rằng mô hình Astra chưa công bố của họ đã giải quyết 10 bài toán toán học tồn tại lâu dài, bao gồm xếp chồng hình cầu, mã sửa lỗi, tồn tại nhóm phi sofic, và nhiều vấn đề khác, đồng thời công bố hơn 250 trang bài báo và kết quả xác thực Lean. 🔗 Đọc bài viết gốc qua AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI đã giải 10 câu đố toán học với mô hình Astra, khiến các nhà toán học vừa hào hứng vừa lo lắng - Tin tức AI Aioga","description":"OpenAI thông báo rằng mô hình Astra chưa công bố của họ đã giải quyết 10 bài toán toán học tồn tại lâu dài, bao gồm xếp chồng hình cầu, mã sửa lỗi, tồn tại nhóm phi sofic, và nhiều...","url":"https://www.aioga.com/vi/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:31:59.018Z"},"id":{"title":"OpenAI telah memecahkan 10 teka-teki matematika dengan model Astra, membuat para matematikawan merasa antusias sekaligus khawatir","summary":"OpenAI mengumumkan bahwa model Astra yang belum dipublikasikan telah memecahkan 10 masalah matematika lama, mencakup penumpukan bola, kode koreksi kesalahan, keberadaan kelompok non-sofic, dan lainnya, serta menerbitkan lebih dari 250 halaman makalah dan hasil validasi Lean. 🔗 Baca artikel asli melalui AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI telah memecahkan 10 teka-teki matematika dengan model Astra, membuat para matematikawan merasa antusias sekaligus khawatir - Berita AI Aioga","description":"OpenAI mengumumkan bahwa model Astra yang belum dipublikasikan telah memecahkan 10 masalah matematika lama, mencakup penumpukan bola, kode koreksi kesalahan, keberadaan kelompok no...","url":"https://www.aioga.com/id/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:32:35.848Z"},"th":{"title":"OpenAI ได้แก้ปริศนาทางคณิตศาสตร์ 10 ข้อด้วยโมเดล Astra ทําให้นักคณิตศาสตร์ทั้งตื่นเต้นและกังวล","summary":"OpenAI ประกาศว่าโมเดล Astra ที่ยังไม่เผยแพร่ได้แก้ปัญหาทางคณิตศาสตร์ที่มีมานาน 10 ข้อ ครอบคลุมการซ้อนทรงกลม รหัสแก้ไขข้อผิดพลาด การมีอยู่ของกลุ่มแบบไม่โซฟิก และอื่น ๆ พร้อมทั้งเผยแพร่บทความและผลการตรวจสอบ Lean มากกว่า 250 หน้า 🔗 อ่านบทความต้นฉบับผ่าน AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI ได้แก้ปริศนาทางคณิตศาสตร์ 10 ข้อด้วยโมเดล Astra ทําให้นักคณิตศาสตร์ทั้งตื่นเต้นและกังวล - ข่าว AI Aioga","description":"OpenAI ประกาศว่าโมเดล Astra ที่ยังไม่เผยแพร่ได้แก้ปัญหาทางคณิตศาสตร์ที่มีมานาน 10 ข้อ ครอบคลุมการซ้อนทรงกลม รหัสแก้ไขข้อผิดพลาด การมีอยู่ของกลุ่มแบบไม่โซฟิก และอื่น ๆ พร้อมทั้งเผยแ...","url":"https://www.aioga.com/th/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:32:35.123Z"},"pl":{"title":"OpenAI rozwiązało 10 zagadek matematycznych za pomocą modelu Astra, co pozostawia matematyków zarówno podekscytowanych, jak i niespokojnych","summary":"OpenAI ogłosiło, że jego nieopublikowany model Astra rozwiązał 10 długo istniejących problemów matematycznych, obejmujących układanie sfer, kody korekcji błędów, istnienie grup nie-soficznych i inne, a także opublikował ponad 250 stron artykułów naukowych i wyników walidacji Lean. 🔗 Przeczytaj oryginalny artykuł za pośrednictwem AIHOT · https://aihot.virxact.com/items/cmsokd2b00viorofwaq9wrsv1","category":"行业动态","source":"The Verge：AI（RSS）","aggregationSource":"The Verge：AI（RSS）","pageTitle":"OpenAI rozwiązało 10 zagadek matematycznych za pomocą modelu Astra, co pozostawia matematyków zarówno podekscytowanych, jak i niespokojnych - Aioga Wiadomości AI","description":"OpenAI ogłosiło, że jego nieopublikowany model Astra rozwiązał 10 długo istniejących problemów matematycznych, obejmujących układanie sfer, kody korekcji błędów, istnienie grup nie...","url":"https://www.aioga.com/pl/news/cmsokd2b00viorofwaq9wrsv1/","contentTranslated":true,"sourceHash":"ec3e1991595f0bf5","translatedAt":"2026-08-11T11:32:44.626Z"}},"evidenceTier":"verified-news","reviewStatus":"editorial-selected","indexable":true,"editorialCover":""}}