{"slug": "ai-proof-of-the-erdos-sos-conjecture", "title": "AI proof of the Erdős–Sós conjecture", "summary": "An arXiv paper posted on 15 September 2026 presents an exposition of a proof of the Erdős–Sós Conjecture, which states that every graph with average degree greater than t-2 contains every tree on t≥2 vertices, attributing the proof's discovery to GPT-6 Astra. The paper, titled \"The Erdős–Sós Theorem\" (arXiv:2609.17877), appears in the math.HO (History and Overview) category.", "body_md": "# Mathematics > History and Overview\n\n  [Submitted on 15 Sep 2026]\n\n# Title:The Erdős--Sós Theorem\n\n[View PDF](https://arxiv.org/pdf/2609.17877)\n\n[HTML (experimental)](https://arxiv.org/html/2609.17877v1)\n\nAbstract:We present an exposition of a proof, discovered by GPT-6 Astra, of the Erdős--Sós Conjecture, which states that every graph with average degree greater than $t-2$ contains every tree on $t\\geq 2$ vertices.\n    \n\n### Current browse context:\n\nmath.HO\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer \n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers \n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps \n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations \n\n*(*[What are Smart Citations?](https://www.scite.ai/))\n# Code, Data and Media Associated with this Article\n\nalphaXiv \n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers \n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub \n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub \n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face \n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast \n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))\n# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower \n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender \n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\n# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.\n\nHave an idea for a project that will add value for arXiv's community? [**Learn more about arXivLabs**](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/ai-proof-of-the-erdos-sos-conjecture", "canonical_source": "https://arxiv.org/abs/2609.17877", "published_at": "2026-09-23 12:31:44+00:00", "updated_at": "2026-09-23 13:00:06.960822+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research", "large-language-models"], "entities": ["GPT-6 Astra", "arXiv", "Erdős–Sós Conjecture"], "alternates": {"html": "https://wpnews.pro/news/ai-proof-of-the-erdos-sos-conjecture", "markdown": "https://wpnews.pro/news/ai-proof-of-the-erdos-sos-conjecture.md", "text": "https://wpnews.pro/news/ai-proof-of-the-erdos-sos-conjecture.txt", "jsonld": "https://wpnews.pro/news/ai-proof-of-the-erdos-sos-conjecture.jsonld"}}