{
  "video_id": "reddit_1vkxpob",
  "channel_slug": "singularity",
  "channel_handle": "r/singularity",
  "title": "Imbalance Conjecture proven and Teschner’s bondage-number conjecture disproven by AI",
  "url": "https://www.reddit.com/r/singularity/comments/1vkxpob/imbalance_conjecture_proven_and_teschners/",
  "external_url": null,
  "upload_date": "20260810",
  "published_at": "2026-08-10T21:19:11+00:00",
  "transcript": "Hi everyone, I'm a 4th year undergraduate student studying and doing research in theoretical CS. After seeing the recent advancements made by AI in mathematics, especially in graph theory, I bought a ChatGPT Pro subscription to see if AI could solve some graph theory problems I found interesting. After a few days of testing, GPT-5.6 Sol Max was able to solve two open problems in graph theory:  \n  \n[Imbalance conjecture](https://en.wikipedia.org/wiki/Imbalance_conjecture) (open for 12+ years) [Teschner's bondage-number conjecture](https://en.wikipedia.org/wiki/Bondage_number#:~:text=%5B3%5D-,Conjectures,edit,-Unsolved%20problem%20in) (open for 30+ years)  \n  \nI verified both results independently and asked a friend of mine who specializes in graph theory to check them as well. I submitted both to arXiv, but they removed one after placing a one-submission-per-calendar-month restriction on my new account. I didn't want to wait another month before making this announcement, so I submitted both to another platform. The results are linked below.  \n  \n[A Proof of the Imbalance Conjecture](https://doi.org/10.6084/m9.figshare.33198750)  \n[A Counterexample to Teschner's Bondage-Number Conjecture](https://doi.org/10.6084/m9.figshare.33198777)  \n  \nThese are preprints and have not yet undergone peer review.\n\nAlso, here are the full chats:   \n[Imbalance Conjecture](https://chatgpt.com/share/6a6e5b95-1418-83ea-8228-e62ca34e24e4)  \n[Teschner's Bondage-Number Conjecture](https://chatgpt.com/share/6a7a08fe-9fd8-83e8-b3b4-392282dc501a)\n\n\n\n--- Top Comments ---\n\n\n[152 upvotes] https://preview.redd.it/sm5mqp5fcmih1.png?width=959&format=png&auto=webp&s=2388be9c9fea89b35c6e0f6b96349db189255701\n\n[60 upvotes] Math boutta be who can cheerlead the hardest 😭good job nonetheless \n\n[44 upvotes] Congrats! You have picked the right area for unleashing llms on. A lot of Graph Theory/Combinatorics is up for grabs is my general feeling. Exciting to see a positive proof. \n\n[36 upvotes] Im no mathematician but this might be for r/math?",
  "transcript_chars": 2034,
  "ingested_at": "2026-08-11T13:30:22.674676+00:00",
  "source": "reddit",
  "yt_meta": {
    "score": 305,
    "upvote_ratio": 0.95,
    "num_comments": 44,
    "author": "No-Performer-2242",
    "is_self": true
  }
}