GPT 5.6 Pro Disproves 30-Year Dinitz-Garg-Goemans Conjecture
A mathematician says a GPT-5.6 Pro session found a counterexample to a long-open unsplittable-flow conjecture, and the proof is being passed around as a public chat log.
Entities: Dmitry Rybin, GPT 5.6 Pro
On X, Dmitry Rybin wrote that the Dinitz-Garg-Goemans conjecture is false, describing it as a graph theory problem that had been open for about 30 years and linking to a public ChatGPT share log where he says GPT-5.6 Pro helped find a counterexample. In Rybin's summary, the graph has fractional flow cost 58, while any unsplittable flow with capacity violation of 15 or less has cost at least 60. As context, a 2023 arXiv paper on single-source unsplittable flows describes the cost version of the conjecture as still open.
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GPT 5.6 Pro Disproves 30-Year Dinitz-Garg-Goemans Conjecture
A mathematician says a GPT-5.6 Pro session found a counterexample to a long-open unsplittable-flow conjecture, and the proof is being passed around as a public chat log.
Entities: Dmitry Rybin, GPT 5.6 Pro
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31 posts
So ppl are gonna really just continue this trend of resolving decade old conjecture within a tweet and chatgpt link?
Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years. The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60. Chat with GPT 5.6 Pro where this was found: https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063
Another one bites the dust. AI is like a hot knife cutting through mathematical butter. No conjecture is safe anymore.
Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years. The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60. Chat with GPT 5.6 Pro where this was found: https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063
Another conjecture falls — 4 prompts with a public model. The pattern (for now) seems to be search for counter-examples to disprove conjectures, rather than constructive proofs. Maybe because the former lend themselves to grinding and persistence more?
Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years. The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60. Chat with GPT 5.6 Pro where this was found: https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063
I hope so!
So ppl are gonna really just continue this trend of resolving decade old conjecture within a tweet and chatgpt link? https://twitter.com/DmitryRybin1/status/2079904005652893709
Who would you give authorship to? The person who wrote 58 words of prompts, or GPT-5.6 Pro?
Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years. The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60. Chat with GPT 5.6 Pro where this was found: https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063
Fortune favors the brave and patient
Its quite likely that main thing that was sitting between us and those counterexamples has been more patience https://twitter.com/dmitryrybin1/status/2079904005652893709