[OT] AI Claude solves open problem unsolved by Knuth

[Georgi Guninski]

The AI gonna own us all.

https://www.toolmesh.ai/news/claude-ai-solves-graph-theory-conjecture-knuth

---
Claude Opus 4.6, an AI model developed by Anthropic, has independently
solved a long-standing graph theory conjecture, prompting computer
scientist Donald Knuth to re-evaluate the role of generative AI in
mathematical research. Knuth, known for his multi-volume work "The Art
of Computer Programming," published a paper on Stanford's official
website detailing the AI's achievement.
---

[Michael Orlitzky]

On 2026-03-05 15:48:24, Georgi Guninski wrote:
> The AI gonna own us all.
>
> https://www.toolmesh.ai/news/claude-ai-solves-graph-theory-conjecture-knuth

How much is the monthly subscription to Donald Knuth?

> While Claude provided the construction method, Knuth subsequently
> provided the rigorous mathematical proof, demonstrating that the
> path visited all m^2 vertices with the same i value, then covered all
> i sequentially, forming a complete cycle of length m^3. Similar
> proofs applied to the other two cycles, thus solving the entire
> problem.
>
> Knuth further discovered that Claude's solution was not unique, with
> 760 similar decomposition methods existing, all sharing the same
> structure. Claude had found just one of these. It is important to
> note that Claude only solved the case where m is odd; a general
> solution for even m remains elusive, and the m=2 case has been
> proven impossible.

Having used the computer to discover things that are probably true is
probably true of everyone here.

[Jaap Spies]

Read what Knuth writes:

https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf

Op do 5 mrt 2026, 15:04 schreef Michael Orlitzky <mic...@orlitzky.com>:

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[Kwankyu Lee]

Thanks for sharing the article,. Reading it, I learned that AI Claude is named after Claude Shannon. 

[Georgi Guninski]

Claude agents built working C compiler in Rust [1], which is very
impressive, despite some critics that it is not "clean room"
experiment.

Just for fun, chatGPT and Gemini wrote jokes about themselves [2], I
am interested have they be helped/trained by humans about the jokes.

[1] https://arstechnica.com/ai/2026/02/sixteen-claude-ai-agents-working-together-created-a-new-c-compiler/
[2] https://www.linkedin.com/pulse/jokes-ai-georgi-guninski-c4jif

[Kwankyu Lee]

Wow, the jokes by Gemini are profound. As Knuth said, we have entered an interesting era.