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Terrence Tao: On Jan 4, ChatGPT was able to produce a proof Erdos #728 (Re: AI solves probl;em Knuth was/is working on!)

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Recently, the application of AI tools to
Erdos problems passed a milestone: an Erdos
problem (#728 https://www.erdosproblems.com/728)
was solved more or less autonomously by AI (after
some feedback from an initial attempt), in the
spirit of the problem (as reconstructed by the
Erdos problem website community), with the result
(to the best of our knowledge) not replicated in
existing literature (although similar results proven
by similar methods were located).

This is a demonstration of the genuine increase in
capability of these tools in recent months, and is
largely consistent with other recent demonstrations
of AI using existing methods to resolve Erdos problems,
although in most previous cases a solution to these
problems was later located in the literature, as
discussed in https://mathstodon.xyz/deck/@tao/115788262274999408 .
This particular case was unusual in that the problem
as stated by Erdos was misformulated, with a
  reconstruction of the problem in the intended spirit
only obtained in the last few months, which helps
explain the lack of prior literature on the problem.
However, I would like to talk here about another
aspect of the story which I find more interesting
than the solution itself, which is the emerging AI-powered
capability to rapidly write and rewrite
expositions of the solution.

https://mathstodon.xyz/@tao/115855840223258103

Mild Shock schrieb:
> 
> Hats off to Claude!
> 
> Jeff Barnett schrieb:
>  > Use Google and search on  "Claude's Cycles". The first hit is a PDF 
> on the Stanford.edu web site. If you copy the URL buried under that hit, 
> you will download the PDF or just click on the Google result.
>  >
>  > 
> https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf&ved=2ahUKEwjI7cfFxYWTAxWUHUQIHXnrABsQFnoECCMQAQ&usg=AOvVaw2ieck2cXsmBf_KGis1B3i2 
> 
>  >
>  > Paper is 5 pages in length. A fried sent it to me. You only need to 
> pay attention to the above goobly gop if you don't trust my friends.
>  >
>  > https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
>  >
> 

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Re: AI solves probl;em Knuth was/is working on! Mild Shock <janburse@fastmail.fm> - 2026-03-04 08:29 +0100
  Terrence Tao: On Jan 4, ChatGPT was able to produce a proof Erdos #728 (Re: AI solves probl;em Knuth was/is working on!) Mild Shock <janburse@fastmail.fm> - 2026-03-07 11:58 +0100
    Aristotle: The Era of Vibe Proving is Here (Re: Terrence Tao: On Jan 4, ChatGPT was able to produce a proof Erdos #728) Mild Shock <janburse@fastmail.fm> - 2026-03-07 12:08 +0100
      Re: Aristotle: The Era of Vibe Proving is Here (Re: Terrence Tao: On Jan 4, ChatGPT was able to produce a proof Erdos #728) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-07 07:21 -0800
        Re: Aristotle: The Era of Vibe Proving is Here (Re: Terrence Tao: On Jan 4, ChatGPT was able to produce a proof Erdos #728) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-07 07:36 -0800
          Only, three decades in software engineering? Re: Aristotle: The Era of Vibe Proving is Here (Re: Terrence Tao: On Jan 4, ChatGPT was able to produce a proof Erdos #728) Mild Shock <janburse@fastmail.fm> - 2026-03-08 10:00 +0100
            Re: Only, three decades in software engineering? Re: Aristotle: The Era of Vibe Proving is Here (Re: Terrence Tao: On Jan 4, ChatGPT was able to produce a proof Erdos #728) Mild Shock <janburse@fastmail.fm> - 2026-03-08 10:19 +0100
              Amazing Visual Perception, even for ASCII Input [GPT 5.3] (Was: Only, three decades in software engineering?) Mild Shock <janburse@fastmail.fm> - 2026-03-08 10:34 +0100
                Visual Perception helps reading Matrices, Fractions, etc.. (Re: Amazing Visual Perception, even for ASCII Input [GPT 5.3]) Mild Shock <janburse@fastmail.fm> - 2026-03-08 20:21 +0100
      Re: Aristotle: The Era of Vibe Proving is Here (Re: Terrence Tao: On Jan 4, ChatGPT was able to produce a proof Erdos #728) x <x@x.net> - 2026-03-08 19:10 -0700
        Biobrain cannot digest "Artificial" in AI (Was: Aristotle: The Era of Vibe Proving is Here) Mild Shock <janburse@fastmail.fm> - 2026-03-09 11:21 +0100
          Prolog vendors don't understand Tabling anymore (Re: When Supercomputing discovered BFS) Mild Shock <janburse@fastmail.fm> - 2026-04-04 14:10 +0200

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