Another interesting example of modern computer assistance in mathematics, again involving the https://www.erdosproblems.com/ site: Problem #707 (https://www.erdosproblems.com/707), previously marked as "open", is now "disproved" - with the disproof formalized in Lean : https://borisalexeev.com/papers/erdos707.html . But the path towards that disproof was quite unusual, not fitting neatly into any of the standard narratives about AI in mathematics:
The authors' initial proof used some numerical computer experiments, but did not get much help from LLMs initially, with even the code generated by hand.
The authors then found a disproof by conventional human arguments (and also obtained some stronger results of a similar nature), and did not turn up any prior solution to this problem in their literature searches. Even the modern AI deep research tools did not locate any hits.
Nevertheless, as part of the process of writing the paper, they found a solution to the problem (slightly different from theirs) had been obtained by Hall, thirty years before Erdos even posed the problem!
Perturbed by this, the authors then decided to formalize both their result and Hall's result in Lean. (1/3)
I'm astonished this was a 2/5 for their playerbase, this one kicked my ass. I fully cheated with another browser to get green without ending the puzzle cause I wanted to try the other ones still
Spoiler
"Warm" in green took me ages, and so did "easy" in blue, and because I couldn't lock down either confidently I couldn't progress. If I had guessed blue with easy I'd have gotten it but I really wasn't convinced that was the answer so I just kept guessing at green.
I think I only would have gotten purple if I could eliminate the others
NYT Strands #707 - Sunday 8 February 2026 Discussion
Link to Strands: https://www.nytimes.com/games/strands ...
Connections #707 2025-05-18
https://www.nytimes.com/games/connections
Travel.earth ( travle.earth )
Name countries to travel from the Start Country to the End Country. Try to get there in the fewest guesses!
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