zlacker

>>nl+(OP)
"Recently, yet another category of low-hanging fruit has been identified as within reach of automated tools: problems which, due to a technical flaw in their description, are unexpectedly easy to resolve. Specifically, problem #124 https://www.erdosproblems.com/124 was a problem that was stated in three separate papers of Erdos, but in two of them he omitted a key hypothesis which made the problem a consequence of a known result (Brown's criterion). However, this fact was not noticed until Boris Alexeev applied the Aristotle tool to this problem, which autonomously located (and formalized in Lean) a solution to this weaker version of the problem within hours."

https://mathstodon.xyz/@tao/115639984077620023

>>newman+9q2
That doesn’t seem very fair. The problem was stated, and remained unsolved for all this time. You can’t take away that accomplishment just because the solution seems easy in hindsight.

>>adastr+KL2
It's technically true that this version of the problem was "low-hanging fruit", so that's an entirely fair assessment. Systematically spotting low-hanging fruit that others had missed is an accomplishment, but it's quite different from solving a genuinely hard problem and we shouldn't conflate the two.

>>zozbot+zM2
My point is stronger than that. Some things only appear low hanging fruit in hindsight. My own field of physics is full of examples. Saying “oh that should’ve been easy” is wrong more often than it is right.

>>adastr+kN2
Sure, but unless all solvable problems can be said to "appear as low-hanging fruit in hindsight" this doesn't detract from Tao's assessment in any way. Solving a genuinely complex problem is a different matter than spotting simpler solutions that others had missed.

In this case, the solution might have been missed before simply because the difference between the "easy" and "hard" formulations of the problem wasn't quite clear, including perhaps to Erdős, prior to it being restated (manually) as a Lean goal to be solved. So this is a success story for formalization as much as AI.