Comment by tensegrist
6 hours ago
Presumably one reason this is of interest here:
The proof proceeds by a modification of the Duffin–Schaeffer argument, together with the two-constant theorem of Nevanlinna (and some standard estimates of harmonic measures on rectangles) to deal with the effect of the localization. (As a side note, this latter argument was provided to me by ChatGPT, as I was not previously aware of the Nevanlinna two-constant theorem.)
Which I find funny in a way: I'm sure that almost no one here understands the article, grasps the significance of this problem in mathematics, or can meaningfully comment on the difficulty of solving it. But we'll still have opinions because the article mentions a popular tool some of us like, some of us dislike, and some are ambivalent about.
It would be surreal if a carpentry forum was regularly abuzz about mountaineering because climbers use a hammer-shaped tool.
Nevanlinna theory isn’t that obscure (in the sense of mathematics, I suppose) but it is very difficult (for me, probably less so for Tao) when working to have the whole of 21st century analysis in your head at once and see what could be applied where. I can see how an LLM would be quicker than a human at recognizing a context where a theorem from an apparently unrelated subfield could be applied.
It is deeply hilarious to watch software engineers become, at long last, bikeshedders.
What do you mean, "at long last"?
We've always been bikeshedders. For example, back in Slashdot days, some company would decide to migrate something from Windows to Linux. Immediately the debate became whether they should have gone with Debian or SuSE instead of Red Hat.