Wikipedia:Reference desk/Archives/Mathematics/2022 November 16

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November 16

Vetting a new result?

This is about Yitang Zhang's recent preprint of a new result about Laundau-Siegel zeroes, that (if correct) makes some progress towards resolving the Riemann hypothesis. You can find more info with a web search if you don't know about it. I don't claim to understand the proof, but a look at the paper (and similar comments on mathoverflow) indicate that it's basically a brute force calculation. You start by bounding some quantities with funny-looking constants like 0.504 or 2022, crunch through 100 pages of formulas, and end up with a thing that shows what you wanted to prove. It's like in calculus where you pick constants at the beginning to make the thing at the end be less than epsilon. That is, it doesn't depend on fancy abstract or subtle considerations all that much.

The preprint has been up for a couple of weeks now, so I'm surprised that nobody seems to be commenting on it. This is different from some other preprints claimed to solve significant open problems, where there is immediately a bunch of attention, typically followed by someone finding a mistake; or even Zhang's earlier now-famous result on prime gaps, which immediately launched a swirl of rumors with big shots saying they had checked the paper and it looked good, modulo the possibility of some subtle error needing closer scrutiny to notice. Green and Tao's theorem on arithmetic progressions in the primes was maybe before my time, but I think it also kicked up a stir with lots of people examining the preprint.

Anyone know if the current silence about Zhang's new paper is typical, with the other cases being exceptional? Has anyone looked at or heard anything about any issues the paper might have? Thanks. 2601:648:8201:5E50:0:0:0:DD22 (talk) 02:39, 16 November 2022 (UTC)

Link to paper: arXiv:2211.02515. In the news: [1], [2], [3]. Tao wrote that he found "a number of misprints and technical issues ... that are hindering the verification process".^[4]  --Lambiam 08:12, 16 November 2022 (UTC)

Thanks, the news media blurbs are useless but Tao's comment was the type of thing I was looking for. 2601:648:8201:5E50:0:0:0:DD22 (talk) 03:20, 17 November 2022 (UTC)