Posted on 11/17/2022 3:39:30 PM PST by nickcarraway
Yitang Zhang, a number theorist at the University of California, Santa Barbara, has posted a paper on arXiv that hints at the possibility that he may have solved the Landau-Siegel zeros conjecture. The paper has not yet been validated by anyone else at this time, and Zhang himself has yet to explain the purpose or even meaning of his paper.
The paper posted by Zhang is not in a traditional format. There is no introduction or summation, or even any sort of explanation of its contents. Instead, it is a proof—a very long proof, 111 pages of math. Zahn does imply that his work is related to the Landau-Siegel zeros conjecture, however, and also implies in the title that it involves discrete estimates. The Landau-Siegel zeros conjecture is a sort of potential counterexample to the Riemann Hypothesis, which is theorized to predict the probability that numbers in a certain range are prime numbers.
Zhang is considered to be somewhat of an eccentric person. He was born and raised in China, and earned a master's degree at Peking University. He then moved to the United States where he earned a Ph.D. in math at Purdue University. But for unknown reasons, he was unable to get a job in his field, instead working a variety of menial labor jobs until finally landing a position at the University of New Hampshire. While there, Zhang toiled away on his own time for several years and then published what he'd been working on in 2013—the twin prime conjecture, which proposed that there are infinite pairs of prime numbers that differ by two.
The paper was considered a major breakthrough and made Zhang a celebrity of sorts in the math world. He has apparently been working on the Landau-Siegel zeros conjecture for many years. In 2007, he posted a paper about it as a preprint, but there were problems with the work, and it was never published in a peer-reviewed journal.
It will likely be some time before others finish reviewing Zhang's paper and offer commentary. And it is not clear if Zhang himself will comment publicly, although he is scheduled to present his paper to colleagues at Peking University sometime in the near future.
More information: Yitang Zhang, Discrete mean estimates and the Landau-Siegel zero, arXiv (2022). DOI: 10.48550/arxiv.2211.02515
Journal information: arXiv
You can write an extremely detailed proof that can be verified by a computer. It could also be verified by humans even without understanding it, like a computer does.
Sum Ting Wong. Never seen a proof that long.
Other mathematicians have to confirm it.
Go Boilers!
but i thought primes were good or bad don’t remember which pertaining to both
Every once in a while something pops up that claims there is a mistake in some old, well established theorem. But I don't think I've ever heard of even one of those claims being confirmed.
But you never know for certain. It's possible, however unlikely.
After centuries of all the world's greatest mathematicians accepting a proof, you'd almost have to be crazy to question it.
See “Uncle Petrose and the Goldbach Conjecture”
The Goldbach Conjecture states that every even natural number greater than 2 is the sum of two primes.
Now prove it and collect your Nobel
Correct, there are an infinite number of primes.
If there were a finite set of primes, one could multiply all of them, and add one to the product. The result would not be divisible by any of these primes, so it would be a new prime.
Andrew Wiles’ proof of Fermat’s Last Theorem was 129 pages long. His original proof had an error.
“The Goldbach Conjecture states that every even natural number greater than 2 is the sum of two primes.
Now prove it and collect your Nobel”
I think it would be easier to show a case that it doesn’t hold.
So far I’m up to 15=(13+2). The conjecture holds so far but I’ll keep you posted.
Want to guess up to what number people verified it using computers?
Even numbers, 15 doesn’t count.
For example, 22=11+11 or 38=37+1 or 100=93+7
I wonder if it’s possible, in theory, for a proof to be infinitely long?
… an infinite number of primes that differ by 2.
Yeah, I was going to ask if these pairs qualify:
1 and 3
3 and 5
5 and 7
and infinity is really, really big, and has lots of pairs.
PS I don’t think 9 is prime.
11 and 13
59 and 61
Well, that's easy.
If you stopped at 110 pages, it would be incomplete.
“Even numbers, 15 doesn’t count.”
WHAT!! Odd numbers do not count?
I made it up to 17 (conjure failed) and thought I had won the Noble Prize for sure. Okay then, back to work and now I’m up to 554=(457+97).
11 fails.
“11 fails”
Hmm. Let me check -—. By golly you are correct but unfortunately for you, I found and publicly disclosed the proof that the conjure does not stand for the number 17 before you disclosed that another odd number (11) that also fails the conjure. Therefore, if the conjure had included odd numbers, the Noble prize would have been mine.
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.