Should I be suspicious that the exponent in the equation is the current year? LOL I still need to read the article. The letter from Moh was interesting.
Yes, you should :)
Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
41–50 of 439 posts
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#42Earlier quoted context omitted.
Even more incredible is that his own advisor refused to write him letters of recommendation upon graduation [1] After graduation, Zhang had trouble finding an academic position. In a 2013 interview with Nautilus magazine, Zhang said he did not get a job after graduation. "During that period it was difficult to find a job in academics. That was a job market problem. Also, my advisor [Tzuong-Tsieng Moh] did not write m…
Yes, if you want to see something incredible (in both the literal sense and the usual sense), read https://www.math.purdue.edu/~ttm/ZhangYt.pdf (by Moh).
In the earlier version I saw (I guess it consists of the non-bold parts), he didn't mention as much negative stuff about Zhang. His claim that Zhang "want to be famous all the time" I regard with suspicion.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#43Earlier quoted context omitted.
Someone needs to make a movie about his life, or at least a documentary.
There is a documentary, but I can't attest to its quality (I haven't watched it yet): http://www.zalafilms.com/films/countingabout.html .
Hmm... thanks, it looks quite good.
But why is streaming rental for 24 hours? Why can't we do rentals for two weeks for videos? Is there a good reason to make it so difficult to stream? I don't want to watch it a million times. I just want to make it through once, but it takes me several sittings typically to finish a movie.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#44I am pretty confident that I will never in my lifetime fully understand stuff like this (not the symbols themselves, but the overall meaning of each term and why it is like that): https://i.snipboard.io/by4tsH.jpg
For the meaning, you just have to retrace back to where the things were defined, just like in programming. I am a mathematician, and I do not understand anything in the linked screenshot either (other than big O notation, which many people here should actually know!). FWIW, the author’s preference for Greek letters is rather excessive for my personal taste.
Ok, but there is a difference between looking up definitions and understanding something.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#45I can't resist saying one last thing about Siegel zeros: number theorists REALLY would like for this result to be correct because the possibility of Siegel zeros is unbelievably annoying. I mean mathematicians are supposed to enjoy challenges / difficulties, but Siegel zeros are just so recurrently irritating. The possibility of Siegel zeros means that in so many theorems you want to write down, you have to write cav…
>I can't resist saying one last thing Please, keep going. This is good reading.
In that case, you might find interesting these two short explanations I posted to Reddit about Siegel zeros (the second is a continuation of the first) :)
https://old.reddit.com/r/math/comments/y93a86/eliundergradua...
https://old.reddit.com/r/math/comments/ymlacu/professor_yita...
The class number formula, mentioned in the second comment, is one of the craziest "bridge results" in all of math (meaning a result that connects two seemingly disparate areas). The class number formula connects the values of Dirichlet L-functions at s = 1 (Dirichlet L-functions are complex functions related to the distribution of primes in arithmetic progressions), to class numbers of number fields. (Remember that the value of Dirichlet L-functions at 1 is exactly what the question of Siegel zeros concerns.)
To give a crash course on what some of those words mean:
1. A number field is what you get when you take the rational numbers, and you throw in the roots of some polynomials to get a bigger object where you can still do all of the usual arithmetic operations, in the same way that we throw in the roots of x^2 + 1 (namely, i, -i) into the real numbers to get the complex numbers.
2. The ring of integers is the right notion of the "integers" in that number field. (That is, rational numbers : integers = number field : ring of integers in that number field.)
3. The class number of a number field tells you how close you are to having unique factorization into primes holding in the ring of integers of that number field*. If the class number is 1, then you have unique factorization; if the class number is 1000, then you are very far from it.
What this connections means is that you can prove things about regular old primes in arithmetic progressions (in the integers) by proving things about these exotic / abstract primes (in rings of integers of number fields), and vice-versa.
Anyway, as a result of the class number formula, there are a lot of results about class numbers that are ineffective because of Siegel's theorem too, e.g., https://en.wikipedia.org/wiki/Brauer%E2%80%93Siegel_theorem. Zhang's result (if correct) would make all of those effective, too.
*While in the integers, it is true that every number factors uniquely into a product of primes, this is unfortunately not true in more general contexts. In fact, algebraic number theory basically began with a mistaken proof of Fermat's Last Theorem, which was mistaken precisely because it assumed that unique factorization always holds in this more general context, which is not true. (If unique factorization did always hold, then that proof of FLT would have been correct.)
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#46I'm not a mathematician, but the story of Yitang Zhang desperately makes me want this paper to be correct. > Prior to getting back to academia, he worked for several years as an accountant and a delivery worker for a New York City restaurant. He also worked in a motel in Kentucky and in a Subway sandwich shop. A profile published in the Quanta Magazine reports that Zhang used to live in his car during the initial job…
Someone needs to make a movie about his life, or at least a documentary.
Sadly, they would probably make it a schmaltzy Oscar-grab of a movie, like they did with Ramanujan's story.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#47Earlier quoted context omitted.
Even more incredible is that his own advisor refused to write him letters of recommendation upon graduation [1] After graduation, Zhang had trouble finding an academic position. In a 2013 interview with Nautilus magazine, Zhang said he did not get a job after graduation. "During that period it was difficult to find a job in academics. That was a job market problem. Also, my advisor [Tzuong-Tsieng Moh] did not write m…
Yes, if you want to see something incredible (in both the literal sense and the usual sense), read https://www.math.purdue.edu/~ttm/ZhangYt.pdf (by Moh).
> For some 10 years, I had recommended 100 mainland Chinese students to the department and all accepted by the department. I am always indebt to the trust of my judgements by the department. Only very few of them misbehaved, bit the hands which fed them, none of them intended to murder their parents/friends, almost all of them performed well and became well-liked.
No murderers, great success!
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#48There was a scientist who did his best stuff while he was working as a patent clerk.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#49As an older person currently working on a PhD, this guy was and is a something of a hero to me. He has an interesting life story. He was very into math at an early age, so he's different from people like me who got interested in it later in life, but he's also different in that his family was sent down to the countryside in China. I remember reading a lot about him a few years ago and relating to some of the professional difficulties he had and also to some of his ways of thinking and approach to doing math.
I never expected to see his name in a context like this again. I'm glad he's still being himself and working hard on what he loves.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#50> To give a sense of the scale of this claim: If correct, Zhang's work is the most significant progress towards the Generalized Riemann Hypothesis in a century. Thanks, that totally failed to give any sense of scale.
It's the moral equivalent of making major headway against P!=NP; or, proving that there are no global hidden variables in QM; or, that there's a clear path ("just engineering") to room-temperature semiconductors.
>room-temperature semiconductors
I suppose superconductors. Semiconductors are well in the room temperature regions :)