Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

news.ycombinator.com

Post reply on HN
Print view View original

421–430 of 439 posts

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#421

Post by danuker »

skyde wrote: post #155
danuker wrote: post #115

Earlier quoted context omitted.

I suspect computers can also help us get deeper. Stuff like computer algebra systems. Maybe some CAS-assisted work gets us into feedback loops allowing us to go indefinitely, as in a technological singularity. But the "shallow" part is also quite wide. You can teach people what you've learned forever, for instance.

do you have experience with CAS? i would love to learn how to use CAS to write proof more effectively

To be honest, my experience is limited to double-checking my algebra with the free Wolfram Alpha. I need it maybe a few times a year.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#422

Post by [deleted] »

ConcernedCoder wrote: post #116
gavagai691 wrote: post #15

Earlier quoted context omitted.

"I think Zhang's previous result was good enough to rebuff Hardy's claims." I agree.

age is just a number, some people may have a prejudice against larger numbers, and that to me, seems irrational

[deleted]

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#423

Post by AtNightWeCode »

When I first read the wiki article it came across as something generated by machine learning.

After spending way to much into this, is it basically that you theoretically in specific cases might get a rouge result? But when working with numeric methods or statistics you already sort this out on a set level. No?

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#424

Post by arrow7000 »

rosywoozlechan wrote: post #405
arrow7000 wrote: post #403

Earlier quoted context omitted.

I'm not sure what you're deriving satisfaction out of. That the market prevented someone from being able to earn a living and fulfilling their potential at the same time? I'm genuinely confused

I don't believe there's enough data in the original comment to assume that the market prevented them from being able to fulfill their living working with physics. It said they could make more money running a restaurant. If that it is the case they could not earn a living at all, and it's due to discrimination, which I asked about, then I agree it's not good. But if it's the case they could make a living in physics bu…

Based on the provided information I judge it more likely that their passion was maths and physics but were prevented from doing so because of certain economic realities than they had more interest in running a restaurant than engaging in research. You may disagree.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#425

Post by rutgersnj22 »

m_nyongesa wrote: post #376
rutgersnj22 wrote: post #226

Earlier quoted context omitted.

you got to read this article from his sister: https://zhishifenzi-com.translate.goog/depth/character/480.h...

Thanks for that link. Wish I could read Mandarin Chinese so I could read the original too. Clearly a flawed person. Not sure why he blew off his family so hardcore for so many years. Too bad to hear he was arrogant as a kid too, although a lot of smart kids are. Some of them turn out to be Peter Thiel, luckily this guy just wanted to work on math. Anyway, I wish he had been better to his parents. On the other hand, h…

What the article doesn't say is the reason why Yitang would not come back visit his family. Not sure if it is his own decision (makes sense as he lost connection with his family for many years) or some political reason (China doesn't allow him to go home).

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#426

Post by ekianjo »

vkou wrote: post #90
ekianjo wrote: post #88

Earlier quoted context omitted.

Why everything has to be a movie?

It's one of the few working ways to get modern societies to learn something, but a catchy musical can work too.

you dont learn anything useful in 2h of heavily romanticized hollywood fiction

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#427

Post by dudeinjapan »

3a2d29 wrote: post #81

I need a “Explain like I’m 5” for Landau--Siegel zeros. This sounds like a hard task as I couldn’t find anything online that does it :(

There is a function called the Riemann Zeta function which is defined as an infinite series ZETA(s) = 1/1^s + 1/2^s + 1/3^s + ...

For certain complex number inputs s, this function ZETA(s) returns zero. Riemann's hypothesis states it returns zero when the real part of the input Re(s) = 1/2, and the imaginary part Im(s) some non-zero value (the first zero occurs at Im(s) = +/- 14.135.) As far as we've checked with computers, all zeroes have Re(s) = 1/2. We are interested in these "zeros" because we can use them to construct a harmonic function (think overlapping waves) which tells us how the prime numbers are distributed.

A Siegel zero is a potential counterexample where a zero could theoretically occur for complex number with Re(s) close to 1 (i.e. not 1/2.) This is based on the study of Dirichlet-L functions which are a generalized version (i.e. superset) of the Riemann Zeta function.

If Zhang's result is correct, it simplifies the problem space for finding Riemann zeros, and thus for understanding the distribution of primes.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#428

Post by bmitc »

fnordpiglet wrote: post #408
bmitc wrote: post #257

Earlier quoted context omitted.

Also, biopics are terrible. I can't think of a single one that is worth it, especially if you consider that for many of the subjects, you could just watch a documentary on the person anyway, often with real footage and interviews with them. Biopics are usually just cash grabs and weird Hollywood flexes about mimicking someone else. The fact that they do so well at the awards ceremonies speaks to this.

I find them useful for teaching my 8 year old something about the person behind the name. After watching Einstein and Eddingiton (pretty ok movie) she has a better appreciation for who he is beyond a name. Obviously you learn almost nothing about his research and it’s a very tiny slice of Einsteins extraordinarily interesting life.

Is that better than just watching a documentary?

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#429

Post by kbrkbr »

Tainnor wrote: post #415
kbrkbr wrote: post #402

Earlier quoted context omitted.

Good point, I agree that it did not. Were those ideas however progress, or a tool that the Committee of Public Safety used because it fit their agenda? Was this philosophy finding truth that guided policy, or was it making up rhetorical arguments in a power struggle on behalf of the rising middle class and its policy? In absence of criteria of non empirical truth that are independent of the very non empirical truths…

Well, the original point was whether philosophy had any influence on world events, not whether that influence was good or not. To me, the idea that ideas don't play a major role in world history and politics seems odd. There's nothing more fundamentally human than trying to understand the world around you and wanting to shape it in a certain way. Of course material conditions are important; the French Revolution woul…

I understood the thread roughly this way: „philosophy makes progress. The evidence is that the modern world has adopted the more progressed rules of enlightement and scientific rules.“ And my reply was that this is highly questionable.

I’m saying that the enlightenment ideas happened because the uprising middle class needed justifications in their power struggle. Not that the ideas formed a middle class that then acted upon them.

I agree with you that humans need ideas to tell a story of themselves. And that story better paint them as good! But that story is usually not the driving force.

So I fail to see progress as I don’t see a criterion to measure progress (in general. Aristoteles‘ logic is a tool. Here I see how to compare it to FOL and judge which is better or worse for specific use cases).

As for human rights: do I agree with them? Yes! Can I justify them? No! Do I know where to exactly draw the lines when two rights collide? No! Is it important to justify them in a philosophical way? I doubt.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#430

Post by n4r9 »

robertlagrant wrote: post #378
n4r9 wrote: post #375

Earlier quoted context omitted.

By "visual explanation" do you mean imagining a square whose sides are length (a + b), and breaking it up into smaller squares and rectangles? Or do you mean mulitplying out the terms: (a + b)(a + b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2 ?

The former, yes.

It's interesting that some people find that way easier to remember. For me, multiplying out the terms seems faster, probably only because I've practised so many times in my life that I can picture the algebra in my head. It also seems more general, as it's a technique which you have to know anyway. I guess it comes down to being more geometrically minded vs algebraically minded. School should try to cater to both!
Post reply on HN