53 ms·
Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
Yitang Zhang, the mathematician behind the 2013 breakthrough on bounded gaps in primes, posted to the arxiv today a result which (if correct) comes close to proving the nonexistence of Landau--Siegel zeros: https://arxiv.org/abs/2211.02515 https://arxiv.org/abs/2211.02515.
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. Moreover, I think this result would not only be a more significant advance than Zhang's previous breakthrough, but also constitute a larger leap for number theory than Wiles' 1994 proof of Fermat's Last Theorem (which was, in my opinion, the greatest single achievement by an individual mathematician in the 20th century).
Some discussion / explanation of Siegel zeros and Zhang's claim can be found here:
https://old.reddit.com/r/math/comments/y93a86/eliundergraduate_the_hype_around_yitang_zhangs/ https://old.reddit.com/r/math/comments/y93a86/eliundergradua...
https://mathoverflow.net/questions/433949/consequences-resulting-from-yitang-zhangs-latest-claimed-results-on-landau-sieg https://mathoverflow.net/questions/433949/consequences-resul...
An account of Zhang's remarkable story (and his previous breakthrough) can be found here. Famously, prior to his breakthrough, he worked at Subway and lived in his car:
https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty
- izzygonzalez 4y agoarXiv https://arxiv.org/abs/2211.02515 https://arxiv.org/abs/2211.02515 Discussion https://old.reddit.com/r/math/comments/y93a86/eliundergraduate_the_hype_around_yitang_zhangs/ https://old.reddit.com/r/math/comments/y93a86/eliundergradua... https://mathoverflow.net/questions/433949/consequences-resulting-from-yitang-zhangs-latest-claimed-results-on-landau-sieg https://mathoverflow.net/questions/433949/consequences-resul... New Yorker article https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty
- deleted 4y ago[deleted]
- gavagai691 4y agoI didn't know how to make the links clickable. Thanks!
- dang 4y agoWe'll do that.
- gavagai691 4y agoTwo additional notes: 1. Zhang posted an attempt at solving this problem in 2007 that he later more or less admitted was flawed: https://mathoverflow.net/questions/131221/yitang-zhangs-2007-preprint-on-landau-siegel-zeros?rq=1 https://mathoverflow.net/questions/131221/yitang-zhangs-2007.... But speaking with mathematicians who are intimately familiar with Zhang's previous work, there seems to be good reason to be optimistic nevertheless. First, the idea behind Zhang's proof is similar to the zero-repulsion ideas appearing in known results about Siegel zeros, and is thus reasonable. Second, Zhang seems to have matured late, and unlike the flawed 2007 paper, his 2013 paper on bounded gaps in primes is meticulously written. He came a long way between those two papers, and he may have come even further since then. 2. Zhang is 67 years old. If the paper is correct, then Zhang constitutes a strong counterexample to G.H. Hardy's famous claims that "mathematics is a young man's game" and nobody alive today could say, as Hardy did, that "I do not know an instance of a major mathematical advance initiated by a man past fifty."
- markus_zhang 4y agoI think Zhang's previous result was good enough to rebuff Hardy's claims. Actually I think Math is more or less a young people's game is because whence someone be super successful and famous it's kinda difficult psychological to retain the previous mental state and push out similar results.
- gavagai691 4y ago"I think Zhang's previous result was good enough to rebuff Hardy's claims." I agree.
- ConcernedCoder 4y agoage is just a number, some people may have a prejudice against larger numbers, and that to me, seems irrational
- deleted 4y ago[deleted]
- cshimmin 4y agoWow, from the 2015 article: [A journal reviewer of his famous paper says]: "you should be careful. This guy posted a paper once, and it was wrong. He never published it, but he didn’t take it down, either.’ ” The reader meant a paper that Zhang posted on the Web site arxiv.org, where mathematicians often post results before submitting them to a journal, in order to have them seen quickly. Zhang posted a paper in 2007 that fell short of a proof. It concerned another famous problem, the Landau-Siegel zeros conjecture, and he left it up because he hopes to correct it. Looks like he might have lived up to that!
- hooloovoo_zoo 4y agoOne can't really take papers down from arXiv anyway.
- leethargo 4y agoWell, you can update them with a disclaimer that points out known issues.
- gavagai691 4y agoIf the proof is right, Zhang is in contention for greatest living mathematician with seven papers total, and on the basis of two of them (and should win all the major prizes he has not won yet and is still eligible for: Abel, Wolf, etc.). Would truly live up to Gauss' motto: "pauca, sed matura!"
- whytai 4y agoEven 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 me letters of recommendation." ... Moh claimed that Zhang never came back to him requesting recommendation letters. In a detailed profile published in The New Yorker magazine in February 2015, Alec Wilkinson wrote Zhang "parted unhappily" with Moh, and that Zhang "left Purdue without Moh's support, and, having published no papers, was unable to find an academic job". In 2018, responding to reports of his treatment of Zhang, Moh posted an update on his website. Moh wrote that Zhang "failed miserably" in proving Jacobian conjecture, "never published any paper on algebraic geometry" after leaving Purdue, and "wasted 7 years of his [Zhang's] own life and my [Moh's] time". 1. https://en.wikipedia.org/wiki/Yitang_Zhang https://en.wikipedia.org/wiki/Yitang_Zhang
- mabbo 4y agoI'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-hunting days. https://en.wikipedia.org/wiki/Yitang_Zhang https://en.wikipedia.org/wiki/Yitang_Zhang
- kenjackson 4y agoSomeone needs to make a movie about his life, or at least a documentary.
- gavagai691 4y agoThere is a documentary, but I can't attest to its quality (I haven't watched it yet): http://www.zalafilms.com/films/countingabout.html http://www.zalafilms.com/films/countingabout.html.
- kenjackson 4y agoHmm... 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.
- gavagai691 4y agoI was thinking about watching this documentary two years ago. That sounds like the reason that I decided not to.
- mikeyouse 4y agoLooks like it's available on Archive.org: https://archive.org/details/countingfrominfinityyitangzhangandthetwinprimeconjecture2015documentary7au3cikb2za https://archive.org/details/countingfrominfinityyitangzhanga...
- flobosg 4y agoAlternative link for the New Yorker article: https://archive.is/TVj2A https://archive.is/TVj2A
- XCSme 4y agoI 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 https://i.snipboard.io/by4tsH.jpg
- postalrat 4y agoMaybe because you haven't tried to understand it? Can't be harder than learning the meaning behind these characters: https://www.pandatree.com/book/DiaryofWorm.jpg https://www.pandatree.com/book/DiaryofWorm.jpg
- gardenhedge 4y agoIt would take a long path to understand it.. and the path would need to be filled with good resources.
- XCSme 4y agoI don't mean the symbols themselves, but how each member was defined and the history behind it. It's like watching a Marvel movie and not only knowing the plot of the current movie but also the deep history of each character and their relationships with other characters. I assume the paper didn't come out of nowhere and it's based on "the shoulders of giants".
- dan_mctree 4y agoPretty sure it's much harder than Chinese. The depth and abstraction of the concepts involved and the density of these concepts in these lines vastly eclipses anything in any natural language
- xyzzyz 4y agoFor 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.
- keepquestioning 4y agoIs Yitang Zhang this century's Ramanujan?
- pishpash 4y agoNot really, he seems a grinding kind of mathematician, vs. Ramanujan who wouldn't bother with proofs.
- daveevad 4y ago> While he never went to school at UK, this will not be his first time on campus. Following his graduate work at Purdue University, Zhang lived in Lexington for a few years and managed the finances at a local Subway franchise. During that time he would also spend hours in the mathematics library at UK, reading journals on algebraic geometry and number theory. A real-life Good Will Hunting, his backstory is incredible.
- CSSer 4y agoThis sounds like the Margaret I. King library building AKA the Science & Engineering library. Otherwise, I'm not sure which library they're referring to. Interestingly, there was a subway on campus too. I wonder if it was that one, by chance. Small world. source: UK is my alma mater.
- daveevad 4y agoIIRC, in the 90s there was a Subway in the same complex that housed the Kentucky Arcade, but maybe it was a Blimpie's. Maps show it as a seven minute walk to the King Library. My hope is that I crossed path with this genius at some point in between epic battles of Tekken 3 or NBA Jams. I grew up in Lexington.
- vecter 4y agoCan someone explain the decimal constants that are used throughout the proof? For example, on page 52. It's rare to see these kinds of numbers used in mathematical proofs, but I'm sure they were chosen for good reasons.
- yifanl 4y agoI'm not an analytic number theorist, but my understanding is that the proof requires some values to be 0.5 + some positive epsilon to be correct, and for the sake of clarity, these somewhat arbitrary constants are chosen to get to the result.
- gavagai691 4y agoUnfortunately, nobody can explain anything like this right now. The paper was posted today, is 111 pages long, and it will likely take even professional mathematicians around a year to understand / check it completely.
- deleted 4y ago[deleted]
- aidos 4y ago0.502 and 0.504? If so, they're introduced as parameters back on page 10. I can't tell you much more than that!
- bigbacaloa 4y agoOften in math papers there is a series of constants appearing in estimates, each of which depends, sometimes in nonobvious ways, on those appearing earlier. Some authors like to give these constants genuine numerical values in order to help keep track of the dependencies between them and, in particular, to make sure that they aren't accidentally treating two different C's as the same. In delicate analytic proofs this sort of thing is particularly important - subtle missed dependencies are one of the places where serious proof attempts can go wrong in hard to find ways. I'm not saying this is what Zhang is doing, but it's one possibility.
- keepquestioning 4y agoIs there a real world outcome to this result?
- gavagai691 4y agoThere are many, many, many consequences for prime numbers--which to me are concrete enough to be interesting (and are way more concrete than what 99% of mathematicians work on!). On the other hand, I doubt this proof will help you to build a faster gizmo or something in the real world.. especially since it's proving something we really think is true (a consequence of the Generalized Riemann Hypothesis), and for real-world applications you can just assume the thing that we think is true is actually true (even if we haven't been able to prove it for a century). (E.g., you don't need to prove that factoring is hard to use cryptography for practical purposes..)
- davesque 4y agoI think it's fair to say that this could lead to certain new things becoming known about the distribution of primes. This could have implications for cryptographic algorithms that depend on prime numbers being hard to find.
- schoen 4y agoCareful, prime numbers are not hard to find. Like, try openssl prime -generate -bits 2048 Congratulations, you just found a prime that is big enough for every cryptographic protocol that uses prime numbers (not counting unusual and non-deployed post-quantum proposals). Some number theory research may impact the security of cryptosystems, but not all results do.
- davesque 4y agoYeah, sorry perhaps I shouldn't have made such a specific sounding claim. I'm not an expert on this topic, but was pretty sure I had heard from reputable sources in the past that the Riemann Hypothesis had some bearing on the distribution of prime numbers. And it feels safe to say that this could have practical implications for cryptography. But maybe I should just leave it to the experts :).
- vbezhenar 4y agoI wish there will be time when "(if correct)" would be nonsense because correctness is checked in a fraction of second by something like CoQ and this proof is accompanied every known theorem.
- gavagai691 4y agoI 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 caveats like "unless a Siegel zero exists," or split into two cases based on if Siegel zeros exist or don't exist, etc. But here is the worst (or "most mysterious," depending on your mood..) thing about Siegel zeros. Our best result about Siegel zeros (excluding for present discussion Zhang's work), namely Siegel's theorem, is ineffective. That is, it says "there exists some constant C > 0 such that..." but it can tell you nothing about that constant beyond that it is positive and finite (we say that the constant is "not effectively computable from the proof").* So then, if you try to use Siegel's theorem to prove things about primes, this ineffectivity trickles down (think "fruit of the poisoned tree"). For example, standard texts on analytic number theory include a proof of the following theorem: any sufficiently large odd integer is the sum of three primes. However, the proof in most standard texts fundamentally cannot tell you what the threshold for "sufficiently large" is, because the proof uses Siegel's theorem! In this particular case, it turns out that one can avoid Siegel's theorem, and in fact the statement "Any odd integer larger than five is the sum of three primes" is now known https://en.wikipedia.org/wiki/Goldbach%27s_weak_conjecture https://en.wikipedia.org/wiki/Goldbach%27s_weak_conjecture. But it is certainly not always possible to avoid Siegel's theorem, and Zhang's result would make so many theorems which right now involve ineffectively computable constants effective. *Why is the constant not effectively computable? Because the proof proceeds basically like this. First: assume the Generalized Riemann Hypothesis. Then the result is trivial, Siegel zeros are exceptions to GRH and don't occur if GRH is true. Next, assume GRH is false. Take a "minimal" counterexample to GRH, and use it to "repel" or "exclude" other possible counterexamples.
- SantalBlush 4y ago>I can't resist saying one last thing Please, keep going. This is good reading.
- gavagai691 4y ago
- EGreg 4y agoBig if true
- aleksiy123 4y agoAppropriately concise.
- plaguepilled 4y agoI was gonna comment this too goddamn
- deleted 4y ago[deleted]
- quickthrower2 4y agoThanks for the ELI-not-a-mathematician. I am super excited for those involved, and understand none of it :-).
- iLoveOncall 4y ago> 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.
- thechao 4y agoIt'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.
- xxs 4y ago>room-temperature semiconductors I suppose superconductors. Semiconductors are well in the room temperature regions :)
- tschwimmer 4y agoI feel like saying this is similar to making progress on P!=NP is not accurate (extreme disclaimer: I have no formal math training). My understanding of P!=NP is that an answer to that has strong implications for the nature of the concept of determinism _of reality_, let alone most cryptography and lots of other stuff too. From my quick scan of the GRH wikipedia article, it doesn't appear that the GRH has the same widespread almost philosophical implications as P!=NP.
- doodlebugging 4y agoShould 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.
- gavagai691 4y agoYes, you should :)
- commandlinefan 4y agoThere was a scientist who did his best stuff while he was working as a patent clerk.
- version_five 4y agoDo you know how much a patent clerk makes?
- aidos 4y agoIn this case, he makes a difference!
- azinman2 4y agoYou’re missing the reference
- deleted 4y ago[deleted]
- wfaris 4y agoYou've never worked in the private sector... They expect results.
- version_five 4y agoThank you, my faith in HN has been restored!
- pasttense01 4y agoFor those of you who don't watch many movies: https://www.youtube.com/watch?v=RjzC1Dgh17A https://www.youtube.com/watch?v=RjzC1Dgh17A
- soperj 4y agoI don't think they are, I think they're stating the difference between being a patent clerk in the early 1900s and working at Subway while living in your car is substantial.
- m_nyongesa 4y agoAs 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.
- mrybczyn 4y agoHe and his parents were victims of Mao's cultural revolution (like millions of others) - and he was forced into agricultural labour instead of attending high school. Amazing cinderella story. A real academic hero.
- dis-sys 4y ago> like millions of others Including Xi Jinping.
- canadiantim 4y agoUnfortunate Xi is repeating past mistakes
- Qtips87 4y agoAt least Xi is much more assertive (not aggressive) in safeguarding his country's territorial integrity whereas Mao didn't give a hoot and let his country land grabbed by its neighbors left and right.
- sebg 4y agoWould love to hear your story about getting a PhD as an older person. Have you written anything about it that's public? If not, would it be possible to contact you? Thanks!
- davidherrero 4y ago
- arturkane7 4y agoComplete aside it is interesting that he announced his result in Peking university given that he has been vocal about his dislike of the Chinese communist party.
- xiaodai 4y agoHe's one of my personal heroes!!! Go Zhang!
- pa7x1 4y agoMath used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach a point where a mathematician's intellectually productive life is not sufficient to contribute anything novel, statistically speaking. And as population seems to be close to peaking, we will also have less chances of exploring the extremes of mathematical dexterity. Perhaps we could then rely on computer assisted theorem provers. Or life extension, as long as intellectually productive years are also increased. Or we will need to focus and specialize kids earlier on.
- tsol 4y ago>Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory >The sad part is that as the trend continues we may reach a point where a mathematician's intellectually productive life is not sufficient Hmm. I had never thought of it like this. Is it possible for human knowledge to become so advanced in a single subject that it takes a persons entire life to learn just one subject? That's already true of something like the human body, which is why doctors specialize in organs or regions of the body. The more human knowledge expands, the more individuals specialize into increasingly smaller niches.
- Frost1x 4y agoThis is a growing problem in many fields, IMHO. I've been wondering for awhile if it's an inherent flaw in knowledge in that if knowledge can't supplant older knowledge in a high compressed reduced form as things progress, we're just building so much information/knowledge for any given field that at some point, it may be quicker to simply rediscover the process than to search the knowledge for the prior work.
- novalis78 4y ago
- 3a2d29 4y agoI 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 :(
- gavagai691 4y agoHey, this comment was my attempt at an ELIUndergraduate (5 is probably a little too ambitious for this topic). I hope it may be helpful! https://old.reddit.com/r/math/comments/y93a86/eliundergraduate_the_hype_around_yitang_zhangs/it4kdrn/ https://old.reddit.com/r/math/comments/y93a86/eliundergradua...
- 3a2d29 4y agoThanks!
- leokennis 4y agoThere are moments I'm pretty proud of my intellect and what I have achieved with it. Reading and not comprehending even the very basics of proofs like Zhang's are a good reality check in that regard.
- dudeinjapan 4y agoThere 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.
- aidos 4y agoFlicking through this paper is very humbling and awe-inspiring. Having studied in this field when I was younger, I have just enough understanding to appreciate the insane amount of thought represented here. Kudos.
- avaldez_ 4y agoAw man we need a SoME2 video about this breakthrough https://youtu.be/cDofhN-RJqg https://youtu.be/cDofhN-RJqg
- stabbles 4y agoIs the 2022 in the bound there cause it's sharpest or because he happened to have the freedom to pick it equal to the year of publication?
- gavagai691 4y agoNot sharpest; he says he thinks it can be improved, but not down to 1 (if it could be improved down to 1, that would prove the nonexistence of Landau--Siegel zeros).
- leemailll 4y agoHe first talked about this breakthrough in a Peking Univ alumni meeting, and a preprint circulating in the field before he submitted to arXiv (https://drive.google.com/file/d/1vTLoh_Cpw6Zr436rD7FnjzND6ngY2VG8/view https://drive.google.com/file/d/1vTLoh_Cpw6Zr436rD7FnjzND6ng...). It's a 111 pages long proof.
- fqye 4y agoI first found out his story from new yorker https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty when the issue came out. I almost busted in tears. I just wish he continue to enjoy mathematics, no matter if this paper is flawed or not.
- ww520 4y agoIt's a fantastic piece. New Yorker has some really in depth writing.
- rutgersnj22 4y agoyou got to read his sister's article: https://zhishifenzi-com.translate.goog/depth/character/480.html?_x_tr_sch=http&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp https://zhishifenzi-com.translate.goog/depth/character/480.h...
- robomartin 4y ago
- bdhe 4y ago> It's the old "I'm from the government and I am here to help" joke. What else is the government for? I understand it's a popular Reagan talking point but I don't really grok it. If you assume the govt doesn't work for us, particularly if you're in politics, it becomes a self-fulfilling prophecy.
- s1artibartfast 4y agoThis is probably not the best thread for a political discussion, but I will take a shot. Nobody disputes that governments should be a force for good. Government's obviously can do both good and bad. Many reason atrocities like the cultural revolution came of under the pretext of trying to help. If you think the government has veered into doing bad, it is natural to want to reform it and make it stop doing that. the talking point and metaphor simply conveys a belief that some of the governments work is bad and should be stopped. It's a lot more complicated, but that's the 5-year-old explanation of it
- civilized 4y agoGovernment that limits its own power by law is humanity's greatest political invention. Anyone can make a government that sometimes does good. The challenge is to create a government that cannot do unfathomable evil.
- joshuamorton 4y ago> the talking point and metaphor simply conveys a belief that some of the governments work is bad and should be stopped This is a nuanced and thoughtful position. The statement "The 9 words you never want to hear are I'm from the government and I'm here to help"" is not nuanced and thoughtful, it doesn't suggest governments do good and bad, it positions governments (and their agents) as incapable of doing good. That someone from the government trying to help you must not be, for whatever reason.
- bottlepalm 4y agoIs this something a proof assistant could be used to help validate?
- bmc7505 4y agoIn theory, yes, but in practice proof assistants are only just starting to become practically useful for research-level mathematics. Validation/verification would likely require an enormous amount of proof engineering to build up the theorems required to verify a proof of this complexity. See the Liquid Tensor Experiment postmortem [1] for the results of a similar undertaking. [1]: https://leanprover-community.github.io/blog/posts/lte-final/ https://leanprover-community.github.io/blog/posts/lte-final/
- grubby 4y agogo boilermakers! unfortunate that he left on bad terms, but cool to see alma mater. his advisor is a prick tho lmao had him one sem
- deleted 4y ago[deleted]
- rutgersnj22 4y agoI just read an article from Yitang Zhang's little sister (in Chinese). It touched my soul. A must-read (translated from Chinese using Google translation): https://zhishifenzi-com.translate.goog/depth/character/480.html?_x_tr_sch=http&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp https://zhishifenzi-com.translate.goog/depth/character/480.h... Part of the translation is not so perfect and you have to use your best guess sometimes. The Chinese version is a masterpiece. In addition, here is an article from Yitang Zhang's PhD advisor. Not so nice: https://www.math.purdue.edu/~ttm/ZhangYt.pdf https://www.math.purdue.edu/~ttm/ZhangYt.pdf
- earthboundkid 4y agoThe “lack of progress” in philosophy comes down to this. By the time of Socrates or Confucius, there had already been a lifetime’s worth of philosophical thought done that you needed to grapple with. Everyone since then has necessarily had to let something slip through in order to move forward at all.
- woodruffw 4y agoI think we sometimes understate philosophy's progress: it's certainly not measurable in decades, but the world of 2022 looks very different (in terms of philosophical priors and their consequences) than the world of Socrates or Confucius. A handful of examples that come to mind: * (Nearly) everybody on our planet lives under a government whose fundamental structure and right to power comes from modern (meaning 17th century) political philosophy. * Everybody posting on this board is using a machine that only existed in the mind games (and works) of math philosophers just over a century ago. * The philosophical foundations for contemporary science are very young, practically within living memory. Popper died less than 30 years ago!
- adalacelove 4y agoWe measure philosophy success relative to finding the meaning of life. On the other hand everybody agrees that computers have advanced enormously without achieving yet AGI.
- LudwigNagasena 4y ago
- happy-go-lucky 4y ago“One does mathematics because one has to, and if it is appreciated, all the better!” –Karen K. Uhlenbeck
- carabiner 4y agoSubway needs to use this guy in an ad.
- bjarneh 4y agoI like the link to old.reddit. New reddit is still such a sluggish site..
- zimpenfish 4y agoBrings to mind Gould's quote - "I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops." https://www.goodreads.com/quotes/99345-i-am-somehow-less-interested-in-the-weight-and-convolutions https://www.goodreads.com/quotes/99345-i-am-somehow-less-int...
- fredley 4y agoI think about this often. Having studied mathematics, it's a field where there is a huge range of talents, even at 18 (and younger). There are genuinely gifted people who stride ahead, but the sad reality is that even at top institutions most of the undergraduate cohort will be merely averagely clever people who have received great (often private) tuition. In a field where finding every genius really matters because of the difficulty of expanding the frontiers it's heartbreaking to realise most just never get the opportunity of good mathematical education in the first place.
- wikfwikf 4y agoI don't think this is the whole story. Of course, it is a tragedy when people who had undeniable raw talent are neglected or passed over and don't get to achieve as they might. It's also sad and disappointing when we observe structural injustices in our society. However, isn't it possible that giving great teaching resources to people who aren't already at the top level in terms of raw talent, allows them to succeed at a very high level? If so, it's not a zero sum game - the 'averagely clever people who have received great tuition' and who go on to succeed might be a sign of the education system working, not its failure. We might focus more on making sure a wider group of 'averagely clever people' get such good tuition, rather than on the finding and promotion of undiscovered geniuses. Two examples that I often think about in this context: firstly the Budapest school of mathematics in the early 20th century. A hugely disproportionate number of the world-class mathematicians from that era were directly taught by Fejer and/or part of his seminar and mentee group. (He stands out as a supervisor to a far greater extent than any mathematician stands out from the pack for his own achievements.) Is it possible that while one or two of this group might have been 'born geniuses', it also includes several who might otherwise have been second-rate, but who became world-class because of the influence both of Fejer and of their high-performing colleagues? Secondly, George Harrison of the Beatles. In the second half of the Beatles' recording career, he wrote some of their best-loved songs, several of which are regarded as absolute classics. Did the Beatles happen to contain three inherently gifted songwriters, by sheer coincidence? Or is it more likely that working for a decade alongside two extremely talented and successful songwriters nurtured and elevated Harrison far beyond what might otherwise have been expected?
- alberto_yaakov 4y agoJust a cultural observation: I wonder how many Chinese geniuses are behind the iron firewall of China. With the number of Chinese population and STEM focus, it's likely that in two decades Chinese dominance of sciences, technology, and later culture (language, art etc) is ensured.
- Sk012 4y agoAdd Comment
- ohlookcake 4y agoThat's NumberZhang!
- syastrov 4y agoHaha, that made my day! (It’s a reference to That Mitchell and Webb Look).
- data_maan 4y agoRegarding Zhang's age: Most Fields medalists these days are very close to exceeding 40 years. Wiles himself just a special silver medal, because of that - which I think is outrageous age discrimination. Mind you he didn't get the silver medal because his results were a bit less spectacular than those of the winners, but rather they were so groundbreaking he couldn't be ignored, but because he was just over 40 they had to downgrade thr medal to a silver one (I guess in order to not be in conflict with the rules that the organization that awards the Fields medal has). This is part of a general trend. As the world population ages, the number of people being able to achieve world-class performance later in life increases. One can see this spectacularly in sports, where older and older people win medals (for example: https://www.npr.org/2022/02/12/1080338798/older-athletes-break-records-at-the-2022-beijing-olympics https://www.npr.org/2022/02/12/1080338798/older-athletes-bre... ) The Fields committee would probably do good updating their statutes, in order to not be so out of step with the times...
- mabbo 4y agoMy understanding is that the Fields medal was always meant to be awarded to someone young and on their way up. But then it became the medal, the Nobel prize of math. Maybe we just need a new Nobel in math.
- dkislyuk 4y agoThe hope is that the Abel Prize becomes the "Nobel Prize of Mathematics", as it is directly modeled after it.
- throwaway81523 4y ago> Most Fields medalists these days are very close to exceeding 40 years They are usually spotted at a much younger age, and they get the medal when they are almost 40 because after that it will be too late. I.e. if there are several deserving mathematicians you give the medal to the one where the clock is about to run out, since the others will have more shots at it.
- yyyyxxxx 4y agoTrue
- yyyyxxxx 4y agoyo
- dontbenebby 4y ago
- new2yc 4y agoAnother one in the books. It reminds me of the quote stating whether the research is flawed or otherwise, only time will tell.
- sniperjoe360 4y agoCheeky of him to use -2022 in the exponent reflecting the year of publication > It is possible to replace the exponent −2022 in Theorem 1 by a larger (negative) value if the current arguments are modified, but we will not discuss it in this paper.
- xhkkffbf 4y agoI can't judge the math directly, but I do know that my local Subway makes good, healthy sandwiches full of vegetables and other things. So that's a plus on his resume.
- theincredulousk 4y agostill blown away that he was my calc II professor in college.
- rakkhi 4y agoSorry for the ELI5, checked the Reddit link also. Any immediate implications of this?
- jmartin2683 4y agoWhat does this enable?
- AtNightWeCode 4y agoWhen 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?