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Undergraduate Math Student Pushes Frontier of Graph Theory
- gumby 6y agoEven though this is in Quanta this is really cool!
- notagoodidea 6y agoEven though? Is there a problem with Quanta that I am not aware of? I find it a nice magazine to read about various math-y subjects and researchers despite the editorial click-bait-ish style sometimes. It is a nice starting point to discover new stuffs.
- gumby 6y agoI find their writing overdramatic and often missing the central point. For an example recently discussed on HN: "Computer Scientists Achieve ‘Crown Jewel’ of Cryptography" -- misunderstanding the science, not investigating the larger context (in which it's just a form of FHE), pulling out the (overwrought) term of one person, to call it the "crown jewel", describing other work as "dazzling newcomers" and, of course, forgetting to investigate the practical constraints. These are errors in the basic craft of journalism. I see the same problems in other articles in areas I have worked in which leads me to doubt the whole enterprise. It also likes "profile of a researcher" articles, which are typical talismanic pieces for the popular press void of any actual science. It's probably fine to surface interesting topics, though there are other sources appear to use writers who are actual scientists, or who at least have scientific training.
- aruss 6y agoI like that their pieces dig into the backgrounds of the researchers, which humanizes and popularizes the science itself. It has to get down from the ivory tower somehow, and storytelling is a great medium. Most Quanta articles are not "void of any science;" rather, I find them to be great lay explanations of high-level concepts that most scientists (including myself) would struggle to articulate to non-academic family and friends. If you want "just the science, ma'am," you can go read the papers themselves. Also, not to nitpick, but I thought the crypto article was well-written and covered the subject properly. It seems you are the one misunderstanding the science if you believe that iO is just a form of FHE, which makes me doubt your whole enterprise of discrediting Quanta's work ;) Speaking as a (former) cryptographer here.
- whbrown 6y agoLooking forward to the numberphile video about it. Related: https://www.youtube.com/watch?v=xdiL-ADRTxQ https://www.youtube.com/watch?v=xdiL-ADRTxQ
- mensetmanusman 6y agoGreat work! I wonder if their expertise would be helpful in understanding deep learning, a rare field that made advances before mathematicians had fully laid the groundwork (sometimes they do a century ahead of time :)); https://deepmath-conference.com/ https://deepmath-conference.com/
- tmsh 6y agoI just don’t get why comments like this are downvoted. But I do suspect this makes Hacker News what it is. Good at surfacing a certain x to y percentile of a certain way of looking at things. It’s not a place to brainstorm or be open minded about new ways of thinking successfully - not very very often. More a place to surface small useful bits of information that people find (a) useful and (b) that people are passionate about already. And there’s a lot of value in that as a reader. And some value as writer in practicing articulation of very clearly thought-out ideas. But yeah - today I realized HN and ‘I wonder if...’ comments don’t really jive together.
- renewiltord 6y agoThink about it. If you use quantum mechanics then maybe the answer will come to you.
- sabas123 6y agoTo create a bit more serieus response. 'I wonder if' is not the problem here, it is that it isn't even wrong on so many levels. https://en.wikipedia.org/wiki/Not_even_wrong https://en.wikipedia.org/wiki/Not_even_wrong
- boyobo 6y agoThis particular comment was probably downvoted because he basically just took the hottest buzzword of the last decade and inserted it with a very weak link to the topic at hand. You could copy and paste this comment to any article about any achievement and it would have the same relevance. It is certainly not a “new way of thinking”. First of all, there is hardly any thought here. Secondly, “understanding deep learning mathematically” is a well known problem to mathematicians. It is a comment that could have been generated by an (old, 2000s era) AI.
- bigdict 6y agoThis sort of news is always like a splash of cold water to the face to me. I haven't produced any breakthrough research as an undergraduate. Have I accomplished enough? Am I too complacent? Should I be doing more, working more, studying more? I always remember that the best way to achievement is to stick to areas that are personally exciting to me, and keep cranking at the best pace I can. Others' success shouldn't make you anxious. Instead, let it motivate you to move faster along your own groove.
- im3w1l 6y agoIf you have a roof over your head and food on the table you are doing enough. Anything beyond that is either for your enjoyment or to feed your ego.
- gigatexal 6y agoThis is the only way to not go insane with I’m-not-not-doing-as-much-as-person-x syndrome.
- bg117 6y ago:)
- ThePadawan 6y agoHey, so, I get the sentiment, and I want to thank you for that. I also want to point out that that sort of thinking also is what traps people in abusive households etc.. If anyone is reading this and all you have is a roof over your head and food on the table, that doesn't mean you have to be happy like that. (Sorry if I'm overstepping).
- princeb 6y agoinstead of breaking new ground in statistics, i'm using 100% of my brain's ability to add, minus, multiply and divide to squeeze another 0.003 bps in trade execution. i sleep soundly at night knowing that there are guys who are way smarter than me doing even sillier things than me.
- prvc 6y agoA bit of a fluff piece; sadly short on details.
- hankchinaski 6y agohttps://arxiv.org/pdf/2005.09251.pdf https://arxiv.org/pdf/2005.09251.pdf
- MaximumYComb 6y agoI was having a discussion recently in another forum where I argued that success at a Math Olympiad is a good indicator of future success. I'm not surprised to see in the slightest he won a gold medal at 16.
- munchbunny 6y agoThat doesn’t seem like a hot take to me. Success at a Math Olympiad (at the international level) is almost certainly a good indicator because you have to be an outlier in both talent and willingness to grind in order to get that far, and that level of achievement is the type of success that snowballs because people respect the achievement.
- MaximumYComb 6y agoYou'd think it would be a hot take but I had someone arguing against me that it's not a good indicator since only approx 20% of competitors get a PhD in Math. I felt that he was emotionally invested in his argument, likely due to wanting to do a math PhD and not being food at the competitions. I even agreed that you don't need to be good at competitions to get a PhD but he still kept to his argument that being good doesn't help at all
- lordnacho 6y agoWhat's a "hot take"? I agree with the answer above. You need to pour a fair bit of effort into getting on an Olympiad team. Whether you get a PhD is more a question of economics, IMO. If you're showing that much promise there will be many other temptations, and bear in mind it's not just rich countries that have math kids, there's plenty of olympiad kids who need to get out and make money when they've done their degrees. The kind of work you do in a PhD is also quite different. A math contest is a few questions with definite answers and a time limit.
- benrbray 6y ago> What's a "hot take"? It's slang for "unsubstantiated opinion likely to incite controversy". Weird how this word started appearing everywhere suddenly in the last few months.
- deleted 6y ago[deleted]
- vjk 6y agoGreat article - very inspiring to hear about his collaboration with another undergraduate at MIT over 3 years, and the joint awards they've won together. My undergraduate graph theory textbook had this quote from Paul Erdos: " Suppose aliens invade the earth and threaten to obliterate it in a year's time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world's best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack." In other words - some of the basic questions about these unbelievably small numbers (that you could count on your hands and toes) are so difficult, they push the limits of human ingenuity.
- spekcular 6y agoEven for R(5,5), we're probably better off with the preemptive attack, according to a researcher in the area: https://mathoverflow.net/questions/210653/algorithms-for-calculating-r5-5-and-r6-6/210746#210746 https://mathoverflow.net/questions/210653/algorithms-for-cal....
- swirepe 6y ago>we're probably better off with the preemptive attack This is true for most problems.
- therein 6y agoWhat if they had been observing us for a while and aware of our true limitations and were posting this question as a test to see if we were capable of recognizing our own limitations as a species and resolve it through rational means rather than conflict? We would have failed greatly in that case with that preemptive attack.
- lupire 6y ago5 is a small number, but "Ramsey" isn't.
- blululu 6y ago"If you're the smartest person in the room, you're probably in the wrong room". Science journalism has its place, but it can simplify things beyond the point of being educational. If you don't mind feeling a little dumb you can get the information straight from the source: https://yufeizhao.com/blog/ https://yufeizhao.com/blog/ https://arxiv.org/search/math?searchtype=author&query=Sah%2C+A https://arxiv.org/search/math?searchtype=author&query=Sah%2C...
- thomasahle 6y agoFor the Ramsay paper in particular (with a short easy to read introduction): https://arxiv.org/pdf/2005.09251.pdf https://arxiv.org/pdf/2005.09251.pdf
- jb775 6y agoWonder how he'd hold up in a modern programming interview. I'd say 75% chance he'd be thrown an obscure curveball and be completely written off by the hiring company.
- qzw 6y agoNah, the IMO gold medal on his resume alone puts him into a different category. Unless the hiring company is completely clueless, he’d get special treatment from the start. People like him are not like you and me.
- Kephael 6y agoThis is wrong, for a programming interview FAANG and friends care greatly about mitigating legal risk and would not treat them any differently. Interviewers typically have their own questions and may have only glanced at the resume.
- darkwizard42 6y agoThis kind of candidate would be handheld by a very specific part of the recruiting team who would no doubt realize that they are dealing with someone VERY exceptional... This is not to say that they would get preferential treatment in getting through the interview, but this person would not be interviewed like a regular SWE but by a specialized committee (one probably filled with more research-minded engineering staff) Similarly, the questions would be tailored differently because the expectation of a research mind would NOT be strictly coding features / fixing bugs, but probably doing research
- Kephael 6y agoThere are very specific coding expectations for applied scientists and research interns at these companies. They are not going to allow someone to skip these.
- darawk 6y agoThere is no legal risk for fast tracking exceptional people.
- ShroudedNight 6y agoI wonder how productive Sah would be if he hadn't encountered Sawhney. In my experience, there's something almost mystical about finding a highly compatible partner-in-crime. While I recognize that we (broadly) like to idolize particularly effective individuals, I feel we risk essentially dishonouring the dynamic when we focus so intently and exclusively on just one member of this kind of deeply collaborative union.
- lordnacho 6y agoThis is perhaps one of my biggest downside surprises about university. Although there were plenty of fun people to hang out with, there were very few people who had a seriousness about getting work done, along with a collaborative instinct. Maybe I was unlucky, but I'd thought that an Oxbridge college would yield a few people who could keep me focussed on the academics. And yes, in another world I would have brought the motivation myself, but like many people, I am influenced by my environment. If you've ever coded with someone you click with, you might have had this experience of generating way more useful code than 2x people working on their own, or what one person could do in 2x the time.
- runawaybottle 6y agoIntellectualism hasn’t matured as Barbarism has (still going through refinement). Your gym partner is never going to even attempt to prove to you they are stronger, and you yourself won’t even care if they are (or vice versa). There’s a natural understanding of the physical, and mostly we as a society realize how futile it is to exert physical dominance on one another. So you are stronger, what are you going to do, beat me up every day? We realize this is a stupid game. Ironically, it’s the intellectual stuff that hasn’t come full circle. So you’re smarter, is your plan to just out smart me everyday? Well actually, yes, that is the plan. I will out smart you, establish dominance, hierarchy, status etc - all of which is systemically quantified via prestige, status, income, life partners (all the stupid shit physical dominance once got us) . It’s hard to find synergy in this realm when we as a society haven’t gotten over ourselves on this front, the same way we got over all that physical beat people up bullshit. We haven’t yet accepted that this too is a waste of time in the context of civilization. We are all more than capable of collaborating intellectually, but as a society we are just too dumb at the moment to do so. Hard to collaborate with barbaric intellectuals. Long story short, you are probably part of the problem, as we all are at this inflection point in humanity.
- divtiwari 6y agoSome times I feel inferior while reading such stories, they are of almost the same age as me. Even though I am very well placed in my career sometimes it just stings :(
- rendall 6y agoBe the best person you can be while also being gentle and loving to yourself. There will always be someone better than you at everything you can think of. Running, mathematics, chess, programming, kite flying, writing whimsical poems, whatever There are also people who are not good at those things who nevertheless gain tremendous satisfaction from doing them and getting better at them. Are you on the side of good? That's all that matters, really
- michaelt 6y ago"It's people like that who make you realize how little you've accomplished. It's a sobering thought, for example, that, when Mozart was my age, he had been dead for two years." -- Tom Lehrer
- commandlinefan 6y agoIf it makes you feel better, I'm over twice his age and don't have anywhere near these types of accomplishments either.
- tester34 6y ago>He has done enough work as an undergraduate to get a faculty position what a reward - academia job!
- boyobo 6y agoMost academic jobs are crap precisely because they are not tenured faculty positions at good universities.
- The_rationalist 6y agoAre there any use case of this discover beyond iet being impressive?
- blankton 6y agoGraph Theory in General is extremly useful for all sorts of algorithms [1]. What the application for this particular discovery might be is also unknown to me. [1]https://mypages.valdosta.edu/dgibson/sjs.pdf https://mypages.valdosta.edu/dgibson/sjs.pdf
- darkwizard42 6y agoI think the initial work is impressive partly because of how broad the range of topics the partnership has tackled AND how young they are. They are barely into their post-doc studies and are already making progress on challenging problems in the graph theory and combi space. Basically, its impressive to make this level of contribution as an undergraduate team AND if they keep up this level of productivity the "big" discoveries will come in the coming years.
- AndrewBissell 6y agoThis reminds me of a story I heard about Paul Erdos while studying graph theory as an undergrad. He is supposed to have said (not sure if this is confirmed or apocryphal) that if all-powerful aliens ever come to earth and demand that we give them the 5:5 Ramsey number, society should marshal all of its resources in trying to find it. If, on the other hand, they demand the 6:6 Ramsey number, we should attempt (hopeless as it may be) to fight the aliens.
- darkwizard42 6y agoAfter reading this I think the most impressive piece is how productive Sah and Sawhney have been in their partnership just as undergrads! For those reading, the work on graph theory they have done is impressive but yes...not about to change our understanding of how the world works or unlock some new technology. What is impressive is how young they are to be pursuing this level of rigor and work. It means there is a potentially really high ceiling of what COULD be produced by these minds. I find it important to recognize great work like this to encourage people to do research, even if the initial result feels incredibly niche or irrelevant. Great research seems to be a combo of time and persistence so this is a relevant first step!
- Cerium 6y agoVery cool. I just took a course on graph theory, and immediately though of the Ramsey numbers. Sure enough he made some progress there. What makes the Ramsey numbers fascinating to me is that they are a problem that goes from pen and paper trivial to computer solvable, to completely intractable in only 3 steps. A brute force proof of the R(5,5) case would involve testing 2⁹⁰⁵ (2^905) graphs.
- TT3351 6y agoThis surprised me: "“We meet once or twice a day for five or six hours,” said Sawhney. “Even when we’re not meeting, we’re just constantly messaging each other.”" That's a lot of math time!
- urmish 6y agoHe did a talk about it too: https://www.youtube.com/watch?v=S_LioI6xJ-g https://www.youtube.com/watch?v=S_LioI6xJ-g