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 :));
I 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.
This 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.
You know, some of us work in the field that you call "hottest buzzword of the last decade", we constantly see problems that could have benefited enormously from geniuses like above.
So for people like me at least, it's not a "very weak link to the topic at hand".
I already agreed that the op was hinting at an important problem. The link is weak because the op put hardly any effort into explaining the (possible) connection to these two particular undergraduates and their work. I am not claiming that math and deep learning are unrelated. Please read the rest of my response for context.
BTW, I am not using 'hottest buzzword of the decade' to denigrate the field of deep learning. I am using it to emphasize the op's shallow reference to the field.
Given that particular link at the end of the comment with no additional commentary on why that particular link, the comment feels like thinly disguised spam to me. I'm glad it got downvoted.
I'm honestly having a hard time picturing what kind of discussion or brainstorming could be had around the statement in said comment. "It might be useful to have more smart people working in [popular field]" in the context of "look at this smart person" is just... unactionable?
Further, it is unclear what the link to a conference is supposed to add - is this actually an attempt to get said mathematician to completely switch fields on a whim? Based on a HN comment? That's just uncalled for... Or is it trying to recruit random HN readers? In that case, how is this at all related to the topic?
Like in any group of humans, it takes a certain perspective and tone to communicate your ideas effectively - doubly so if you want to engage in "new ways of thinking" with others. The comment in question is lacking that (in my - subjective - eyes). I don't think "I wonder if" is misplaced on HN, but I would concur that (as you hinted at) a certain way of articulation is rewarded.
This 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.
instead 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.
I don't think having one's life satisfaction being a function of comparing yourself to other people is ever healthy, but this attitude seems especially unfortunate. Maybe their doing sillier things means they are, ipso facto, not smarter than you, or at least better than you in a way that matters?
He's one in a 1000/10000/100000/etc. - don't feel too bad.
Most work is never going to anywhere, no mater how smart or talented you are. Tons of highly intelligent and motivated people out there, working on dead-end projects. (not that there's not any value in such work, but for the vast majority, we're not going to be single contributors that significantly move the needle).
Most post-graduate researchers don't produce any breakthrough research. The produce incremental improvements, moderately interesting findings, etc. Or often, inconclusive results. Breakthroughs are rare.
I think you need a confluence of fortuitous circumstances to get things like this done:
- You need to have your own psychology in order. A lot of people have things going on in their lives that make it impossible to concentrate on this sort of thing.
- You need to be close enough, background wise. No prereqs -> can't learn this subject.
- You need to be aware of where the low hanging fruit is. This might be some random comment by a lecturer or a line in a paper that makes you investigate something.
- You need access to resources. Anything from a sparring partner to a hadron collider might be needed.
- Timing. Bunch of stuff coming together, might happen 10 years before you or 10 years after.
So there's reasons why undergrads don't always come up with groundbreaking things. Not to worry. You can still try to understand stuff after someone else has found it.
It’s important to focus on the pleasure of practicing and honing a craft. I don’t think either of these guys are doing this for notoriety. They’re doing it because they love math.
If you're getting imposter syndrome while still in school, buckle up :)
If getting things done is your goal, then put energy into it. That's what very accomplished people do. Just accept that's not always enough and accept that's alright. Doing the best you can is literally all you can do.
I 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.
That 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.
You'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
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.
It's slang for "unsubstantiated opinion likely to incite controversy". Weird how this word started appearing everywhere suddenly in the last few months.
It's an easy form of self-effacement. If I state my opinion and someone proves me wrong, I'd look silly at best, or risk cancellation at worst. If I preface by saying it's a hot take, I can easily distance myself from what I said if it's received badly.
I use "hot take" to mean someone is stating an opinion (there is not enough evidence so this is an opinion at best), that they're stating it with probably more intensity/confidence than it deserves, and that you'd expect the opinion to be controversial.
In this case, by "that doesn't seem like a hot take to me" I mean that as far as opinions go this seems pretty uncontroversial.
> I had someone arguing against me that it's not a good indicator since only approx 20% of competitors get a PhD in Math
As lordnacho says, that argument doesn't hold up at all. 20% seems really high, to me. A PhD in math isn't like scoring highly on an IQ test, it's not purely the result of being mathematically capable, it's also the result of undertaking a PhD in math. Plenty of smart people apply their abilities elsewhere. Perhaps in finance, for instance.
Also, I'd guess that the Olympiad winners who started a math PhD were more likely to succeed than the average math PhD student, and more likely than average to eventually get tenure.
I had multiple typos. When I made these comments I was coming off a 40.1 degree fever and was laying in bed with my phone when I saw this post. I wrote some hand notes too and they're even worse. The same word is spelled incorrectly in two different ways.
In computer science world, I've personally noticed there is a dismissive attitude towards programming competitions among many, including some of my teachers. Here, it is a hot take.
I never understood this sentiment though. Competitions like ICPC aren't like silly quizzes, you need to have incredibly good understanding of algorithms and data structures. Now I understand that the breadth required here is of course broader than anything a programmer likely to use in an "average" programming task, but then again you shouldn't compare a ICPC finalist with an average programmer either.
It really depends on what you're trying to correlate. When it comes to trying to read anything out of how someone does in something like ICPC, I compare it to doing well as an athlete: there's definitely something transferrable in there, but it's hard to claim that it's any specific technical skills.
If you're good at competition programming, you can probably sling code pretty well, but that doesn't mean you're good at writing maintainable code in team contexts. But if there aren't other red flags I'd take it as positive signal that you're smart enough and hard-working enough to learn to do it quickly.
I think this difference stems from how easy it is to apply and display your skills to projects outside of competitions. I mean, how are you going to demonstrate your mathematical problem solving skills to an employer in a side project? "I research the Collatz conjecture in my free time?"
Contrast that with programming, where there are practical challenges abound whichever way you look. So those choosing to participate in competitions instead presumably have a much more narrow range of motivations. I can't tell you why this should translate into dismissing these people, but there is certainly a difference.
The math olympiad success underestimates him.
I would say that in terms of mathematical abilities, Gold on the IMO <---> tenure at a top-100 university.
I think the level of productivity he has shown in just his undergrad is crazy! I think you are right that if he holds this up it will be exciting to see what comes next.
Even 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.
I 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.
I 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.
Great 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.
What 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.
"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/
Nah, 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.
This 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.
This 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
There are very specific coding expectations for applied scientists and research interns at these companies. They are not going to allow someone to skip these.
I 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.
This 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.
Intellectualism 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.
As a follow-up to this line of thought (which I find insightful): if we were to become mature with regards to intellectualism as you say - do you think we would then go on to the next thing to be competitive about? Or maybe we need that next thing to trigger our maturing, as a consequence of competition switching to another domain?
Or, is it possible that competition about important matters is not an inherently human trait, and we could actually just all switch to deeply caring about who is best at Trackmania or who follows the best football team or whatever?
In some sense a sizeable portion of the human population has already done the latter - perhaps they are actually the enlightened ones?
(I'm assuming that competition is important for humans, since this seems to be a well established fact. The question here is whether the competitiveness needs to be about factors related to your intellect and studies/workplace achievements.)
I guess I’ll use the lame saying
‘Bar is closing, you don’t have to go home, but you can’t stay here’ as to what will solve it.
I get people have underpinnings of nature that enflame instincts. That’s great, but you know, when it impacts people’s lives - it needs to find another place to party.
I hope that makes sense. Hitler ad-reductio incoming. Hey, Germany, I get your bullshit pulled you out of the depths of WW1, but look, your nonsense is killing millions of people.
Just find another abstract gutter for your nonsense, find another means of self fulfillment, please, and don’t hurt anyone.
We don’t have to placate every human instinct and constantly romanticize every aspect of the human struggle. Life is absolutely requires empathy and stability.
I've never seen this verbalized before, but it makes a lot of sense.
> 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)
This seems like it will be very hard to get rid of compared to physical dominance. Partly because smarts are far less straightforward than physicality, and partly because it would be a systemic change.
> we as a society realize how futile it is to exert physical dominance on one another
A more cynical explanation may say it only disappeared was because we discovered the more /effective/ way to exert dominance on others was mentally, not physically. It wasn't due to any collective enlightenment about the sociological futility of domination -- it was merely a desire to achieve better logistics.
Very well written. I always preferred mathematics to chess, because the competitive aspect of chess always seemed to hinder collaboration.
Seeing the same lack of collaboration in university was really disappointing. Friendly people listened passively, less friendly people liked to listen and contradict. The willingness to actually share knowledge seemed to be almost non-existent.
I haven't solved the puzzle yet why sharing knowledge is so hard. Some people don't have knowledge to share, some want to keep an advantage, and the barbaric instincts to reject unfamiliar ideas tramples the remaining few sparks.
Noticing my own barbaric instincts in action was enlightening.
What a bizarre claim. Physical competitiveness is a huge part of culture. You don't need to beat someot up to physically intimidate and dominate someone, and you don't need to mentally abuse someone to have a valuable experience in a relationship.
Physical dominance found many abstract gutters to empty into, and necessarily so. It was literally destroying the world with violence.
The Roman identity was literally built on conquering. It took a long time until we were able to say ‘yeah, why can’t this small little land mass be it’s own country?’. Why would a country have to fight for independence? Can you imagine that in today’s society? It’s absurd. Yet, many of our countries had to ... fight for independence. What kind of world was that? A world where dominance wasn’t an undercurrent?
Intellectual dominance hasn’t found socially acceptable gutters, it literally pays in society. Esports and video games is a band aid. The underlying trait is dominance. I can’t prove my thesis in two paragraphs I suppose, but you’ll have to forgive me for that.
Dominant behavior is dysfunctional, and since it is an underlying human trait, it reincarnates itself constantly. Racism and classism are all forms of it, under the umbrella of elitism.
Why can’t my unfit brother go to the same gym I worked hard to get into? Sounds crazy right? Well he’s fat, he didn’t earn it, etc. We don’t even contemplate this anymore physically. Yet, why can’t someone also work at Google because they aren’t the best? Intellectualism at the moment rejects ‘it takes a village’, and it rejects ‘the hand cannot say I am not of the body’.
So be it, it’s just the dark ages. One day we’ll figure it out, as we did with the other manifestation of dominance.
My most serious point is this - the nonsense cannot and should not affect people’s livelihoods. Find the abstract gutter for the nonsense already, and do not fuck with people with your meta game.
Would you agree that the fastest/least harmful way to get to that place is to codify practices/laws at the level of a nation-state, or do you think that's ridiculous and it'll just be some organic development of individuals opting for that type of behavior?
So, I’ll give away a little bit of my teenage naivety (pretty old now relative to my 20s, still a child to some here) in that lately I’ve been influenced by some serious reading on the Holocaust and Nazi-Soviet dystopian ideas. In a sense, we really didn’t see the insanity until it fulfilled it’s natural conclusion (a disgusting simile to the final solution). Such a pattern is more common place amongst addicts, who basically need to bottom out until they get it.
The sadness is that I know it must play out before we can come to the table and solve it.
In other words, there’s no shortcuts, and we have to see it through to the end to prove it, no inductive step. No theory in this.
This is the reason I struggle so much with distance learning during corona. Usually I find partners in my classes to review the lecture with and work on the assignment in parallel. I get so much drive, energy and fun just by not being alone and discussing concepts together. Since I am in my masters, I can freely choose the lectures I want and often don't know anyone in class and rely on making friends in the first week(s). So I am way more on my own during corona and feel like I am fighting alone against the quite demanding lectures. It's not easy and it's just not as fun anymore. I feel like I am only trying to survive the exams without the drive to learn and explore.
Agreed, and this one of the worst aspects of our PhD system - graduate students need to have a body of work that is theirs. Even amongst a collaboration, they need to carve out sections that are unquestionably theirs so they can defend a dissertation that is also theirs.
I am now at IBM Research. In my career here, I have experienced multiple working relationships where I feel we were able to accomplish far, far more than at least I know I could have achieved on my own. Maybe they didn't need me, but I know for certain I needed them to be so productive. That this kind of working relationship is disincentivized for graduate students is, to me, tragic.
Some 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 :(
Be 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
"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
Graph 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.
I 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.
This 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.
After 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!
Very 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.
This 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!
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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/
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.
'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
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.
So for people like me at least, it's not a "very weak link to the topic at hand".
BTW, I am not using 'hottest buzzword of the decade' to denigrate the field of deep learning. I am using it to emphasize the op's shallow reference to the field.
Further, it is unclear what the link to a conference is supposed to add - is this actually an attempt to get said mathematician to completely switch fields on a whim? Based on a HN comment? That's just uncalled for... Or is it trying to recruit random HN readers? In that case, how is this at all related to the topic?
Like in any group of humans, it takes a certain perspective and tone to communicate your ideas effectively - doubly so if you want to engage in "new ways of thinking" with others. The comment in question is lacking that (in my - subjective - eyes). I don't think "I wonder if" is misplaced on HN, but I would concur that (as you hinted at) a certain way of articulation is rewarded.
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.
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).
i sleep soundly at night knowing that there are guys who are way smarter than me doing even sillier things than me.
Most work is never going to anywhere, no mater how smart or talented you are. Tons of highly intelligent and motivated people out there, working on dead-end projects. (not that there's not any value in such work, but for the vast majority, we're not going to be single contributors that significantly move the needle).
- You need to have your own psychology in order. A lot of people have things going on in their lives that make it impossible to concentrate on this sort of thing.
- You need to be close enough, background wise. No prereqs -> can't learn this subject.
- You need to be aware of where the low hanging fruit is. This might be some random comment by a lecturer or a line in a paper that makes you investigate something.
- You need access to resources. Anything from a sparring partner to a hadron collider might be needed.
- Timing. Bunch of stuff coming together, might happen 10 years before you or 10 years after.
So there's reasons why undergrads don't always come up with groundbreaking things. Not to worry. You can still try to understand stuff after someone else has found it.
If getting things done is your goal, then put energy into it. That's what very accomplished people do. Just accept that's not always enough and accept that's alright. Doing the best you can is literally all you can do.
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.
It's slang for "unsubstantiated opinion likely to incite controversy". Weird how this word started appearing everywhere suddenly in the last few months.
In this case, by "that doesn't seem like a hot take to me" I mean that as far as opinions go this seems pretty uncontroversial.
As lordnacho says, that argument doesn't hold up at all. 20% seems really high, to me. A PhD in math isn't like scoring highly on an IQ test, it's not purely the result of being mathematically capable, it's also the result of undertaking a PhD in math. Plenty of smart people apply their abilities elsewhere. Perhaps in finance, for instance.
Also, I'd guess that the Olympiad winners who started a math PhD were more likely to succeed than the average math PhD student, and more likely than average to eventually get tenure.
> not being food at the competitions
I rather like this typo ;-P
I never understood this sentiment though. Competitions like ICPC aren't like silly quizzes, you need to have incredibly good understanding of algorithms and data structures. Now I understand that the breadth required here is of course broader than anything a programmer likely to use in an "average" programming task, but then again you shouldn't compare a ICPC finalist with an average programmer either.
If you're good at competition programming, you can probably sling code pretty well, but that doesn't mean you're good at writing maintainable code in team contexts. But if there aren't other red flags I'd take it as positive signal that you're smart enough and hard-working enough to learn to do it quickly.
Contrast that with programming, where there are practical challenges abound whichever way you look. So those choosing to participate in competitions instead presumably have a much more narrow range of motivations. I can't tell you why this should translate into dismissing these people, but there is certainly a difference.
Aswhin will maybe be a Fields medal candidate.
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.
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.
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.
This is true for most problems.
We would have failed greatly in that case with that preemptive attack.
https://arxiv.org/search/math?searchtype=author&query=Sah%2C...
I'd say 75% chance he'd be thrown an obscure curveball and be completely written off by the hiring company.
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
As an undergrad, I got cold emails from the following companies: Jane Street, Citadel, Two Sigma, and several less known hedge fund/quant stuff.
Those were all for trading/analyst positions. Western companies never reply for software internship applications.
Google mails me every year and as if I want to interview for full-time, but they don't interview me when I apply for internships.
I got an intership offer from a big non-Western company, but I didn't get a work visa.
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.
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.
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.
Or, is it possible that competition about important matters is not an inherently human trait, and we could actually just all switch to deeply caring about who is best at Trackmania or who follows the best football team or whatever?
In some sense a sizeable portion of the human population has already done the latter - perhaps they are actually the enlightened ones?
(I'm assuming that competition is important for humans, since this seems to be a well established fact. The question here is whether the competitiveness needs to be about factors related to your intellect and studies/workplace achievements.)
I get people have underpinnings of nature that enflame instincts. That’s great, but you know, when it impacts people’s lives - it needs to find another place to party.
I hope that makes sense. Hitler ad-reductio incoming. Hey, Germany, I get your bullshit pulled you out of the depths of WW1, but look, your nonsense is killing millions of people.
Just find another abstract gutter for your nonsense, find another means of self fulfillment, please, and don’t hurt anyone.
We don’t have to placate every human instinct and constantly romanticize every aspect of the human struggle. Life is absolutely requires empathy and stability.
> 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)
This seems like it will be very hard to get rid of compared to physical dominance. Partly because smarts are far less straightforward than physicality, and partly because it would be a systemic change.
A more cynical explanation may say it only disappeared was because we discovered the more /effective/ way to exert dominance on others was mentally, not physically. It wasn't due to any collective enlightenment about the sociological futility of domination -- it was merely a desire to achieve better logistics.
Seeing the same lack of collaboration in university was really disappointing. Friendly people listened passively, less friendly people liked to listen and contradict. The willingness to actually share knowledge seemed to be almost non-existent.
I haven't solved the puzzle yet why sharing knowledge is so hard. Some people don't have knowledge to share, some want to keep an advantage, and the barbaric instincts to reject unfamiliar ideas tramples the remaining few sparks.
Noticing my own barbaric instincts in action was enlightening.
It’s why the paradise birds dance.
Being physically fit used to be the main factor and while it still helps today, it’s only one smaller component of status.
I don’t see the physical fitness and intellectual posturing as two distinct areas that have separately matured.
It’s one sexual selection continuum - only the environment and what’s adaptive for attracting mates has changed.
There’s a new dance to learn.
I don’t think this is something we can easily overcome.
The Roman identity was literally built on conquering. It took a long time until we were able to say ‘yeah, why can’t this small little land mass be it’s own country?’. Why would a country have to fight for independence? Can you imagine that in today’s society? It’s absurd. Yet, many of our countries had to ... fight for independence. What kind of world was that? A world where dominance wasn’t an undercurrent?
Intellectual dominance hasn’t found socially acceptable gutters, it literally pays in society. Esports and video games is a band aid. The underlying trait is dominance. I can’t prove my thesis in two paragraphs I suppose, but you’ll have to forgive me for that.
Dominant behavior is dysfunctional, and since it is an underlying human trait, it reincarnates itself constantly. Racism and classism are all forms of it, under the umbrella of elitism.
Why can’t my unfit brother go to the same gym I worked hard to get into? Sounds crazy right? Well he’s fat, he didn’t earn it, etc. We don’t even contemplate this anymore physically. Yet, why can’t someone also work at Google because they aren’t the best? Intellectualism at the moment rejects ‘it takes a village’, and it rejects ‘the hand cannot say I am not of the body’.
So be it, it’s just the dark ages. One day we’ll figure it out, as we did with the other manifestation of dominance.
My most serious point is this - the nonsense cannot and should not affect people’s livelihoods. Find the abstract gutter for the nonsense already, and do not fuck with people with your meta game.
The sadness is that I know it must play out before we can come to the table and solve it.
In other words, there’s no shortcuts, and we have to see it through to the end to prove it, no inductive step. No theory in this.
Except you get to see it without any of the rationalizations that we make. You get the raw distillation of this behavior.
It'll never change.
I am now at IBM Research. In my career here, I have experienced multiple working relationships where I feel we were able to accomplish far, far more than at least I know I could have achieved on my own. Maybe they didn't need me, but I know for certain I needed them to be so productive. That this kind of working relationship is disincentivized for graduate students is, to me, tragic.
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
what a reward - academia job!
[1]https://mypages.valdosta.edu/dgibson/sjs.pdf
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.
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!