Undergraduate Math Student Pushes Frontier of Graph Theory
quantamagazine.org
quantamagazine.org
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.
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.
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.
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.
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.
> 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.
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.
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.
- 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.
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).
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.
https://arxiv.org/search/math?searchtype=author&query=Sah%2C...
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 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.
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 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!
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
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 :));
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.
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.
'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
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.
what a reward - academia job!
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.
I'd say 75% chance he'd be thrown an obscure curveball and be completely written off by the hiring company.
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.
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
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.