"The work showed that “you don’t need space to do geometry,” Huh said. “That made me really fundamentally rethink what geometry is.”"
That is one of the most thought provoking things I have ever read.
creakingstairs · 11h ago
It wasn’t the case for him but I’d like people to also note that in Korea, one of the strategy for getting into good universities is to actually drop out of high school and grind for the national exam by going to cram schools (hagwon)
People do this because there are certain admission categories where the university only looks at the test results. So they go “okay, by not going to school, my child can fully focus on exam instead of wasting time on useless subjects like art and PE. And school math curriculum is too easy anyway”
This really saddens me because schools should be more than gateways to universities, but I digress.
DrBenCarson · 11h ago
That is very sad but understandable, incentivize is hard to overcome
Universities should be looking at more and discouraging 1 dimensional applicants
331c8c71 · 9h ago
> Universities should be looking at more and discouraging 1 dimensional applicants
Sure. Like there is a whole field of consultants who would help your child to develop a suitable profile.
Moreover, I the US I heard there is an industry for generating experiences for the "young minds" (if their parents are rich enough) e.g. discovering rennaissance via a trip to Italy etc.
Also remember the tennis scam for admissions? Gordon Ernst from Georgetown U.
DrBenCarson · 9h ago
Look I’m a first generation American with a sister 3 years younger. We grew up in poverty in the 2008 aftermath. Like food stamps and stretching leftovers by mixing them with pasta broke
I navigated the system alone for myself then again to help her after I had learned from all my college friends. We both went to “prestigious private schools” with single digit acceptance rates and have similarly “prestigious” jobs
Here’s the truth: yes, like everything else in this world it’s a LOT easier with money. But it’s not impossible if you’re willing to understand the expectations and put in the work to meet them.
lordnacho · 8h ago
"I did it so it isn't impossible"
Not really convincing. How many poor kids did not even come to an understanding of how the admission system works? How many kids did not even know what work was to be put in?
I am also someone born at the bottom (my first passport was a convention of 1951 passport), who went to a world famous university. As I've gotten older, I've realized it's not really a useful way to think about it. We like to say "you can do it if you really try", but it's just not true. Not only is it not true, it's a thought-ending statement that makes it easier for rich kids and harder for poor kids, because why would you need to support the poor kids if they can just work really hard?
Even you have to be able to see that you got lucky. When I applied, the entrance rate for my course was about 8%. I had no idea that I could have tried easier courses, or that I could have filled the form in slightly differently for a better shot. A single-digit acceptance rate is a lottery. You could do everything the same again and not get in. You don't realize it when you get in, because you happen to get questions that you can answer, but there's a heck of a lot of questions an Oxford professor can ask an 18 year old that will make him look bad.
When I arrived, of course all the other kids were ordinary upper middle class kids. People went to feeder schools where they teach you how to do the Oxbridge interview. People who didn't grow up pinching every penny. What happened to the poor, hard-working kids? They're mostly not there.
jajko · 6h ago
What about stepping back a bit and realizing that proper life success has almost nothing to do with school you go to? I am not saying not going to school per se, but this hard focus on career as soon as possible... where is focus on quality of life for example?
Optimizing hard for some rat race for some soulless (or soul crushing) office jobs among high functioning sociopaths that management inevitably always is. Most of those folks are not properly happy by any measure, thats not a win in life to end up there nor something to respect.
We are in rather unique period of time, especially folks here, that life fulfillment and happiness can be achieved for almost everybody and not just some top 0.1% if correct direction is taken. How about we realized that and focused more on actually long term important aspects of life?
(here is another guy who went the proverbial rags-to-modest-riches on my own but I would never had such mindset, when talking about successes of my life its about countries I've travelled, people I've met and intense experiences that shaped me more than career paths taken)
lordnacho · 5h ago
Yes, absolutely. The one thing I have quipped about with my kid's school is this: Everyone is scared to death of their kid not being able to get the job that they are hating.
I live in a bit of a bubble where pretty much every kid's parents are professionals. Some of these people are off to London before the kids are in school, and arrive back home after they are asleep.
People spend a lot of money on top of private school to get a tutor in order to get into the grammar schools. This is a pure loss for society: the wrong kids get in, since not everyone can afford to learn this particular test. And money is spent on reducing the kids' free time for exploration.
smus · 1h ago
What school you attend super measurably affects future earnings
lazyasciiart · 4h ago
It's not impossible to be the fastest Olympic swimmer in the world, and it's a LOT easier with money. But, just like your story, you can't guarantee it will happen by "understanding the expectations and putting in the work to meet them".
monkeyelite · 1h ago
Let me tell an alternative story. I didn’t even apply to college because nobody told me I should, or explained when that happens, etc.
pbhjpbhj · 5h ago
As orphans (?) did you get scholarships to the private school? I'm curious if you couldn't afford to eat, how the school worked out? Did the jobs come through school connections?
piva00 · 7h ago
> Here’s the truth: yes, like everything else in this world it’s a LOT easier with money. But it’s not impossible if you’re willing to understand the expectations and put in the work to meet them.
How many others have tried to put the work you did and didn't achieve it?
I think that's the crux of it, being possible doesn't mean anything if it shuts out the majority of the ones who attempt it. It's possible to become a professional athlete and still a lot more kids fail to achieve that even if they put the work for it. Contrary to being a professional athlete, good education is both much more accessible and much more needed.
Exactly because you managed to achieve it that I believe there should be more empathy for how fucked up the system is, imagine how much less suffering you would have gone through if there was a better way? Why not work for it to be a better way even though it's already possible?
rcxdude · 3h ago
University admissions are generally aware such things exist, though. And if they're actually evaluating on chance of success at university, will take that kind of thing into account. (I.e. a kid from a poor background and a bad school who manages to get good grades will be given priority over a rich kid who went to a good school and got perfect grades. Often the limiting factor for the former in terms of admission to a top university is that they're not ever told that it's a realistic option for them and so they don't even apply).
david927 · 1h ago
> Universities should be looking at more and discouraging 1 dimensional applicants
They really, really do. Admission to top universities has become hyper competitive. They're getting tens of thousands of highly qualified applicants with perfect GPAs and great SAT scores. So what they're looking at is more, "Will admission to this university help them to do something special?" or is admission the end goal for the student. And one way to see that is if the applicant is well-rounded and explorative. Are they setting creative fires everywhere they go?
klooney · 58m ago
> discouraging 1 dimensional applicants
Often when you look at the other dimensions, it's a way for the admissions office to smuggle in criteria that other people find objectionable.
android521 · 6h ago
Massive corruption and discrimination (like discrimination against asian students in US universities) would take place if you introduce more dimensions (most of them are subjective and can be gamed)
willvarfar · 3h ago
Are all the applicants who find school unfulfilling so skip it to go straight to university 1 dimensional? For example, some might be more mature than their peers and are going to flower at university.
bko · 3h ago
Disagree. Peter Thiel wrote about this in zero to one. The "well rounded" candidate is essentially hedging their bets. An indefinite optimist.
> You can expect the future to take a definite form or you can treat it as hazily uncertain. If you treat the
future as something definite, it makes sense to understand it in advance and to work to shape it. But if
you expect an indefinite future ruled by randomness, you’ll give up on trying to master it.
Indefinite attitudes to the future explain what’s most dysfunctional in our world today. Process
trumps substance: when people lack concrete plans to carry out, they use formal rules to assemble a
portfolio of various options. This describes Americans today. In middle school, we’re encouraged to
start hoarding “extracurricular activities.” In high school, ambitious students compete even harder to
appear omnicompetent. By the time a student gets to college, he’s spent a decade curating a
bewilderingly diverse résumé to prepare for a completely unknowable future. Come what may, he’s
ready—for nothing in particular.
> A definite view, by contrast, favors firm convictions. Instead of pursuing many-sided mediocrity
and calling it “well-roundedness,” a definite person determines the one best thing to do and then does
it. Instead of working tirelessly to make herself indistinguishable, she strives to be great at something
substantive—to be a monopoly of one. This is not what young people do today, because everyone
around them has long since lost faith in a definite world. No one gets into Stanford by excelling at just
one thing, unless that thing happens to involve throwing or catching a leather ball.
Cramming entrance exams is not super useful, but it does select for motivation and ability to focus intensely. Much more useful measure than having your parents set up a fake charity for you to volunteer at.
trylfthsk · 2h ago
I can understand his distaste for the indefinite, but does he actually make a strong case for the opposite?
To me this reads as claiming "making fragile choices is good", which outside of very niche situations I'd say is bad advice: like telling a college basketball player to not waste time outside of practice and later watching him go undrafted in the pros.
dagw · 2h ago
You also have to look at who is giving the advice. For him it is great if more people take huge risks and burn their youth on moon shot start-ups since, as a VC, he makes all his money off of those people. A world where everybody is a well rounded liberal arts graduate, working a steady job, with comfortable middle class lifestyle and great work life balance would be terrible for him. If you ruin your life following this advice it has zero impact on his life.
He's giving this advice to make his life better, not necessarily to make your life better.
strken · 2h ago
Cramming for an entrance exam is a revolting waste of a life. It's enabled by a system that cannot and will not evaluate students on their ability to commit to something that actually matters.
I agree that "well-rounded" people without depth are not as interesting or as valuable as people who've picked one or more topics to learn in detail, especially since the latter can often be well-rounded and also have an area of expertise. However, a bit part of their value comes from their ability to do something without anyone telling them to do it. An engineer who spent six months writing a protein folding simulator out of obsessive interest is a much better pick for a computational chemistry course than one who spent that time in a cram school.
dkural · 2h ago
This is a straw-man argument. There's value in a well-rounded liberal arts education beyond job preparation. I say this as a math major with a molecular biology PhD. I took multiple classes in history, economics, etc. It allows one to develop healthy critical thinking skills; and also not underestimate the complexity of social issues facing us - in other words, it fortifies you against the likes of Thiel, who has no problem buying politicians with $$ and pushing for his extreme and frankly dangerous political agenda. Conservatives used to understand and value a classical Western education with room for the great works. Authoritarians don't like thinking citizens, however.
asdsadasdasd123 · 11h ago
this whole thing is like a crypto currency exercise where you input x compute for an expected value of y prestige points over 3 yrs
charcircuit · 11h ago
If they look at more than it makes sense to spend more time improving all of those aspects instead of wasting time at school.
DrBenCarson · 10h ago
Which is why American universities require a HS diploma and good grades in a variety of subjects
mattmcknight · 2h ago
But why waste time getting the grade if you could pass the final today?
graycat · 8h ago
The story includes some skipping class yet
getting a Fields Medal.
At least here in the US:
In academics, a grade of A is better than
the rest yet still some independent or
from outside school results can mean more
than grades and even make poor grades
irrelevant.
Some examples:
E.g., for getting into a selective
college, SAT Math scores (from outside of
school) the highest in my high school
class made everything else irrelevant.
E.g., overlooked my F in Typing!
Actually, the Typing class was very
worthwhile and learned touch typing, but
the class was nearly all girls, GORGEOUS,
who buzzed away with perfect accuracy at
maybe 30 characters a second!
E.g., in graduate school, found a problem
and in two weeks got a solution accepted
right away by Mathematical Programming.
Suddenly had an impenetrable shield and
all grades and everything else were
irrelevant.
E.g., before grad school thought of a
problem and had a first solution; in grad school wrote a
first draft; wrote and ran the related
software; and wrote the document, all
independently. Stood for orals and
graduated.
Again, course grades are not everything,
and good independent work can make
everything else irrelevant.
ken47 · 7h ago
Not really possible when success in South Korea is literally like the Squid Games and entrance exams are extremely difficult compared to what Westerners may be accustomed to. I agree the signal provided by this is low-dimensional, but it’s an objective way to measure applicants.
Contains a couple of pop narrative cliches that always turn out to be gaudy exaggerations for journalistic effect: "he came from art, he is driven by beauty! he stunned the mathematical world!", it's bollocks really, and he's no doubt quite embarrassed by this article. He once thought about being a poet, but actually didn't like the work. His parents had a mathematical academic background and he picked that up as an undergraduate. He exhibits fairly typical neurodivergent behaviour of people with ADHD and/or autism. I would like to see journalists start writing about actual poets, or sculptors etc, in this absurdly valourizing, mythologizing way.
jll29 · 7h ago
Imagine every kid had had a maths professor that demonstrated live research in the classroom, like the Japanese teacher that June Huh benefitted from - who knows, the world may be full of similar talent, we will never know.
We should remember not to just present results, but to teach, demonstrate and live how to get there more. It's not even abour rich vs. poor education - almost all go through the whole system never seeing this, and for June Huh, sleeper maths genius, meeting that one person changed everything!
pm215 · 7h ago
There's definitely scope for doing more of that. But notice also that of the 200 students who also got that opportunity alongside him, 195 stopped attending those lectures after just a few weeks;
we don't know about the other 4 but I'm guessing they didn't all change their life trajectories as a result. So you're looking for needles in haystacks, and if you do too much of it you're providing an experience that 95% of your audience concludes is a waste of their time.
smackay · 6h ago
The path of progress is strewn with needles.
wvh · 6h ago
I'm a trail runner. When I look at the ultra runner community, there definitely is a sense that some people have gamified their ancient brains and mastered the skill of short-term inconvenience to obtain long-term success, and it translates to many areas of life. I don't think it's unlikely that somebody is successful in multiple areas; surely you need some natural ability to reach the top in any specific discipline, but if you learn to apply yourself and persist, clearly that can help you in many areas, regardless of innate talent.
My point being that maybe it's not unique sleeper inborn talent, but just learning grit, persistence and well, not being stupid, that will lead to success in life. If one thing doesn't hit, try another. So maybe you don't become a poet, but a math genius, or a soccer player, or a dancer; something else than a TV consumer.
I wonder if this helpful service of integrating past comments on the same story ould be easily automated by looking for repeat URLs (and perhaps clustering old and new comments to integrate them so they can be presented as topical threads).
pbhjpbhj · 5h ago
Dang is a mod here, he's commented previously on how these posts are made, saying they're 'semi-automated'. I imagine if you search for "comments" in their comments you'll find threads with more details.
dhruv3006 · 1h ago
Modern education system is broken.
fjfaase · 16h ago
I wonder if the recurrence equations for the number of spanning trees in the GxP_n graphs also meet the log recuirement.
fjfaase · 8h ago
I wonder if somebody already has scanned the OEIS for all recurrent relations that are "log concave". These are mentioned on https://oeis.org/wiki/Index_to_OEIS:_Section_Rec . just scanning the page, I guess there are not so many that are unimodal and log concave.
jjallen · 4h ago
Very cool that at least in S. Korea one can "mess up" by dropping out of high school and eventually go on to study under, work with, and finally win one of the most prestigious medals in the world. I think this _may_ be possible in the US, but would be much harder. This is isad because the US has a more anyone can do anything culture, which is normally great. But maybe it doesn't exist in some fields/schools/industries.
vonneumannstan · 1h ago
But he did it in the US? Got his PhD at a US University. Works at a US University, did his award winning work in the US. Not sure how this is anything but a US success story?
CommenterPerson · 14h ago
I share quite a few of his quirks. I was also rejected by most of the grad schools I applied to. So how come I didn't amount to anything?
Seriously, a well written article including the accessible explanations of his work. Plus, LoL funny. Thank you.
OisinMoran · 14h ago
It's not over yet my friend
wafflemaker · 12h ago
I've started my bachelor's at 35y, last year. Still waiting for grade on last exam, but it looks like after 4 tries (since 2008) I finally passed the first semester.
mmooss · 12h ago
Congratulations! That takes so much courage - more than most of your classmates have ever had to exercise. The next semester should be easier!
mlsu · 11h ago
I did this too, a little before you (started around 27ish)
The B.S. changed my life. I graduated, you will too.
atonse · 10h ago
Congrats. You’ll get there! Just take it one semester at a time.
jaredhansen · 9h ago
This is the friendliest comment I've seen on the World Wide Web today. Thank you for posting.
jll29 · 7h ago
Quanta Magazine was already brilliant before, but this article has improved the way the cutting-edge work is presented acessibly to (relatifve) laypeople.
So grateful to the late Jim Simons for funding basic research and its popularization (and Quanta Mag.)!
vogon_laureate · 2h ago
Fine, but can he solve the Riemann Hypothesis in iambic pentameter?
6stringmerc · 39m ago
So he belongs to a wealthy family then, correct? Poetry is typically the pursuit of the bourgeoisie. It does not pay very well, especially to afford a family and only work three hours per day, as per the article. It’s great that he gets to live this lifestyle, for him, but there are some of us who pursue poetry at a net loss to quality of life. I’d possibly even contend that most people who actively engage in creative writing do so to their own detriment in a consumerist society with little to no safety net such as the US. Perhaps South Korea has a generous public endowment for poetry, and I would love to hear about it if so.
Otherwise, I’m not particularly moved by another chronicle of superior outcomes in creative pursuits due to hereditary wealth articles.
jebarker · 16h ago
Accelerated hero's journey.
noelwelsh · 6h ago
Clearly a very neurodivergent person. Glad he found a place in society where he could contribute within the quirks of his personality.
fromMars · 13h ago
This story is a bit of a misnomer when you look deeper. His dad is a statistics professor and he was mentored by well known mathematician in undergraduate so it's not like he didn't have a lot of schooling.
haiku2077 · 13h ago
I don't think his dad helped him that much? The article says his dad gave up on trying to teach him.
fromMars · 13h ago
We can't really know for sure. We have the anecdote about the workbook but what about earlier and did he absorb any of his dad's teachings or aptitude by osmosis.
Even if we accept he didn't he still went to college and had an unusual experience as an undergrad in being mentored by an excellent mathematician.
That he took a gap year in h.s. doesn't seem that noteworthy to me.
dgfitz · 16h ago
> he dropped out of high school to become a poet.
Not even college, high school. Really misleading/unfortunate title.
As an aside, why would anyone need to drop out of anything to become a poet?
gyomu · 15h ago
In case you’re asking the question not rhetorically - this is the kind of thing you can afford to do when you have an extremely strong/privileged support system.
It’s myth-making, and shouldn’t be confused with “dropping out to take care of your sick parent” or “dropping out and going to work at McDonald’s”.
signatoremo · 14h ago
> the kind of thing you can afford to do when you have an extremely strong/privileged support system.
Are you talking about his family specifically, or South Korea in general? What makes it extremely strong or privileged?
Barrin92 · 13h ago
>What makes it extremely strong or privileged?
The fact that his parents were math and literature professors who entertained him dropping out of school to write poetry. If I had done that my parents would have offered me exactly three choices, get a job, go back to school, or pack your bags and pay your own rent which would have forced me to get a job, understandably so because as working class people they didn't have the resources to sponsor me for another decade while I go soul searching
signatoremo · 13h ago
He wasn’t born into a wealthy family. His parents may support his decision, or not, but it isn’t like money wasn’t a concern.
I would say that was a pretty brave decision, or perhaps he is special
5123125 · 11h ago
Yes it is not a wealthy family, but in terms of education for children, having parents already in academia is just as good of a privilege as wealthy parents.
OldManAndTheCpp · 13h ago
What does your definition of privilege mean? Bemoaning parents who supported their children in the combination of the parents interests does not seem like an egregious sin.
jonathanlb · 13h ago
The person you're responding to didn't imply that privilege is a "sin". Not sure how you're interpreting that.
Sinply put, most working class parents simply don't have the financial respurces to support an older child's artistic pursuits. It is a privilege, i.e., an _advantage_, to have those means and werewithal to do so.
kelipso · 13h ago
There are plenty of working class parents who support an older child who lives at home. The difference is the child is not pursuing anything, so most parents would not want that for their child and would want him to get a job or something.
My point being that it’s not about finances, it’s not that much more difficult for most working class families to support an extra mouth to feed, especially when it’s an adult. It’s more about the difference in perspective and future financial stability.
vaidhy · 11h ago
Exactly this!! US has a very lone-wolf culture. In India, it is perfectly normal for an adult to live with parents and I am assuming SK is similar. The money aspect is overblown a lot.
While typing it, I realized it is actually more expensive in US than just a mouth to feed. Medical insurance, car insurance, car payments (you need a car), all add up to much more.
kelipso · 3h ago
Well Medicaid is free and for a car, you can get and old one for $2000 and pay <$50 a month for car insurance. Food costs more than that monthly, so it’s not a huge burden even for working class people.
I_AM_A_SMURF · 10h ago
The US Health Insurance system is specifically used to keep working class people (and most middle class) at work. You can't really go without a job here.
melling · 15h ago
I’m not familiar with the privileged support system in South Korea. Is it different than in the US or Europe?
I believe Einstein dropped out of high school and traveled a bit through Italy.
We definitely need a world where more young people can drop out for a few years.
jvkersch · 13h ago
The educational track in South Korea is extremely competitive, and everything hinges on how well you do on the Suneung (a kind of SAT on steroids). If you drop out, it is usually because you have intergenerational wealth, exceptional non-scholastic talents, or a route to study/work abroad.
creakingstairs · 12h ago
Or you just don’t like studying. There are plenty of Koreans who drop out of high school because they don’t feel like studying is for them. Yes, parents are more likely to try to force them to stay in school compared to other countries. But South Koreans are people too.
DetroitThrow · 15h ago
It feels disengenuous if you're seriously stating you're not familiar with how people with stable families and familial wealth have a much larger level of freedom in their choices to pursue the arts compared the average person.
Maxatar · 14h ago
I am also not familiar with how it works in South Korea, do you have any insight?
cma · 14h ago
From the article it sounds like he was able to do something like the GED and knew he would be attending college later in South Korea still.
Where's the myth making?
gyomu · 14h ago
The exercise of how one drops out of the first year of high school to “become a poet”, gets a GED, and then proceeds to enter one of the top universities in Korea (notorious for its particularly cutthroat academic culture) right on time at 19 is left to the reader.
aianus · 14h ago
Isn’t college admission there based solely on a single standardized test? If so it makes sense that a super-genius could ace it despite dropping out of high school.
creakingstairs · 11h ago
No there is also admission based on school grades, essays and achievements(수시). You still have to take the national test and get the minimum required grades though.
cma · 6h ago
I bet this guy Fields Medal recipient did pretty good on the test and didn't need that alternate, is it even available for dropouts by looking at grades before they dropped out?
creakingstairs · 2h ago
I just looked into it and it looks like he actually went to a private cram school for a year to study for the national exam then got into Seoul National University.
beyonddream · 13h ago
what is the GED you are referring to here ?
cma · 6h ago
I just read between the lines in the article that he must have gotten something like that since he said in the article that when he dropped out to be a poet he knew he would not have to attend college in two years.
Looking into it, I think they actually translate their version of it as GED too:
Spend more time on what, exactly? Writing poetry actively, all day, every day? That’s a lot of writing.
jjallen · 16h ago
How often do people become very good at something without spending the vast majority of their time on it for a long time?
iterance · 12h ago
I do not think you are aware that most people's process of writing good poetry is quite involved. It's okay not to understand, but be cautious about implying that another person's artistic work could be done in a spare hour here or there between coursework. It is disrespectful to the hard work of the written word.
eviks · 10h ago
It can also involve a lot of reading and thinking, also stuff you need time for
dhosek · 15h ago
I was thinking that this was my path, I was a Math major (well actually Math-English double major) and I dropped out to focus on English. Of course I never got a Field Medal (or much success as a poet for that matter).
mmooss · 12h ago
Sounds great. You don't need a Fields Medal for life to be worthwhile, or it's hopeless for all of humanity.
senderista · 16h ago
Joseph Brodsky dropped out of communism to become a poet, which did not amuse the authorities.
brador · 6h ago
I would be interested to know if any of the latest AI models can 1. Verify the solution (should be easy). 2. Produce the solution.
tim333 · 2h ago
Trouble with 2 is they've probably already read the article and similar.
pinewurst · 17h ago
(2022)
dang · 13h ago
Added. Thanks!
ldjkfkdsjnv · 16h ago
[flagged]
dang · 13h ago
"Please don't post shallow dismissals, especially of other people's work. A good critical comment teaches us something."
Is "Don't be curmudgeonly" a new addition? I don't remember that one before.
dang · 12h ago
Indeed it is! Comments seem way too curmudgeonly lately.
krapp · 3h ago
You're really kicking against the goads with this one.
ldjkfkdsjnv · 3h ago
Dang, with all due respect, this comment was really not that bad. You are too heavy handed
defrost · 3h ago
As a late observer, equally respectfully, it very likely wasn't dang's hand that downvoted and or flagged your comment.
You're responding to an after action review comment by moderator as to what might have caused the flag.
sno129 · 14h ago
My academic work was very close to June Huh's; my Ph.D. thesis was directly inspired by his Fields Medal winning work. His accomplishments have undoubtedly moved the field forward and connected various ostensibly disparate areas of math, not to mention he is one of the clearest writers and speakers in all of mathematics.
There are very few people in pure math that care about transformers; they have had practically zero impact on the sort of research mathematics that the Fields Medal is concerned with.
zeroonetwothree · 16h ago
How did transformers move forward pure math?
ldjkfkdsjnv · 16h ago
there is a straight-faced argument that transformers are already a mathematical research tool and even a source of new theorems. and if true, surely more revolutionary than some ultra complicated corner of math
markgall · 15h ago
Does there exist a person who would make this argument straight-faced? I am a professional mathematician and have yet to hear of anyone coaxing an even slightly interesting new theorem out of AI. I think the day is clearly coming but it's not here.
ldjkfkdsjnv · 15h ago
fair enough, i suppose im a believer that the seeds are planted, the day is soon. and i must say, it seems more worhtwhile trying to figure out how to finetune an llm/implement reinforcement learning that could do some form of pure math, than it is to try and do new pure math by hand
wizzwizz4 · 4h ago
I do research in this field. LLMs can be used as (ridiculously inefficient) implementations of some search algorithms that we haven't yet identified and implemented in software ourselves, but which can be inferred from a statistical analysis of the literature. Sometimes those search algorithms generalise to new areas, but more often than not, they flail. The primary advantage of a language model is that it's one big algorithm: when one subcomponent would flail, another (more "confident") subcomponent becomes dominant; but that doesn't solve the case where none of the subcomponents are competent and confident in equal measure. In short: to the extent it's useful, it's a research dead-end. Any potential improvements we understand are better implemented as actual search algorithms.
You've probably seen that thing where ChatGPT cracked Enigma[0]. It used several orders of magnitude more computational power than a Bombe (even given Moore's Law, still thousands of times more electrical power), and still took two dozen times longer. You would literally be better off doing brute-force search with a German dictionary. Thus is it with mathematics: a brute-force search is usually cheaper and better than trying to use a language model.
Terry Tao is one of the staunchest knowledgeable advocates of GPT models in mathematical research, and afaik he doesn't even bother trying to use the models for proof search. It's like trying to build a house with a box of shoes: sure, the shoe is technically more versatile because you can't use a hammer for tightening bolts (the shoe's sole has enough friction to do this) or foot protection (the shoe is the right shape for this) or electrical isolation (the bottom surface of the shoe is largely rubber), but please just use a hammer if you want to manipulate nails.
That is one of the most thought provoking things I have ever read.
People do this because there are certain admission categories where the university only looks at the test results. So they go “okay, by not going to school, my child can fully focus on exam instead of wasting time on useless subjects like art and PE. And school math curriculum is too easy anyway”
This really saddens me because schools should be more than gateways to universities, but I digress.
Universities should be looking at more and discouraging 1 dimensional applicants
Sure. Like there is a whole field of consultants who would help your child to develop a suitable profile.
Moreover, I the US I heard there is an industry for generating experiences for the "young minds" (if their parents are rich enough) e.g. discovering rennaissance via a trip to Italy etc.
Also remember the tennis scam for admissions? Gordon Ernst from Georgetown U.
I navigated the system alone for myself then again to help her after I had learned from all my college friends. We both went to “prestigious private schools” with single digit acceptance rates and have similarly “prestigious” jobs
Here’s the truth: yes, like everything else in this world it’s a LOT easier with money. But it’s not impossible if you’re willing to understand the expectations and put in the work to meet them.
Not really convincing. How many poor kids did not even come to an understanding of how the admission system works? How many kids did not even know what work was to be put in?
I am also someone born at the bottom (my first passport was a convention of 1951 passport), who went to a world famous university. As I've gotten older, I've realized it's not really a useful way to think about it. We like to say "you can do it if you really try", but it's just not true. Not only is it not true, it's a thought-ending statement that makes it easier for rich kids and harder for poor kids, because why would you need to support the poor kids if they can just work really hard?
Even you have to be able to see that you got lucky. When I applied, the entrance rate for my course was about 8%. I had no idea that I could have tried easier courses, or that I could have filled the form in slightly differently for a better shot. A single-digit acceptance rate is a lottery. You could do everything the same again and not get in. You don't realize it when you get in, because you happen to get questions that you can answer, but there's a heck of a lot of questions an Oxford professor can ask an 18 year old that will make him look bad.
When I arrived, of course all the other kids were ordinary upper middle class kids. People went to feeder schools where they teach you how to do the Oxbridge interview. People who didn't grow up pinching every penny. What happened to the poor, hard-working kids? They're mostly not there.
Optimizing hard for some rat race for some soulless (or soul crushing) office jobs among high functioning sociopaths that management inevitably always is. Most of those folks are not properly happy by any measure, thats not a win in life to end up there nor something to respect.
We are in rather unique period of time, especially folks here, that life fulfillment and happiness can be achieved for almost everybody and not just some top 0.1% if correct direction is taken. How about we realized that and focused more on actually long term important aspects of life?
(here is another guy who went the proverbial rags-to-modest-riches on my own but I would never had such mindset, when talking about successes of my life its about countries I've travelled, people I've met and intense experiences that shaped me more than career paths taken)
I live in a bit of a bubble where pretty much every kid's parents are professionals. Some of these people are off to London before the kids are in school, and arrive back home after they are asleep.
People spend a lot of money on top of private school to get a tutor in order to get into the grammar schools. This is a pure loss for society: the wrong kids get in, since not everyone can afford to learn this particular test. And money is spent on reducing the kids' free time for exploration.
How many others have tried to put the work you did and didn't achieve it?
I think that's the crux of it, being possible doesn't mean anything if it shuts out the majority of the ones who attempt it. It's possible to become a professional athlete and still a lot more kids fail to achieve that even if they put the work for it. Contrary to being a professional athlete, good education is both much more accessible and much more needed.
Exactly because you managed to achieve it that I believe there should be more empathy for how fucked up the system is, imagine how much less suffering you would have gone through if there was a better way? Why not work for it to be a better way even though it's already possible?
They really, really do. Admission to top universities has become hyper competitive. They're getting tens of thousands of highly qualified applicants with perfect GPAs and great SAT scores. So what they're looking at is more, "Will admission to this university help them to do something special?" or is admission the end goal for the student. And one way to see that is if the applicant is well-rounded and explorative. Are they setting creative fires everywhere they go?
Often when you look at the other dimensions, it's a way for the admissions office to smuggle in criteria that other people find objectionable.
> You can expect the future to take a definite form or you can treat it as hazily uncertain. If you treat the future as something definite, it makes sense to understand it in advance and to work to shape it. But if you expect an indefinite future ruled by randomness, you’ll give up on trying to master it. Indefinite attitudes to the future explain what’s most dysfunctional in our world today. Process trumps substance: when people lack concrete plans to carry out, they use formal rules to assemble a portfolio of various options. This describes Americans today. In middle school, we’re encouraged to start hoarding “extracurricular activities.” In high school, ambitious students compete even harder to appear omnicompetent. By the time a student gets to college, he’s spent a decade curating a bewilderingly diverse résumé to prepare for a completely unknowable future. Come what may, he’s ready—for nothing in particular.
> A definite view, by contrast, favors firm convictions. Instead of pursuing many-sided mediocrity and calling it “well-roundedness,” a definite person determines the one best thing to do and then does it. Instead of working tirelessly to make herself indistinguishable, she strives to be great at something substantive—to be a monopoly of one. This is not what young people do today, because everyone around them has long since lost faith in a definite world. No one gets into Stanford by excelling at just one thing, unless that thing happens to involve throwing or catching a leather ball.
Cramming entrance exams is not super useful, but it does select for motivation and ability to focus intensely. Much more useful measure than having your parents set up a fake charity for you to volunteer at.
To me this reads as claiming "making fragile choices is good", which outside of very niche situations I'd say is bad advice: like telling a college basketball player to not waste time outside of practice and later watching him go undrafted in the pros.
He's giving this advice to make his life better, not necessarily to make your life better.
I agree that "well-rounded" people without depth are not as interesting or as valuable as people who've picked one or more topics to learn in detail, especially since the latter can often be well-rounded and also have an area of expertise. However, a bit part of their value comes from their ability to do something without anyone telling them to do it. An engineer who spent six months writing a protein folding simulator out of obsessive interest is a much better pick for a computational chemistry course than one who spent that time in a cram school.
At least here in the US:
In academics, a grade of A is better than the rest yet still some independent or from outside school results can mean more than grades and even make poor grades irrelevant.
Some examples:
E.g., for getting into a selective college, SAT Math scores (from outside of school) the highest in my high school class made everything else irrelevant. E.g., overlooked my F in Typing!
Actually, the Typing class was very worthwhile and learned touch typing, but the class was nearly all girls, GORGEOUS, who buzzed away with perfect accuracy at maybe 30 characters a second!
E.g., in graduate school, found a problem and in two weeks got a solution accepted right away by Mathematical Programming. Suddenly had an impenetrable shield and all grades and everything else were irrelevant.
E.g., before grad school thought of a problem and had a first solution; in grad school wrote a first draft; wrote and ran the related software; and wrote the document, all independently. Stood for orals and graduated.
Again, course grades are not everything, and good independent work can make everything else irrelevant.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4064129
> https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4064129
How does this paper relate to GP's comment?
We should remember not to just present results, but to teach, demonstrate and live how to get there more. It's not even abour rich vs. poor education - almost all go through the whole system never seeing this, and for June Huh, sleeper maths genius, meeting that one person changed everything!
My point being that maybe it's not unique sleeper inborn talent, but just learning grit, persistence and well, not being stupid, that will lead to success in life. If one thing doesn't hit, try another. So maybe you don't become a poet, but a math genius, or a soccer player, or a dancer; something else than a TV consumer.
He dropped out to become a poet – now he’s won a Fields Medal (2022) - https://news.ycombinator.com/item?id=37010709 - Aug 2023 (75 comments)
He dropped out to become a poet – now he’s won a Fields Medal - https://news.ycombinator.com/item?id=31985400 - July 2022 (136 comments)
I wonder if this helpful service of integrating past comments on the same story ould be easily automated by looking for repeat URLs (and perhaps clustering old and new comments to integrate them so they can be presented as topical threads).
Seriously, a well written article including the accessible explanations of his work. Plus, LoL funny. Thank you.
The B.S. changed my life. I graduated, you will too.
So grateful to the late Jim Simons for funding basic research and its popularization (and Quanta Mag.)!
Otherwise, I’m not particularly moved by another chronicle of superior outcomes in creative pursuits due to hereditary wealth articles.
Even if we accept he didn't he still went to college and had an unusual experience as an undergrad in being mentored by an excellent mathematician.
That he took a gap year in h.s. doesn't seem that noteworthy to me.
Not even college, high school. Really misleading/unfortunate title.
As an aside, why would anyone need to drop out of anything to become a poet?
It’s myth-making, and shouldn’t be confused with “dropping out to take care of your sick parent” or “dropping out and going to work at McDonald’s”.
Are you talking about his family specifically, or South Korea in general? What makes it extremely strong or privileged?
The fact that his parents were math and literature professors who entertained him dropping out of school to write poetry. If I had done that my parents would have offered me exactly three choices, get a job, go back to school, or pack your bags and pay your own rent which would have forced me to get a job, understandably so because as working class people they didn't have the resources to sponsor me for another decade while I go soul searching
I would say that was a pretty brave decision, or perhaps he is special
Sinply put, most working class parents simply don't have the financial respurces to support an older child's artistic pursuits. It is a privilege, i.e., an _advantage_, to have those means and werewithal to do so.
My point being that it’s not about finances, it’s not that much more difficult for most working class families to support an extra mouth to feed, especially when it’s an adult. It’s more about the difference in perspective and future financial stability.
While typing it, I realized it is actually more expensive in US than just a mouth to feed. Medical insurance, car insurance, car payments (you need a car), all add up to much more.
I believe Einstein dropped out of high school and traveled a bit through Italy.
We definitely need a world where more young people can drop out for a few years.
Where's the myth making?
Looking into it, I think they actually translate their version of it as GED too:
https://www.ice.go.kr/en/cm/cntnts/cntntsView.do?mi=10019&cn...
"Don't be curmudgeonly."
https://news.ycombinator.com/newsguidelines.html
You're responding to an after action review comment by moderator as to what might have caused the flag.
There are very few people in pure math that care about transformers; they have had practically zero impact on the sort of research mathematics that the Fields Medal is concerned with.
You've probably seen that thing where ChatGPT cracked Enigma[0]. It used several orders of magnitude more computational power than a Bombe (even given Moore's Law, still thousands of times more electrical power), and still took two dozen times longer. You would literally be better off doing brute-force search with a German dictionary. Thus is it with mathematics: a brute-force search is usually cheaper and better than trying to use a language model.
Terry Tao is one of the staunchest knowledgeable advocates of GPT models in mathematical research, and afaik he doesn't even bother trying to use the models for proof search. It's like trying to build a house with a box of shoes: sure, the shoe is technically more versatile because you can't use a hammer for tightening bolts (the shoe's sole has enough friction to do this) or foot protection (the shoe is the right shape for this) or electrical isolation (the bottom surface of the shoe is largely rubber), but please just use a hammer if you want to manipulate nails.
[0]: https://www.techradar.com/news/we-watched-an-ai-crack-the-en... – and I know that's not the original ChatGPT®, but I am not rewarding this company for such a wasteful and pointless publicity stunt.
Somewhere inside openai is a reinforcement learning loop that looks like:
current_code = read(code_base_from_file.txt)
modify_prompt = "some prompt to modify code with expected outcome"
result = model.run(modify_prompt, current_code)
if check(result):
else: and its clear that not only does this work, it maybe the future of what unravels software engineering.the current models are being trained for coding, but theres no reason this couldnt be tried for other domains, like pure math.