[HN Gopher] At 17, Hannah Cairo solved a major math mystery
___________________________________________________________________
At 17, Hannah Cairo solved a major math mystery
Author : baruchel
Score : 176 points
Date : 2025-08-01 16:35 UTC (6 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| tocs3 wrote:
| Earlier discussion: https://news.ycombinator.com/item?id=44481441
|
| I wish her the best in her coming career.
| dang wrote:
| Thanks! Macroexpanded:
|
| _Hannah Cairo: 17-year-old teen refutes a math conjecture
| proposed 40 years ago_ -
| https://news.ycombinator.com/item?id=44481441 - July 2025 (105
| comments)
| OutOfHere wrote:
| What is the general basis for skipping college and getting
| admission directly in a Ph.D. program? What does one have to
| generally do to qualify?
| ameliaquining wrote:
| AFAIK there's no general procedure; it's just that the
| admissions committee can admit anyone whom they're convinced
| can do Ph.D.-level work, and that almost always involves
| getting an undergraduate degree first but in extremely
| exceptional cases it might not.
| joe_the_user wrote:
| Essentially, you have to convince a math professor that you
| able to complete the Ph.D program. There are a variety of ways
| to do that. Solving a major open conjuncture is clearly one of
| them but just getting to know one or another professors can
| work (I went to school with the semi-famous Paul Lockhart who
| also did this).
| TMWNN wrote:
| For context, Stephen Wolfram dropped out of Eton to start at
| Oxford, then was admitted to Caltech's physics PhD before
| finishing his Oxford BA, receiving his doctorate at the age of
| 21.
|
| (He was publishing papers in high school.)
| oldpersonintx2 wrote:
| be actually gifted
|
| this is what gifted looks like, not legions of students who are
| told they are "gifted" but are just pretty smart
| pinewurst wrote:
| I knew someone who was admitted to a Masters program at
| Stanford sans undergraduate degree. His employer at the time
| was a large donor.
| anonzzzies wrote:
| As a pupil of Dijkstra and seeing at least some rise in formal
| verification because of the modern tooling and as a follower of
| Lean (and Agda, Coq, Idris* etc), I hope it will be at least a
| strive to deliver parts of proofs in code verifiable form. More
| machine verifiable building blocks will lead to a bettering of
| everything.
| Imustaskforhelp wrote:
| Offtopic, but I am 17 too just like Hannah Cairo but nothing
| too groundbreaking till now I suppose and it absolutely brings
| me delight that I can talk to somebody who was a pupil of
| Dijkstra, I have heard a lot about dijkstra's algorithm's and I
| had forgotten about it and so I searched it right now, but the
| only thing I knew is that it is pretty popular algorithm.
|
| If I had to ask you kind sir, what would be the biggest life
| lesson (in coding, or anything general) that you could give me
| be?
| hadlock wrote:
| A less click-baity headline might be "17 year old Hannah Cairo
| has solved the Mizohata-Takeuchi conjecture"
| noqc wrote:
| probably add "in the negative", to that.
| 1024core wrote:
| "17 year old Hannah Cairo has disproved the Mizohata-Takeuchi
| conjecture"
| sdenton4 wrote:
| Is it an important conjecture, or just something someone came
| up with last week?
| cgh wrote:
| This is answered in the article's second paragraph.
| sdenton4 wrote:
| But I don't know that from the proposed re-titling of the
| article. The importance of the conjecture is more salient
| for the general reader than the (uninformative) names of
| the people who conjectured in the first place.
| spiderxxxx wrote:
| There's so many photos of just her staring off into the
| distance, and only one photo with her presenting the actual
| thing that she's supposedly famous for. I don't get the point
| of just all these random photos of this girl.
| azornathogron wrote:
| It's not very easy to take photos of mathematics, and the
| girl is the central subject of the article anyway. What
| images would you expect to see?
| AtlasBarfed wrote:
| "Cairo applied to 10 graduate programs. Six rejected her because
| she didn't have a college degree. Two admitted her, but then
| higher-ups in those universities' administrations overrode those
| decisions."
|
| This is both unsurprising and shocking to me at the same time.
|
| For institutions of allegedly pure higher learning in a field
| where it's known that youth is where the advancement happens, the
| fact 80% axle wrap over a piece of paper that, let's face it, in
| modern times of grade inflation is pretty much worthless of
| anything beyond money and sitting in a seat for four years.
| kurthr wrote:
| A lot of programs don't want to have to babysit a teenager no
| matter how talented they are. Some of the more prestigious
| programs both have some experience with it and extra staff to
| (give profs warm fuzzies) handle any issues that come up. I'd
| expect it depends a lot on her interests and the particular
| professors that study that at any particular institution.
|
| Even as a student, I'd be more interested in which professors
| at Johns Hopkins were accepting students, than which school.
| xandrius wrote:
| As if that was the reason.
|
| Also, I've seen a great deal of adult babies in academia, so
| let's not be ageist here.
| gus_massa wrote:
| In my university, when someone is accepted as a graduate
| student of a different topic (let's say phisics -> biology)
| it's usual to include a few of the last courses of the major as
| a mandatory part of the Ph.D.
| neilv wrote:
| > _Two admitted her, but then higher-ups in those universities'
| administrations overrode those decisions._
|
| I've personally seen universities go both ways, and it comes
| down both to individuals, and to the culture of the
| department/university faculty and administration.
|
| (Not to the culture of the student body, which is influenced by
| the administration culture, but has very little institutional
| memory, and almost zero power. If you draw an analogy to
| nations, there might be one with the most awful 'leaders'
| seizing and abusing power, but that's "way above the pay grade"
| of the many nice citizens you will meet -- who didn't know what
| they were being born into, and will do their best to be decent
| to each other, despite whatever bits they're unfortunate to
| learn about the upper powers.)
| amelius wrote:
| What I'd like to know is how many 17 year olds failed to solve
| their math mystery, and chose a career in programming instead.
| geodel wrote:
| Almost all of them?
| 1659447091 wrote:
| I never got excited for math, thus didn't care much to start
| with. But then add the issues of high school math and that
| solidified it for me. Math word problems were the worst. With a
| dyslexic brain I would consistently read the important words as
| something different, thus correctly solving the wrong problem
| and being derided for it.
|
| Geometry required rote memory exceptionalism which also works
| against my brain design (adhd as well), but let me have the
| formulas to choose from and I'll get it done. Algebra II? I
| kept getting in trouble because I would do homework assignments
| in class instead of paying attention to the teacher trying to
| teach concepts that were easier for me to learn by reading the
| examples and following the book. After that, who would ever
| want to continue beyond the required credits and not think of
| further math as a masochist hellscape
| kevinventullo wrote:
| Many people who succeed in solving their math mystery still end
| up choosing a career in programming
| carabiner wrote:
| I hope she doesn't burn out and move into the woods like
| Grothendieck, Kaczynski,
| gspencley wrote:
| I have yet to move into the woods but, given my current levels
| of burnout, I think such a proposition is highly underrated.
| What's wrong with moving into the woods?
|
| Wait, if everyone moves into the woods there will be no more
| woods that offer seclusion. Yeah moving into the woods is
| awful! I hope she doesn't burn out!
| bee_rider wrote:
| One option could be to get a hammock and go program in a
| tree. That's sort of like moving to the woods, but you don't
| have to live there full time and you still get to program.
| laurent_du wrote:
| Kaczynski was really not on the same level. By several orders
| of magnitude.
| BizarroLand wrote:
| I mean, force feed her massive doses of LSD and use elite
| psyops to incessantly harass her as a prank science
| experiment and maybe
| 1024core wrote:
| > Only the University of Maryland and Johns Hopkins University
| were willing to welcome her straight into a doctoral program.
| She'll start at Maryland in the fall. When she finishes, it will
| be her first degree.
|
| Jeez... what a damning indictment of today's Universities.
|
| She could just use her publication as a dissertation and be done
| with it!
| rahkiin wrote:
| Normally you have a master of science as well. And for that you
| require a bachelors. So to do it directly you need to do it all
| at once?
| morleytj wrote:
| In the US a doctorate usually doesn't require a master's,
| most people go straight from undergrad to phd.
| sdenton4 wrote:
| To add slightly more detail: Most research math programs in
| the US are 5(ish) year 'combined' masters+phd programs. The
| first couple years are basically course work, seminars,
| finding your area and advisor, and then the rest is the
| actual research work. It's not uncommon to leave after the
| first couple years with a Master's degree.
| general1726 wrote:
| Hey, you are not getting your degree without paying for it.
| pinewurst wrote:
| The interesting part is that two others admitted her but
| retracted after "higher-ups in those universities'
| administrations overrode those decisions".
|
| Was she not considered properly conditioned?
| MathMonkeyMan wrote:
| "I'm in charge, I enforce the rules, I'm a big deal."
| terminalshort wrote:
| Of course she was, but that's not what this is about. Letting
| her in proves that the bureaucratic credentials offered by
| schools are meaningless. The university system in its present
| form in the US is entirely predicated on the fiction that
| those credentials actually mean something and are worth
| paying six figures for.
| whatshisface wrote:
| Two out of ten is pretty good for anything involving individual
| decisions, just ask any salesperson.
| skeptrune wrote:
| I think the biggest flaw with higher education today is that
| we're pushing people into doing undergraduate degrees who are
| already well beyond coming out of self learning from high
| school or other experiences.
| jonhohle wrote:
| That's one of the biggest problems? Not pushing people into
| higher educational programs with little societal or economic
| value but huge loads of debt?
| skeptrune wrote:
| I think research and higher education does have value for
| the most part. It's undergrad that's really worthless and
| something people only do for the experience.
| xp84 wrote:
| Indeed. I've long felt that most undergrad students would
| be better served by a typical college minus the formal
| classes. Basically dorms and all the other amenities
| found in a typical college campus, where you mainly gain
| life skills and mingle with other people your age.
| Because most people I met at an average 4-year school
| were there because it's a societal expectation among
| certain classes, it's less scary than just getting a job
| and figuring out life completely on your own, and it is
| 10x-100x easier to make friends at college than just "out
| in the world." Not on the list: to learn from college
| classes, which at an average school teach you less than
| you'd get from a $200 a year subscription to Great
| Courses Plus or Brilliant. Or free from Khan Academy.
|
| I know a few very special schools give undergrads access
| to brilliant minds in their field, but I also have been
| told that undergrads at those schools are mostly taught
| by grad students, so I'm not sure that Ivies provide a
| lot either, beyond the opportunity to hobnob with the
| legacies that will be running Goldman Sachs in 20 years.
| psyklic wrote:
| Undergrads who care about learning and research will take
| the most challenging classes, do research with
| professors, and surround themselves with other strong
| students who will push them.
|
| Even at top universities, very very few freshmen are
| capable of doing high-quality research immediately.
| They'd be better served learning the foundations inside
| and out with a cohort of similarly strong students to
| challenge them.
| skeptrune wrote:
| If you do research during your 4 year undergrad. You
| shouldn't have been undergrad. It's really that simple.
| psyklic wrote:
| I'm not sure that's a simple argument and can't imagine
| many would agree.
|
| Undergrads who do research generally aren't very good at
| research yet. A major reason is they either lack or don't
| fully understand the pre-reqs, which they progressively
| and cumulatively learn during undergrad. A student can be
| incredibly smart, but acquiring a strong rigorous math
| background will still take years.
| skeptrune wrote:
| Working on that skill and ability is the entire point of
| postgrad. If those are the skills you're working on then
| you should be in a postgrad program.
| psyklic wrote:
| If you don't know the foundations well, you don't belong
| in a postgrad program. That's the reality and how it
| currently works. Undergrad teaches you those foundations.
|
| Anyone can try doing research, even undergrads who half-
| know the foundations. However, trying research doesn't
| mean you have the background to do great research or to
| succeed in a postgrad program.
| skeptrune wrote:
| Let me ammend my statement. *"Anyone who succeeds at
| publishing research deserves to be in a postgrad
| program."
|
| Plenty of people in postgrad programs don't know the
| foundations. It's ok. You are there to learn.
|
| Completely unfair to expect someone already doing
| research to slog out 4yrs of classes not furthering their
| career.
| dh2022 wrote:
| About pre-reqs: third and fourth year PureMath classes at
| UofWaterloo consisted of math I already took in
| HighSchool in Romania: group theory, ring theory. Plus
| some calculus I already read in high school out of
| curiosity: measure theory and the Lebesgue integral.
| Another Romanian guy at UofW was auditing 4th year
| classes while in his first year (he is now a math
| professor at an American university)
|
| I can see a committed and gifted student being able to
| get most of the pre-reqs for doctoral studies in America
| or Canada while in high school.
| Quekid5 wrote:
| People sometimes _accidentally_ do research. I 'm not
| joking.
| cge wrote:
| To agree with you: I've worked with several really
| brilliant undergrads doing and publishing great research.
| But all of them were rightfully undergrads. Even if they
| were actually capable of doing great research, they
| benefited from the breadth.
|
| If you have bright enough undergrads, you change the
| curriculum for them within their field of expertise, so
| that they still get the breadth of things outside it
| while not wasting time with things they know. You let
| them not take as many classes, take graduate courses, do
| more research, take more courses from other departments
| in related areas but with different perspectives, and so
| on.
|
| When I was an undergrad, in physics, there was a
| professor in the department who had done his undergrad
| there and was legendary, as was quietly mentioned in awe,
| for not taking any undergraduate physics courses while
| there; the department had let him skip _all_ of them, and
| instead take graduate courses and do research.
| franga2000 wrote:
| The debt part is just a US thing, but the rest of us still
| have the other problems.
| globalnode wrote:
| australia copied the US in that regard. they used to say
| we were the 51st state but i dont even think we qualify
| as that... a territory perhaps?
| contravariant wrote:
| To the right people a university education can be an asset
| rather than a barrier to entry.
| conorbergin wrote:
| Very few people are too "advanced" to be challenged by a
| sufficiently difficult undergraduate degree, ridiculous thing
| to say imho, I went to a UK university this decade and I can
| give you a laundry list of issues more significant than
| "exceptional students being slowed down".
| TheOtherHobbes wrote:
| This woman is undoubtedly exceptional. But we don't know
| how exceptional, because she's an outlier, educated using
| different methods.
|
| We have no idea how many other people would achieve
| something similar with a similar background. Personally I'd
| bet almost anything it's a larger number than most people
| expect.
|
| I'd also be surprised if she doesn't already have a pretty
| solid background in undergrad-level math.
|
| The irony is she's actually more typical than not.
| Universities in the past were open to giving unusual
| talents special treatment.
|
| Historically, the idea that everyone _must_ follow the same
| path on the same timetable is unusual.
| Aurornis wrote:
| The number of high schoolers who _might_ be ready to go into
| postgrad programs is very small.
|
| There is no way this could be the "biggest flaw" in higher
| education today because the number of people possibly
| impacted is so tiny.
|
| Although I think you're striking at something that is a real
| problem with undergraduate degrees today: Many universities
| have become so watered down and softened that students spend
| the first 1-2 years doing what they should have been learning
| in high school.
|
| My friends who still teach at university constantly complain
| about students arriving for undergrad with very poor writing,
| communication, and listening skills.
| TheRealPomax wrote:
| Conversely: if that's all it takes, there is no point in going
| to University just to get a piece of paper that says "you did
| the thing you already did".
|
| University (for folks serious about continuing in academia
| after) is (obviously) about making sure you have the same base
| knowledge as everyone else, but also for you to come to terms
| with how academia actually works, who the bad players are, who
| the good players are, and who you need to know to get shit to
| happen for you. So in that sense, most Universities going "no"
| is literally the most accurate reflection of what life's going
| to be like on a continuous basis on the inside.
| jackero wrote:
| 50% of my college education was general education though.
|
| And frankly I find it just as valuable.
| assword wrote:
| > Jeez... what a damning indictment of today's Universities.
|
| There's a modern phenomenon I've been thinking about but have
| struggled to put a name to.
|
| Everything just becomes so generalized, streamlined that it
| becomes impossible to operate outside of the pre defined "happy
| path".
|
| AI will make this increase 100x as taking humans out of the
| loop seems to accelerate this process.
| ninala wrote:
| Perhaps the term "canalization" fits? Coined by C.H.
| Waddington, describing the process of forming a chreode in a
| homeorhetic system. But it doesn't really encompass the
| "everything becomes overly generalized" concept you
| mentioned. Rather, it's more about robustness against
| perturbation of a trajectory in a conceptual space.
| Christopher Alexander called them 'paths in configuration
| space'.
| willhslade wrote:
| Object orientation applied to life.
| TrackerFF wrote:
| I see your point, but undergraduate degrees should provide a
| wide foundation, with little specialization. As you progress to
| a masters degree, you become more specialized. A doctorate is
| as specialized as it gets.
|
| It is entirely possible for people to intensely focus on a
| very, very narrow thing - and ignore everything else. Even to
| such a degree that they can write a doctorate on it.
|
| But I don't think that's a good excuse to make them forego
| other curriculum, especially if it is required for other
| students to take. Schools have a responsibility to educate
| people to a certain standard, and give them some general
| breadth.
| thrawa8387336 wrote:
| No, that was the purpose of high school. As not practiced in
| public schools, as not practiced in the US
| amradio1989 wrote:
| I'm not sure higher ed's educational philosophy is serving
| students all that well. The breadth of education is a shallow
| survey at best that is quickly forgotten exactly one semester
| later.
|
| Thankfully the workforce has common sense and will happily
| snap her up into employment.
| JAlexoid wrote:
| This is ignoring the value of the whole education process, that
| you go through the years at a university.
|
| I disagree that she should skip the general education.
| xp84 wrote:
| Thinking about my GE requirements at undergrad, I think it
| would be a waste of this girl's time to be forced to learn
| about and write about random subjects that don't interest
| her. She has but one lifetime, and can contribute much to her
| field.
|
| The subjects such as English composition, she should be
| allowed to test out of if she is already a good writer.
| com2kid wrote:
| > I think it would be a waste of this girl's time to be
| forced to learn about and write about random subjects that
| don't interest her.
|
| This is a common STEM view, but it is inherently wrong.
| IMHO it dates back to the unfortunate divide between
| science and the liberal arts, whereas both were once
| considered a single field, now days there is disdain and
| mistrust between the two sides.
|
| The point of history classes isn't to memorize the dates of
| wars, is it to understand the motivations of humans, it is
| to understand how the world we lived in has been shaped
| throughout time, and it is to learn how to do, and
| understand, research about the history of a place.
|
| The point of English classes isn't just to get good at
| writing, it is to get good at various types of writing, it
| is to learn how to read different forms of literature, and
| it is to have a guided tour through a chosen selection of
| literature to hopefully develop one's character and
| thoughtfulness.
|
| One of the most valuable classes I ever took at University
| was the Art Of Listening To Music. We started off around
| 500ad or so and went forward through time up until about
| 1920. We learned the vocabulary of music, how to sit down
| and listen to a piece of music and describe what we were
| hearing. After I was done with the class I went from
| appreciating a handfuls of genres of music to appreciating
| music itself no matter the genre. It was a 3 credit
| guaranteed A class that had enriched my life by an enormous
| amount.
|
| If you really love your major, then the point of going to
| university was _NOT_ your major, odds are you would 've
| studied that field with or without the school. (Barring
| fields that require large capital investments, chemistry,
| physics, playing with an entire orchestra, building
| airplanes, etc) The point is _everything else_.
| terminalshort wrote:
| But that isn't how it works in reality, at least in the
| US. In reality, outside of their major (and sometimes
| inside it too), students usually pick the absolute
| easiest classes that satisfy the requirements. The ones
| that are known that the teacher doesn't take attendance
| are heavily desired. And the university is happy to
| oblige. Departments are funded based on a formula of how
| many students are in their classes, and they know that if
| they gain a reputation for being hard, students won't
| take their classes for GE requirements. It's a race to
| the bottom. So most departments offer enormous 1 level
| classes with 200 students taught with minimal rigor, and
| where you really only have to study a few days before the
| final to collect your A. And on top of that the frats all
| keep collections of graded tests from every class for
| years past, so basically anyone who wants to cheat is
| able to do so easily. This isn't education. This isn't
| worth six figures.
| com2kid wrote:
| > In reality, outside of their major (and sometimes
| inside it too), students usually pick the absolute
| easiest classes that satisfy the requirements.
|
| In reality, no one eats healthy food, everyone eats fast
| food hamburgers all day. Just look at the sales numbers
| of fast food / junk food VS organic lunch salad bars!
|
| Except, that isn't true. Some people eat junk food all
| day, and some people choose to eat healthy. Obviously in
| America we have a bit of a bias, but just looking at
| averages doesn't give a complete picture.
|
| > The ones that are known that the teacher doesn't take
| attendance are heavily desired.
|
| Almost none of my university classes took attendance. Why
| would they? We were paying to be there, if we wanted to
| waste our money, it wasn't the university's problem.
|
| > So most departments offer enormous 1 level classes with
| 200 students taught with minimal rigor
|
| Reading books and writing essay's doesn't require rigor,
| the learning is in the doing. I put in honest work to
| learn and I got honest feedback from my 100 and 200 level
| professors, which was all I expected.
|
| > And on top of that the frats all keep collections of
| graded tests from every class for years past
|
| Almost none of my GE classes used multiple choice tests.
| They were typically essay tests, written in class.
|
| I should note I did my GE requirements at a local
| community college, where class sizes averaged ~20-30
| students, professors had office hours, and I think I only
| saw a TA once.
|
| > This isn't education. This isn't worth six figures.
|
| The price is too high yes, but a university is place to
| go where you can dedicate yourself fully to learning,
| hopefully w/o other outside worries (sky high tuition
| ruins that...). What a person chooses to do with that
| time is up to them.
|
| Now one can argue that the worth of a degree is lessened
| by students who didn't actually learn all that much also
| being in possession of one. That is a closely related,
| but separate topic.
|
| That said, the poster I was originally replying to was
| indirectly advocating for not caring about one's GE
| classes, and I was replying that one should indeed care,
| because those classes are incredibly important!
| thechao wrote:
| In my teens I worked with the statistics department at UTMB.
| That had a cast of characters there; many profs in the 70s and
| 80s, who'd gotten their degrees before WW2. A number of them
| had schooling of the form: Start school at 9-10, do 5 years of
| public school, got to a 1 year prep, do a year or two of
| college, do a two year PhD. Most of them had their PhD's by 22.
| nurettin wrote:
| > what a damning indictment of today's Universities.
|
| Prodigy skips undergrad -> Universities are doomed? What?
| JohnKemeny wrote:
| > _She could just use her publication as a dissertation and be
| done with it!_
|
| The purpose of a PhD is not writing a dissertation. It is a
| research school, and I'm sure she could still learn a thing or
| two about research (and teaching).
| Quekid5 wrote:
| That's a nice quip, but aren't degrees meant to offer _breadth_
| of knowledge? (I 'm sure she has lots, but perhaps is weak in
| other areas.)
| Aurornis wrote:
| > Jeez... what a damning indictment of today's Universities.
|
| > She could just use her publication as a dissertation and be
| done with it.
|
| I'm not suggesting this person is doing anything fraudulent as
| she seems quite impressive.
|
| However, educational institutions get constant requests from
| parents who want their children to skip far ahead before
| they're ready. It's a competitive world and they know that
| being able to claim a child skipped several grades or even
| skipped undergrad entirely is a unique and very impressive
| achievement for the resume. It also theoretically provides a
| few additional years of earning potential by giving a career
| head start.
|
| The first problem is that many of these parents (again, no
| accusations for this specific case) see this and want to make
| it happen for their child at any cost. There are some wild
| stories about parents trying to cheat their kids forward or
| falsifying their accomplishments to try to skip grades.
|
| The secondary problem is that it can be hard on kids to be
| thrust forward so far past their peers. I had several friends
| who skipped a grade in middle school and most of them didn't
| have a great experience for social reasons. Skipping undergrad
| altogether would thrust someone into a foreign world with a lot
| of baseline expectations and norms that they hadn't yet
| learned, combined with no peers their age to discuss it with.
|
| It creates a high chance for burnout or failure, which could
| leave them worse off than when they started.
|
| That's why the recommendation is generally to do undergrad at a
| challenging institution that allows students some upward
| mobility in specific areas where they're ahead. No reasonable
| undergrad program is going to have this person taking Algebra
| 101, but there are a lot of opportunities for them to jump
| right into advanced programs and go deep and broad.
| fn-mote wrote:
| Clearly the correct method is: publish your "dissertation"
| first, then apply for admittance to the PhD program.
| throwaway81523 wrote:
| IIRC Erik Demaine was also homeschooled, skipped college, got
| a very early PhD, and joined the MIT math faculty as a
| teenager (he is a full professor there now). Johnny von
| Neumann OTOH went through a "normal" secondary education
| partly because his parents wanted him to have traditional
| social exposure to kids his age while he was growing up. His
| math training was very accelerated though, and he had
| professional level research publications at 17.
| conferza wrote:
| Wow, this is remarkable. So inspiring to read, even though I'm
| terrible at mathematics.
| impish9208 wrote:
| "There was this inescapable sameness, in a way. No matter what I
| did, I was in the same place doing mostly the same things," she
| said. "I was very isolated, and nothing I could do could really
| change that. I'd wake up on certain days and realize, I'm just
| older."
|
| I finally have something in common with a math prodigy.
| munificent wrote:
| Thank God she found math instead of Factorio.
| MathMonkeyMan wrote:
| Here's a link to the paper on the arxiv:
| https://arxiv.org/abs/2502.06137
| shermantanktop wrote:
| - moved between countries or first/second gen immigrant? check
|
| - home schooled? check
|
| This on top of her extraordinary talent and hard work.
| Institutional education truly is a great leveler, at both the top
| and bottom.
| zahlman wrote:
| Previously: Hannah Cairo: 17-year-old teen refutes a math
| conjecture proposed 40 years ago
| (https://news.ycombinator.com/item?id=44481441)
| fnord77 wrote:
| Wait, what software engineering jobs require you to move to the
| Bahamas?
| cgh wrote:
| In my experience, online gambling or banking.
| smithkl42 wrote:
| Insurance is a pretty common one. Lots of insurance companies
| have offices there - and if you're a top-notch dev, you can
| make a crap-ton of money as well.
| myth_drannon wrote:
| I find the Soviet idea of Math Circles so interesting and
| important. I bought books on the subject, but it's difficult to
| implement for your own children only. Nothing beats it like
| having an actual one, run by math teachers and in your city.
| zavg wrote:
| This is the most impressive thing I've seen in years.
| AlanYx wrote:
| It's wonderful that Khan Academy played a role in enriching her
| early education. It's proving to be a solid resource across the
| spectrum of math ability.
| debo_ wrote:
| Her notes are so clear and so artfully wrought! I wonder if
| learning from online resources makes one naturally focus more on
| presentation.
|
| From the article:
|
| https://www.quantamagazine.org/wp-content/uploads/2025/08/Ha...
| larodi wrote:
| Zvezdalina Stankova who comments on miss Cairo is on her own
| super out of the ordinary.
|
| https://math.berkeley.edu/~stankova/
|
| Not only she did grow in Bulgaria during the most turbolent times
| of regime change from communism to democracy, but later graduates
| with a PHD from Harvard, and later becomes Director and Founder
| of the Berkeley Math Circle, and is also organizer of math
| competitions in Bay Area, and publisher of what seems to be a
| complete set of Math Books, carefully crafted with her peers from
| BG and presented here
|
| https://archi-math.com/
|
| Curious whether miss Cairo was a student of hers or is to be.
| rossant wrote:
| Amazing story on a no-less amazing teenager.
|
| Also, I love the handwritten slide on one of the photos. Very
| nice.
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