Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

At 17, Hannah Cairo solved a major math mystery

quantamagazine.org

Post reply on HN
Print view View original

161–170 of 186 posts

Re: At 17, Hannah Cairo solved a major math mystery

#161

Post by thrance »

debo_ wrote: post #83

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...

I studied math and knew a girl like that, spending an inordinate amount of times making sure to understand every single details of what we were taught, even going further when I could barely keep up. She would also make those pretty, colorful notes with visual interpretations and drawings in the margin. It takes a special form of love for the discipline. She just finished her PhD and is now starting a postdoctoral contract.

Re: At 17, Hannah Cairo solved a major math mystery

#162

Post by thrance »

corimaith wrote: post #158

>Cairo kept reading and thinking. Eventually, she found a way to construct a strange, complicated function out of waves whose frequencies all lay on a curved surface — the type of surface the conjecture required. Usually, when you add these kinds of waves together, they interfere, canceling each other out in some places and reinforcing each other elsewhere. Rather than speaking about her age or the vague notion of ta…

Heh, take a look at her paper [0]. It is much more complex that TFA makes it out to be: once you have the intuition you need to prove it actually disproves the theorem.

Also, it's probably a not very well known conjecture that people wouldn't care too much about. Also also, it was a conjecture: people were probably looking to prove it rather that disprove it, failing and then giving up.

[0] https://arxiv.org/abs/2502.06137

Re: At 17, Hannah Cairo solved a major math mystery

#163

Post by thrance »

diimdeep wrote: post #148

– were all homeschooled. Cairo started learning math using Khan Academy’s online lessons, and she quickly advanced through its standard curriculum. By the time she was 11 years old, she’d finished calculus No normal childhood and certain kinds of parents, disproportionately more math education, there is certain downsides to all this, that articles like this conveniently avoid to mention.

    “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 don't think they're omitting it, but yeah. A lot of homeschooled kids don't fare nearly as well.

Re: At 17, Hannah Cairo solved a major math mystery

#164

Post by SJC_Hacker »

cultofmetatron wrote: post #123
_benj wrote: post #112

Earlier quoted context omitted.

Maybe hot take… I can see the point of sameness in homeschooling, but compared to traditional education? I’m not sure how much flexibility one would have to teach oneself calculus by 11 or the equivalent of an undergrad in math by 14! That flexibility must be found in something non-traditional! I’m no prodigy at all whatsoever but school was mostly dull and filled with teenager drama! Nobody knew what Linux was, care…

its so much better nowadays. I"m 40 now and I'm low key jelous of kids today. Today if you want to learn to code, you have freecode camp and chatgpt to ask questions. Math? there's mathacademy and khanacademy. There are so many options now for learning stuff that we didn't have

So many options but also a corresponding amount of competition and pressure

And with social media, you aren't just comparing yourself to your classmates, but with basically the entire world

Re: At 17, Hannah Cairo solved a major math mystery

#167

Post by throwaway81523 »

larodi wrote: post #88

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…

Alexander Givental is also involved with that, I think.

https://sumizdat.com/homepage/index.html scroll down.

Re: At 17, Hannah Cairo solved a major math mystery

#168

Post by anonzzzies »

Timwi wrote: post #141
Imustaskforhelp wrote: post #54

Earlier quoted context omitted.

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 bigge…

> what would be the biggest life lesson (in coding, or anything general) Pursue what interests you and what fires up your passion, not what grown-ups tell you is “lucrative”, “prestigious”, “profitable” or somesuch.

I have nothing to add to that.

Re: At 17, Hannah Cairo solved a major math mystery

#169

Post by dekhn »

ykonstant wrote: post #145
dekhn wrote: post #115

Earlier quoted context omitted.

It's generally well documented that Kacynski was a highly talented mathematician.

Yes, but like the gp said, not even remotely close in skill.

how would you know for sure? I don't have the skill to evaluate somebody who has disproved one conjecture (maybe some recent techniques made it easier?) versus somebody who had an established pattern of doing excellent work.

Re: At 17, Hannah Cairo solved a major math mystery

#170

Post by wiredfool »

TrackerFF wrote: post #40
1024core wrote: post #18

> 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!

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…

You say that like it’s a universal thing. It’s much more of a Liberal Arts thing, which is much more prevalent in the US then in Europe.
Post reply on HN