At 17, Hannah Cairo solved a major math mystery
139 comments
·August 1, 2025impish9208
“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.”
munificent
Thank God she found math instead of Factorio.
_benj
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, cared about music production or anything interesting! The talk was which boy/girl whatever
cultofmetatron
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
pmdr
Learning opportunities are indeed better. But time sinks such as TikTok and YouTube have gotten exponentially better (read: addictive). I think there's a higher overall likelihood that a kid gets trapped in doomscrolling than in Khan Academy.
yumraj
Wonder why Berkeley didn’t offer her PhD admission given that she was already working with the Prof there.
AlanYx
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.
shermantanktop
- 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.
stockresearcher
> moved between countries or first/second gen immigrant?
“Cairo grew up in Nassau, the Bahamas, where her parents had moved so that her dad could take a job as a software developer”
“Travel restrictions stranded her family at her grandparents’ house in Chicago. While they were there, she joined the Math Circles of Chicago”
This doesn’t read like an immigrant. It kind of reads like her dad is a fully American finance dev.
coderatlarge
“After the spring semester ended, her family moved from Davis to Berkeley — her brother had decided to transfer there — and Cairo finally felt able to settle in.”
fascinating that the family follows the kids’ educational steps.
debo_
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...
jagged-chisel
Looks like a prepared presentation rather than notes.
baq
If all presentations were prepared like this I’d probably attend them
myth_drannon
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.
jarvist
Absolutely. Key for me was to invite children's friends (and family) along, host it in our house and make it a recurring weekly thing. The books (presumably you also have these from the MSRI's 'Mathematical Circles Library') are great, but week-to-week I've found the free online NRICH resources much more directly useful: https://nrich.maths.org/about-nrich
tocs3
Earlier discussion: https://news.ycombinator.com/item?id=44481441
I wish her the best in her coming career.
dang
Thanks! Macroexpanded:
A 17-year-old teen refutes a mathematical conjecture proposed 40 years ago - https://news.ycombinator.com/item?id=44481441 - July 2025 (105 comments)
MathMonkeyMan
Here's a link to the paper on the arxiv: https://arxiv.org/abs/2502.06137
larodi
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
Curious whether miss Cairo was a student of hers or is to be.
shusaku
I feel like a constructive proof is the best scenario for a young talent like this, they really can use their vivid imagination and manipulate what they are after.
anonzzzies
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
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?
valenterry
I'm on the practical side of things and have dabbled quite a bit with languages like Idris, I think we are mostly far from using them because of ergonomics.
Even in Scala (which is a very advanced language, but still far behind Idris) I deliberately don't use certain type-level features because it increases the compilation times too much (even with incremental compile!). It's very sad, but this is reality.
So, the problem isn't really that we need to "invent airplanes" - we already have them! What we need to do is make them usable and affordable by everyone.
I see more and more languages trying to add type-level features or try to embed other languages like Prolog-like ones into them. I hope that gets traction and becomes ergonomic, otherwise no one will use it in practice.
anonzzzies
I agree; I would say that most can be taught to people without advanced math/logic degrees/backgrounds, but because the tools are created by (and usually for) people with formal verification majors), they are just quite bad ergonomically as you say. I think we are in a good place of making it these types of proofs easier and faster more mainstream effort, not just one professor and their students, is put behind it. I believe AI will play a part here.
rossant
Amazing story on a no-less amazing teenager.
Also, I love the handwritten slide on one of the photos. Very nice.
Related: https://news.ycombinator.com/item?id=44481441 - July 2025 (105 comments)