Related: https://news.ycombinator.com/item?id=44481441 - July 2025 (105 comments)
At 17, Hannah Cairo solved a major math mystery
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At 17, Hannah Cairo solved a major math mystery
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Re: At 17, Hannah Cairo solved a major math mystery
#2Earlier discussion: https://news.ycombinator.com/item?id=44481441
I wish her the best in her coming career.
Re: At 17, Hannah Cairo solved a major math mystery
#3What 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?
Re: At 17, Hannah Cairo solved a major math mystery
#4Earlier discussion: https://news.ycombinator.com/item?id=44481441 I wish her the best in her coming career.
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)
Re: At 17, Hannah Cairo solved a major math mystery
#5As 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.
Re: At 17, Hannah Cairo solved a major math mystery
#6What 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?
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.
Re: At 17, Hannah Cairo solved a major math mystery
#7A less click-baity headline might be "17 year old Hannah Cairo has solved the Mizohata-Takeuchi conjecture"
Re: At 17, Hannah Cairo solved a major math mystery
#8”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.
Re: At 17, Hannah Cairo solved a major math mystery
#9What 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?
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).
Re: At 17, Hannah Cairo solved a major math mystery
#10”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…
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.