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At 17, Hannah Cairo solved a major math mystery

quantamagazine.org

121–130 of 186 posts

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

#121

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?

be actually gifted this is what gifted looks like, not legions of students who are told they are "gifted" but are just pretty smart

Yes, but it's not enough.

Be actually gifted and apply to a university that isn't run by dickheads.

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

#122
post #10

Earlier quoted context omitted.

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 profes…

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.

I suspect the reason is not about babying her as much as it is a concern for her development, about whether she would be "missing out" on the opportunities for social and intellectual growth in college. This kind of thing is usually why well intentioned higher ed people put roadblocks in front of precocious young people.

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

#123
post #112

“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.

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

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

#124

> 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 don't see why it would matter. she could quit math now and still be ahead of the majority of mathematician in terms of contributions. The rest is just formalities. I can see her breezing through the undergrad, quals, etc . It would just be a small delay.

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

#125
post #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 profes…

i can understand a university administrator not feeling they can give a good educational experience to a 14 year old.

but she'd be the same age as all the first years on campus, any university must be institutionally equipped to deal with a 17/18 year old. seems like an odd choice to personally intervene to cancel an admission.

like presumably if she enrolled in a bachelor's program, and then signed up for grad math classes while doing independent research, this would be fine. but if she takes the same classes and does the same research for PhD credits instead, no good?

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

#126

Earlier quoted context omitted.

Cairo may have a way out: Commonly the main criteria for a Ph.D. is: (1) Pass qualifying exams in several important topics in the field. (2) Do some research that is an "original contribution to knowledge worthy of publication" where the main criteria for publication is "new, correct, and significant". No professor or university Dean can keep her from doing well on both (1) and (2). It looks like (1) would be easy en…

PhDs in the USA also have curricular requirements, with at least some required courses. These courses are only available after a bunch of paperwork is given to the university. So, it's not so easy.

My Ph.D., applied math, Johns Hopkins, supports my post.

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

#127

- 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.

> 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…

“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.

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

#128

> 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…

> especially if it is required for other students to take

How many of the other students disproved 2 conjectures in advanced calculus that were open for decades?

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

#129
post #58

Earlier quoted context omitted.

This is answered in the article’s second paragraph.

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.

It's loosely explained deep down in the article.

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

#130

Earlier quoted context omitted.

This is the entire premise of a liberal arts education. Not everyone pursues one, but it's certainly well-represented at the tertiary education level.

I've not studied this, but my guess is that the liberal arts education as the foundation is necessary to allow young people a chance to figure out who they are. I certainly found this to be true for me and would guess for my closest college friends. If a young person is exceptional, do we force them into a liberal arts box? Surely there is value in literature and history. But this one young woman had found her passio…

Maybe. What interested me at 17 certainly does not interest me now.
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