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At 17, Hannah Cairo solved a major math mystery

quantamagazine.org

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

#71

Post by JohnKemeny »

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!

> 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).

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

#72

Post by skeptrune »

psyklic wrote: post #70
skeptrune wrote: post #69

Earlier quoted context omitted.

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.

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.

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.

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

#73

Post by Quekid5 »

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!

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.)

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

#74

Post by Quekid5 »

skeptrune wrote: post #64
psyklic wrote: post #61

Earlier quoted context omitted.

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.

If you do research during your 4 year undergrad. You shouldn't have been undergrad. It's really that simple.

People sometimes accidentally do research. I'm not joking.

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

#75

Post by thrawa8387336 »

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…

No, that was the purpose of high school. As not practiced in public schools, as not practiced in the US

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

#76

Post by dh2022 »

psyklic wrote: post #68
skeptrune wrote: post #64

Earlier quoted context omitted.

If you do research during your 4 year undergrad. You shouldn't have been undergrad. It's really that simple.

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.

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.

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

#77

Post by conorbergin »

skeptrune wrote: post #29
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 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.

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”.

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

#79

Post by TheOtherHobbes »

conorbergin wrote: post #77
skeptrune wrote: post #29

Earlier quoted context omitted.

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.

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”.

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.

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

#80

Post by Aurornis »

skeptrune wrote: post #29
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 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.

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.

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