[ledauphin]

here's a dumb question:

she's starting her Ph.D. this fall - hasn't she already achieved it? What is the theory behind expecting someone who has solved a decades-old problem to do some "second" thing to prove that they have extended the bounds of human knowledge?

[EvgeniyZh]

Ph.D. is training in how to do research. Solving one, even very hard problem not necessarily means that you don't need such training. It's especially tricky with counterexamples which sometimes question of raw talent and luck rather than skill.

The next step for someone who has PhD and want to stay in academia is postdoc. After solving one problem, you would not necessarily have what's needed to get a good postdoc, such as clear research agenda or proof of ability to publish consistently.

[andy99]

Modern PhDs are not designed for people that are smart like this. She's a math savant that obviously has a unique and demonstrably effective way of looking at things, why destroy that with "training how to do research".

I hope she's found a program that will support her while realizing she's smarter than whomever is setting the rules, rather than something stifling.

[mkl]

This is not true at all. Maths PhDs are excellent for this kind of person, and foster and grow such abilities. No matter how smart you are, training on how to do research is going to improve your capabilities and success.

[parpfish]

But what does somebody do with a PhD at age 17? I can’t imagine hiring them as a prof when they’re so young. It’s not a bad idea to just take a couple years to continue your already productive collaboration while getting mentored on the non-math parts of being a mathematician.

[beezlebroxxxxxx]

> I can’t imagine hiring them as a prof when they’re so young

Many institutions would actually jump at the chance. That's way better than a 35 or 37 year old burnt out from just finishing their PhD and getting onto the tenure track suffer-fest. Think of how many years of productive research she has in her. It used to be way more common until academia became so professionalized and bureaucratic.

[j7ake]

In math or theoretical fields it’s not unheard of to have young professors. Terence Tao was full professor at 24. Wolfram at 21

[parpfish]

She could still do a few years of PhD training and still be a super young prof like those two.

At 17 she’s so young that a uni hiring her would need to think about child labor laws

[ics]

IIRC Erik Demaine (https://en.wikipedia.org/wiki/Erik_Demaine) started teaching at 20 and had his PhD. I can't remember if I first saw his name because of the MacArthur Grant or one of those science documentaries but one of his pages was on the frontpage here a week or two ago and it seems like he's been thriving.

[daxfohl]

Noam Elkies too, the youngest ever tenured prof at Harvard. Another parallel he had a pretty famous contradiction proof, of Euler's conjecture. But he didn't find that until age 22, so seems like this girl has a good head start!

[ekaryotic]

theodore kacsynski started teaching at 22. a damn bright spark before he was victimised by the mind control experiment.

[lupire]

Kasynski got his masters degree at 22, which just slightly younger than average.

[tehjoker]

When she graduates she'll probably be between 20 to 23 years old.

[CurtMonash]

I was one of several math grad students who started at Harvard at age 16 or 17 aroud the same time. Ofer Gabber and Ran Donagi went on to conventional academic math careers. I took a less straightforward career path.

But I was offered an assistant professorship at the Kellogg School of Business at age 21, and have often wondered whether I should perhaps have taken that, or else the research position I was offered at RAND.

[jovial_cavalier]

What does someone do with a PhD at age 35? Go into industry? Continue as a postdoc? Open a juice bar? It doesn't matter what she's going to "do" with it. It's accreditation of a certain degree of academic achievement, which she has achieved. Arguing that she doesn't deserve it or needs to earn it the "normal" way is stupid.

[bsoles]

Norbert Wiener got his PhD from Harvard when he was 19: https://en.wikipedia.org/wiki/Norbert_Wiener.

[ledauphin]

start on a postdoc :)

[nextos]

A PhD in the US requires a lot of coursework, aside from research. Perhaps, she is interested in that. Otherwise, some universities, especially in EU, offer PhDs by publication. She could simply wrap up her counter-example publication (https://arxiv.org/pdf/2502.06137) as a thesis and possibly graduate. Sometimes, you can even do this without a supervisor.

[xg15]

Sounds as if she even has a potential supervisor:

> “It took me a while to convince Ruixiang Zhang [the professor of the course where the problem had been posed] that my proposal was actually correct,” Cairo says

> At the University of Maryland, she will continue working under the supervision of Zhang. “He helped me so much, and I’m really grateful. Beyond his class, which I loved, he spent countless hours tutoring me,” she recalls.

[pclmulqdq]

PhD by publication usually takes a bit more work. I think they tend to want 3 related papers in a field.

[stogot]

What level or type of publication is required?

[pclmulqdq]

They must be peer-reviewed journal papers and I believe they tend to prefer if at least one is well-cited or significant, especially if you have only three papers. It is generally harder to get a PhD by publication than to get a PhD the normal way.

[almostgotcaught]

That's a rule of thumb for applied sciences. Plenty of theory PhDs graduate with 1 or 0 papers.

[pclmulqdq]

Nobody gets a PhD by publication with 0 publications. This is usually a backdoor for people who have done a lot of work in a field, certainly far more than a PhD thesis, and have just never gotten the credential.

[pcrh]

A PhD thesis is itself a publication.

PhDs "by publication" refers to not having to submit work additional that already published to the examining committee.

[almostgotcaught]

> Nobody gets a PhD by publication with 0 publications.

Do you have a PhD from a theory department? I do. You're wrong.

[pclmulqdq]

Lots of people get PhDs with no publications.

Nobody gets a PhD by publication without publications. It's literally axiomatic.

[skissane]

A PhD by publication sounds very similar to a higher doctorate (DSc, DLitt, etc). Substantive (as opposed to honoris causa) higher doctorates are awarded based on publication record only. To be eligible for a substantive higher doctorate, you generally are expected to have a PhD first - but it might not be an absolute requirement. You’d generally expect a bunch of papers, but in principle a single publication (if sufficiently groundbreaking) could be enough. While this is very impressive for a 17 year old (I wish I could have done that at 17, or at any other age for that matter), it probably isn’t significant enough for a higher doctorate all by itself. If she’d proved P=NP, different story. (Who knows, maybe she shall-well, probably not, but I’d be very happy to be proven wrong about that.)

[daxfohl]

A PhD is as much a stamp of endurance as it is a stamp of intelligence or accomplishment.

[MPSFounder]

Great question. I have a PhD. People forgot the purpose of a PhD. Hannah effectively achieved what many with a PhD fail to do, and that is contribute novel research. A PhD in the US (only place I can comment on) has lately been focused first and foremost on a) preparing for academia, which entails teaching and a lot of courses, and b) research for industry positions (many students in my cohort were from China or India and this was their segway into a job in the US). I agree a PhD should be purely focused on research and extending human knowledge. In practice, it is a business where students go to conferences to promote their PI's work, where Universities get cheap lecturers in the form of TAs, and where many mediocre students write incremental papers to secure an RnD position (change this by a little and see how it affects your results. This is your paper). I am very impressed by Hannah's work though and she embodies the selfless nature of research that is very much missing. I see too often people seeking to advance their own career and pick a PhD route of least resistance. While they are entitled to maximize profits, and oftentimes do not want to go to academia where solving the impossible is admired, we must remember discoveries often hinge on challenging problems and a selfless pursuit of the impossible. This is just my opinion based on what I saw in my cohort and at 30+ conferences

[vladms]

I do not think there is "one" purpose for a PhD, and not everyone gets the same thing from it - it depends on what are a person's strong and weak points. I have seen very smart people not able to explain at all their work and during a PhD they were forced to improve. I have seen very good presenters that were forced to do some actual work. I have seen people that were convinced they can solve anything (as in some parts of the world the bachelor and master focus to much on solvable problems) understand that sometimes there just isn't a clear, nice solution to a problem.

On average someone that does have a PhD will have a wider set of skills, like understanding of the complexities of the field, resistance to frustration, capability to do research and ability to communicate.

[eviks]

There is no deep theory here, bureaucracy doesn't think deep.

[YeGoblynQueenne]

A PhD can be an opportunity to learn, or an opportunity to brag. I'm guessing the teen in the article is going to go for the first one.