5 ms·

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 decad

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?

deleted 1y ago
[deleted]
nextos 1y ago
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 https://arxiv.org/pdf/2502.06137) as a thesis and possibly graduate. Sometimes, you can even do this without a supervisor.
- xg15 1y ago
  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 1y ago
  PhD by publication usually takes a bit more work. I think they tend to want 3 related papers in a field.
  - stogot 1y ago
    What level or type of publication is required?
    - pclmulqdq 1y ago
      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 1y ago
    That's a rule of thumb for applied sciences. Plenty of theory PhDs graduate with 1 or 0 papers.
    - pclmulqdq 1y ago
      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.
      - almostgotcaught 1y ago
        > Nobody gets a PhD by publication with 0 publications. Do you have a PhD from a theory department? I do. You're wrong.
        pclmulqdq 1y ago
        Lots of people get PhDs with no publications. Nobody gets a PhD by publication without publications. It's literally axiomatic.
        almostgotcaught 1y ago
        It's amazing how many people on hn are experts on things they do not have the qualifications to be expert on. > It's literally axiomatic. You've made up some axiomatic definition of "by publication" that does not bear any resemblance to the actual definition. Consider that it's possible to 1. Submit a preprint to arxiv and have it count 2. Submit a preprint to a journal and defend before it accepted (or rejected) 3. Not submit anything anywhere and have the PhD itself count (almost all PhDs get an ORCID)
        pclmulqdq 1y ago
        Are you aware that "PhD by publication" is a real thing that is a separate path than a normal PhD? It is relatively common for schools in some European countries to offer these, but not that common outside Europe. This is a process where you can write your "dissertation" by putting an intro and a conclusion on ~3 papers you have already published and get a PhD that way. You enroll in the school for ~3 months, write the missing parts, and that's it. This is a flexible path to a PhD for industry researchers or other people who have a lot of expertise and have pushed the boundaries of a field but did not do a formal PhD program. I have never heard of anyone doing this with ArXiV preprints or any school accepting this path if they are not referreed papers. I would love to see an actual counterexample if you have one.
- skissane 1y ago
  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.)
parpfish 1y ago
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.
- ics 1y ago
  IIRC Erik Demaine (https://en.wikipedia.org/wiki/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 1y ago
    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 1y ago
    theodore kacsynski started teaching at 22. a damn bright spark before he was victimised by the mind control experiment.
    - lupire 1y ago
      Kasynski got his masters degree at 22, which just slightly younger than average.
- tehjoker 1y ago
  When she graduates she'll probably be between 20 to 23 years old.
- j7ake 1y ago
  In math or theoretical fields it’s not unheard of to have young professors. Terence Tao was full professor at 24. Wolfram at 21
EvgeniyZh 1y ago
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 1y ago
  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 1y ago
    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.
eviks 1y ago
There is no deep theory here, bureaucracy doesn't think deep.
daxfohl 1y ago
A PhD is as much a stamp of endurance as it is a stamp of intelligence or accomplishment.
MPSFounder 1y ago
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 1y ago
  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.
YeGoblynQueenne 1y ago
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.
coolguy5642 1y ago
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deleted 1y ago

[deleted]

nextos 1y ago

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 https://arxiv.org/pdf/2502.06137) as a thesis and possibly graduate. Sometimes, you can even do this without a supervisor.

xg15 1y ago
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 1y ago
PhD by publication usually takes a bit more work. I think they tend to want 3 related papers in a field.
- stogot 1y ago
  What level or type of publication is required?
  - pclmulqdq 1y ago
    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 1y ago
  That's a rule of thumb for applied sciences. Plenty of theory PhDs graduate with 1 or 0 papers.
  - pclmulqdq 1y ago
    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.
    - almostgotcaught 1y ago
      > Nobody gets a PhD by publication with 0 publications. Do you have a PhD from a theory department? I do. You're wrong.
      - pclmulqdq 1y ago
        Lots of people get PhDs with no publications. Nobody gets a PhD by publication without publications. It's literally axiomatic.
        almostgotcaught 1y ago
        It's amazing how many people on hn are experts on things they do not have the qualifications to be expert on. > It's literally axiomatic. You've made up some axiomatic definition of "by publication" that does not bear any resemblance to the actual definition. Consider that it's possible to 1. Submit a preprint to arxiv and have it count 2. Submit a preprint to a journal and defend before it accepted (or rejected) 3. Not submit anything anywhere and have the PhD itself count (almost all PhDs get an ORCID)
        pclmulqdq 1y ago
        Are you aware that "PhD by publication" is a real thing that is a separate path than a normal PhD? It is relatively common for schools in some European countries to offer these, but not that common outside Europe. This is a process where you can write your "dissertation" by putting an intro and a conclusion on ~3 papers you have already published and get a PhD that way. You enroll in the school for ~3 months, write the missing parts, and that's it. This is a flexible path to a PhD for industry researchers or other people who have a lot of expertise and have pushed the boundaries of a field but did not do a formal PhD program. I have never heard of anyone doing this with ArXiV preprints or any school accepting this path if they are not referreed papers. I would love to see an actual counterexample if you have one.
skissane 1y ago
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.)

parpfish 1y ago

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.

ics 1y ago
IIRC Erik Demaine (https://en.wikipedia.org/wiki/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 1y ago
  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 1y ago
  theodore kacsynski started teaching at 22. a damn bright spark before he was victimised by the mind control experiment.
  - lupire 1y ago
    Kasynski got his masters degree at 22, which just slightly younger than average.
tehjoker 1y ago
When she graduates she'll probably be between 20 to 23 years old.
j7ake 1y ago
In math or theoretical fields it’s not unheard of to have young professors. Terence Tao was full professor at 24. Wolfram at 21

EvgeniyZh 1y ago

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 1y ago
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 1y ago
  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.

eviks 1y ago

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

daxfohl 1y ago

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

MPSFounder 1y ago

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 1y ago
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.

YeGoblynQueenne 1y ago

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.

coolguy5642 1y ago

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