[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.

[almostgotcaught]

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)

[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.)