> Jeez... what a damning indictment of today's Universities.

> She could just use her publication as a dissertation and be done with it.

I’m not suggesting this person is doing anything fraudulent as she seems quite impressive.

However, educational institutions get constant requests from parents who want their children to skip far ahead before they’re ready. It’s a competitive world and they know that being able to claim a child skipped several grades or even skipped undergrad entirely is a unique and very impressive achievement for the resume. It also theoretically provides a few additional years of earning potential by giving a career head start.

The first problem is that many of these parents (again, no accusations for this specific case) see this and want to make it happen for their child at any cost. There are some wild stories about parents trying to cheat their kids forward or falsifying their accomplishments to try to skip grades.

The secondary problem is that it can be hard on kids to be thrust forward so far past their peers. I had several friends who skipped a grade in middle school and most of them didn’t have a great experience for social reasons. Skipping undergrad altogether would thrust someone into a foreign world with a lot of baseline expectations and norms that they hadn’t yet learned, combined with no peers their age to discuss it with.

It creates a high chance for burnout or failure, which could leave them worse off than when they started.

That’s why the recommendation is generally to do undergrad at a challenging institution that allows students some upward mobility in specific areas where they’re ahead. No reasonable undergrad program is going to have this person taking Algebra 101, but there are a lot of opportunities for them to jump right into advanced programs and go deep and broad.

IIRC Erik Demaine was also homeschooled, skipped college, got a very early PhD, and joined the MIT math faculty as a teenager (he is a full professor there now). Johnny von Neumann OTOH went through a "normal" secondary education partly because his parents wanted him to have traditional social exposure to kids his age while he was growing up. His math training was very accelerated though, and he had professional level research publications at 17.

Clearly the correct method is: publish your “dissertation” first, then apply for admittance to the PhD program.