11-yr-old’s Ultimate Goal: phd Theoretical Mathematics

[cookderosa]

Good Morning America yesterday-

homeschooled / dual enrolled entering law school.

https://www.goodmorningamerica.com/livin...l-61805537

[sicdrag]

A few thoughts:

1. Obviously keeping options open is good. One important thing to note is that upper level math is far far different from what you encounter through calculus. Earlier math courses are primarily computational based (i.e. finding the right answer) while upper level math is almost entirely about proving results. A lot of people find that they don't like proofs as much as they thought (sometimes it is opposite though!). Just something to keep in mind. The good news is that a degree or knowledge in math can be easily extended to other disciplines if you want something more applied.

2. The job market for math professors is very bad. If your son is sure he wants to do that, the goal should be to get into a top 10 (or at least top 20) school to do his PhD. Otherwise, it is very unlikely to find a tenure track position in math. I know people who got PhDs from pretty good schools and completely struck out on even landing a postdoc position, let alone anything better than that.

3. The most important factor in math PhD admissions is doing well in upper level proof based math classes and getting good letters of recommendation from well known/respected professors. In my view, you really have to do a traditional undergrad in order to get this. It doesn't necessarily have to be at an elite school, but it certainly would help.

[TorsMama]

Once he passes Calculus, I would look for mentors for him at your local university where he could even audit courses. 
I know of several gifted math or physics students who got full rides to college because of their advanced knowledge in coursework. I also know a few where the university just picked the student up as a graded student offering free tuition once they prove themselves in the classroom... good PR for the college. 
You just have to be ready for the publicity. 
Once the story of your son is out, you have to be ready for everyone and their brother giving you advice on how to raise your child. Publicity is a double edged sword. 
We have thus far been able to steer away from the publicity but my son1 switched from being math/science kid to history/lit kid which made the avoidance of publicity easier.
Another note, if your son is not a Davidson Young Scholar, you probably want to get your son tested for the program. 
It it free once you qualify and will help tremendously in finding mentors as well as it will open doors for your son.

Best wishes.

Thank you. He is a Davidson Young Scholar but I have not found it helpful as far as finding mentors though it has been helpful in other ways. Perhaps I am not asking the right questions of looking in the right places. I think once he is wanting to start dual enrollment for math (in a year or so) I will work harder trying to find a mentor.