Congrats!
No advice per se, but I do have a bit of experience. My oldest went to college at 16, she received a full academic scholarship to TCU and lived on campus in the "Honors" dorm. The college was only an hour away, so we figured it wasn't such a big deal since she could come home on weekends if she wanted to.

For us, it turned out to be a bit of a disappointment. My DD enjoyed the academics but outside of class, she did not really enjoy herself too much, I think for several reasons but primarily she felt out of place socially.

She tried to get involved and joined organizations etc, but she found that she could not participate in many of the activities due to her age (i.e. in the service fraternity, she couldn't even volunteer to walk dogs in the shelter and many of the social gatherings occurred at clubs that you had to be 18 to go to).

Additionally, even in the Honors dorm, there was a lot of partying and alcohol which my DD wanted no parts of, several times she found a passed out girl laying on her bed with a barf pail - my DD's room-mates would be keeping an eye on on a friend that would binge periodically(!).

In hindsight, I think it might have been easier if she had gone further away because in our case it was just too easy for her to give up trying to assimilate at the University. She would just meet up with her high school buddies off campus on the weekends.

After a year, despite a 3.5 college GPA and a great scholarship, my DD transferred to a State University where some of her friends were going. She had a much better time although she was no longer being challenged as much academically. She is now in Grad school at 20, and very happy being the big fish in the little pond, so to speak.

Perhaps your son's involvement in the math clubs will make the assimilation easier for him. He will at least have an automatic base group to be a part of. Or perhaps your son is less dependent on that sense of "belonging" than my DD. I do think things might have gone very differently if my DD would have joined the marching band in College - then she would have belonged to a group and I suspect that would have made a big difference. No regrets though, she is doing great and I am very proud of her.

Good luck!