My son is a very mathy kid who does math problems for fun. He is going into 8th grade and will be doing PreCalculus this coming Fall. PreCalculus in 8th grade is not unusual in my area where there are many kids who are advanced in math.
We would be applying to private schools for his 9th grade year. I am looking at both Harker and Proof school for High School. More specifically, I am looking at their post-AP math program. I see that Harker offers the usual Linear Algebra, Differential Equations, Discrete math and a few other topics. I looked at Proof school and they offer a lot more options for post-Calculus level (obviously, because they are a math oriented school). My son ultimately wants to double major in physics and math when he goes to college. He has zero interest in math competitions and has instead spent time participating in university Math Circles, reading fun math books and working on challenging math proofs as a hobby. Given this temperament, I am wondering if he will thrive in Harker where the math department seems to be oriented towards mentoring its top talented students for competition success. I am not sure if he is mathy enough to get into Proof School given that he has a rather broad exposure to various areas of math rather than a deep focus on any one area.
Could anyone help me out with information on how a mathy but not very competitive kid might fare in the admissions process in both of these schools?