<p>If majoring in math is a possibility, take a look at each school’s math course offerings to ensure that it has sufficient offerings to keep him interested. Use the larger universities with good math departments as a basis for comparison. Typical math major courses at the junior and senior level include real analysis, complex analysis, abstract algebra, advanced linear algebra, geometry, set theory, logic, numerical analysis, ordinary and partial differential equations, history of math, and various applied areas like cryptography, computability, mathematical economics, quantum mechanics, etc… Statistics and computer science may be their own departments, but are sometimes combined with the math department in smaller schools.</p>
<p>If he is more than a year advanced (i.e. will have taken college math courses beyond the calculus BC level while still in high school), consider schools which have a good graduate program in math.</p>