We have math kids. Schools vary a lot in terms of “advanced” math. Many state they have advanced math, but check the curriculum carefully. Make sure there is flexibility so your math kid can skip things if needed. Also, not all schools have teachers with advanced math degrees while others are outstanding. It’s great if your kid can create their own path with guidance.
You can likely speak to the math chair ( after acceptance). Math kids like yours are pretty rare in the US (but not in other nations which are often 2+ years ahead of US students).
You also have to check to ensure your math kid can take science classes that mesh together. Sometimes a kid cannot take a particular science unless they have a particular math ( even if the skill is there). You should also check to see how far the schools math team has gone in national/international contests. And check out their science dept as well. Many schools are stronger in one dept. or another. Some also require that kids not only do well but also get particular scores in order to pursue particular classes.
Lastly, ask your kid for input. One of my kids took an easier math path since they realized it was an unlikely path that they would take in college. Ending at level X in math was the plan. Why take independent study if there are so many other things to delve into. ( This was my kids thinking).