> To be fair, I did spend a lot of time thinking about math because I liked it.
Spending childhood doing things you enjoy and which also have economic utility is a secret power.
Most people in the top 5th percentile of academic things also happened to spend a truly absurd amount of their youth obsessing over that academic thing. They may also be gifted, but spending all that free time in youth thinking about things is probably way more important than IQ.
(For me it was programming and law... I was reading legal briefs and slinging code most evenings of middle school through high school, which set me up with a rather absurd advantage over my peers once I got to college.)
BTW: elite unis/programs are looking for those types of people. It's not the extra curricular box checking that interests them, it's evidence of thousands of hours of practice at high value add skills. The practice can be forced with absurd amounts of grit, which is why it's a secret power when it comes out of intellectual curiosity.
Legal theory is a joy I discovered much later in life. The LSAT brain-teaser questions are also pretty fun. I've considered switching careers (now in my 30s), but I expect the realities of the job are much less thought-provoking.
Law is cool because it's like math, but because language is less precise than math, the rules are more malleable, and there is more room for creativity.
To be fair, I did spend a lot of time thinking about math because I liked it.