Rationalist!Harry is calibrated to match the knowledge and recall of a 34-year-old autodidact. Even presuming a very friendly environment and that said 34-year-old autodidact's training was not optimal, I just don't think there's enough time.
I can buy a 10 year old reading Ender's Game and The Lord of the Rings and maybe even Lensmen. It's a bit harder to imagine one that would consider wanting to want the math behind proving N=NP, nevermind going further than that.
I wanted the maths behind relativity and QM at age 10. And I wasted a lot of time in school.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.