<p>That, in my own opinion, is a better bet indeed - mainly because of the whole thing about learning to formally manipulate something more intrinsically formal. </p>
<p>Also villager, my personal suggestion - before you get immersed in math, try some reasonably serious physics too. I think as you get older, your resistance to spending serious time on stuff outside your immediate comfort increases. I remember reading a bunch of these math books in high school, and wish I poked around other subjects more.</p>
<p>The key difference is that physics is the kind of subject you have to really do to start getting the intuition, and it’s of a different nature, which is harder to dive into once you’re far down another path.</p>