I studied mathematics at university (though in the UK at Oxford so a different system) and studied a good proportion of the first year course independently from

I studied mathematics at university (though in the UK at Oxford so a different system) and studied a good proportion of the first year course independently from text books before I go there. But I still learned so much more in my first year by being taught by the experts, having my thinking dissected and generally being put through my paces. I don't think I could have become as good a mathematician as I did just by studying independently. Obviously, the tutorial system at Oxford was a great benefit though and I don't know how that compares to teaching at Princeton. (This was also long enough ago that I didn't have to pay for tuition so it was a no-brainer decision to go there rather than study independently!)