I love the following quote from Andrew Wiles: "Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go int

I love the following quote from Andrew Wiles: "Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room." I find this rings true--I didn't really understand the purpose of some of the material in differential calculus (Calc I) until I studied integral calculus (Calc II), and I didn't understand some of the material in integral calculus (II) until I took multivariable calculus (Calc III). Funnily enough, it was only after taking a combination of real analysis and discrete math (two years into undergraduate studies) that I finally had the A-ha moment when my real analysis class taught me how to actually read and write proofs, and my discrete math class finally made sets clear. THEN Calculus's proofs and its set-based conditions finally made sense. I could go on, but there's really something to the frustration that beginners in math have. It's ironical, but the best way to learn calculus is reproducing calculus's underlying proofs; but at the same time, the best way to learn how to read and write proofs is to use calculus as an example of a system you already know intuitively, and just need to learn the formal language of proofs to explain it. I guess my point is that there are genuine structural challenges/interactions in math's component knowledge systems which make the difficulty of learning math natural, if not to be expected. All of this to say, chin up lads, the only way out is through, and sometimes you're running blind. But that's okay, Andrew Wiles did too and he proved Fermat's Last Theorem.