Is it possible to pick up programming skills by studying computer science books? In particular I enjoy reading SICP because of its mathematical nature. So far I have been using SICP like a math book without any REPL. Just pen and paper problem solving. But I was told that won't teach you any useful coding skills. Just learning how to code seems to be an unbelievably painful task. Are there any math oriented compsci books that double as coding boot camp? Thanks.
If you understand the math, give coding a try. I suspect you'll find it easier than you're anticipating it will be.
The REPL is an incredibly user-friendly way to learn to program. Try it. I'm surprised you like math and don't want to use the REPL, since the REPL in many ways resembles a powerful calculator (and can be used as such)
If you really like the math approach, and grow to appreciate the REPL, give "The Haskell Road to Logic, Maths and Programming" by Doets and van Eijck a try.
But no, you can't pick up programming just from reading books without attempting to program. You could pick up a good bit of computer science like that, but not programming. Programming must be experienced.
Instead of pen and paper, fire up that REPL and learn you some scheme. The book is called "Structure and Interpretation of Computer Programs" for a reason.