They tell you it's useful (it is) and beautiful (in a way, for a slightly stretched definition of beauty). What they don't tell you right away is that there's no end to the stuff. Sooner or later you have to say "enough." And since a significant fraction of what I learned before I said that was useless [1], I wish I had said it sooner.
[1] I know you're not supposed to say math is useless. It's the kind of thing a disaffected sixth grader would do. But there are a lot of unnecessary proofs in math: things that seem perfectly obvious and are in fact true, but that require a long and counterintuitive argument to prove. Time and again I read the argument, pondered it, more than half-memorized it when the books could just as easily have said "A complex argument is necessary to establish what is obviously the case. Find it if you want to in Appendix J."
They tell you it's useful (it is) and beautiful (in a way, for a slightly stretched definition of beauty). What they don't tell you right away is that there's no end to the stuff. Sooner or later you have to say "enough." And since a significant fraction of what I learned before I said that was useless [1], I wish I had said it sooner.
[1] I know you're not supposed to say math is useless. It's the kind of thing a disaffected sixth grader would do. But there are a lot of unnecessary proofs in math: things that seem perfectly obvious and are in fact true, but that require a long and counterintuitive argument to prove. Time and again I read the argument, pondered it, more than half-memorized it when the books could just as easily have said "A complex argument is necessary to establish what is obviously the case. Find it if you want to in Appendix J."