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math is not a spectator sport. Just like you cannot learn to program by reading books, people have to really dive into problems and rediscover certain facts by

• hervature 5y ago
  I taught myself PHP from an old LAMP stack for dummies book years before any formal education in programming. Are you saying you need to actually program in addition to reading? No one is debating you need to work on math problems in addition to reading the definitions to learn math.
  • username90 5y ago
    Programming is a lot easier to self teach than math since you can test your programs by running them while you can't test your math work. The end result is that basically everyone who learns math creates a lot of errors in their understanding of it, and then those errors gets hammered out after countless exams as they progress through their education. Without the pressure of education most people just continue to accumulate errors in their understanding until they no longer can progress since the backlog of stuff is too long and they don't know where to start.
    • hervature 5y ago
      Can't test your math work? That's just completely false. The process is the test. Does each step make sense. Lower level math books include answers which will give you confidence the procedure was correct but no way ensures it. At a higher level, it changes to proofs where again, it doesn't matter if you know something is true or false, as long as each intermediate step it true. Of course, I'm not going to suggest that learning math solely from a book is optimal (neither is learning programming from a book), but it certainly isn't impossible.