I solve mathematical problems every day, some by hand and some with the computer. I wonder: What will I lose if I start doing the mathematical problems only by computer? I've read this text and the author says that as techonology progress happens, we should change our focus to things that are more important. (You can see his suggestions on what is more important, in the suggested text.)
I'm in search of something a little more deep than the conventional cataclysmic hypothesis: "What will you do when a EMP hit us?!" and also considering an environment without exams which also exclude the "Computers are not allowed in exams" answer.
This is of crucial importance to me because as I'm building some mathematical knowledge, I want to have a safe house in the future. I'm also open to references on this, I've asked something similar before and got a few indications.
Best Answer
This highly depends on the level at which you want to solve problems. You will be able to solve linear algebra and calculus problems with a computer, but you will not be able to prove theorems and various results. However, there are very good reasons for using a computer in mathematics. In particular, you can make very technical computations and save a lot of time, but again, these computations always rest on a good conceptual understanding.