But the distinction is generally not as clear as you may think. (1) Much of the mathematics came from real world problems (so, in particular, one may get drawn

But the distinction is generally not as clear as you may think. (1) Much of the mathematics came from real world problems (so, in particular, one may get drawn into some kind of mathematical research and even end up discovering new mathematical facts). (2) Sometimes when applying mathematics one still needs to employ deduction (derive a formula, prove a statement one wants to rely on, etc.).