What do people mean when they say learn math in depth, and not just memorizing formulae? How is "mathematics in depth" defined? I want to make sure I learn "in depth", so I try to play around with the rules of math, for example multiplication with exponents: How come a^m*a^n = a^m+n? Obviously, this example was very simple. But when it comes to more advanced methods: How are you sure that you're actually _learning_ and not memorizing?