No matter how much advanced mathematics you study, the great thing is that you rarely have to accept anything as-is. If you come across a procedure, technique, or result and you wonder how in the world it works, you can always retrace your steps and get back to the foundational reasons as to why it works. If you keep on asking “why”, you will eventually get back to your starting axioms. In between that and your starting point, you should be able to understand the concept as obvious¹.

We like being recognized for the work we do. This is even more relevant now, with the idea of documenting everything you do. (If it isn’t documented, did it happen?) We don’t want to do work unless there is some reward attached.

This is a question that students encounter over and over throughout their education. It crops up when deciding what classes to take, what projects to embark on, and what programs to study. It is a natural question, because we don’t like embarrassing ourselves. Therefore, we want to avoid pursuits that are too difficult if possible.

Learning mathematics is an additive process. What I mean by this is that new mathematics often builds on what came before. Learning mathematics isn’t exactly a linear journey, but it’s a good enough rough approximation.