This comment is mainly for the OP but I really enjoyed your reply. I’m currently reading A Programmer’s Introduction to Mathematics by Jeremy Khun which is abso

This comment is mainly for the OP but I really enjoyed your reply. I’m currently reading A Programmer’s Introduction to Mathematics by Jeremy Khun which is absolutely phenomenal so far. But he gives the same advice as above. He states that as soon as you see a theorem or problem in math you need to instantly start writing down examples. Write down examples and then see that they fit the rule. I found when I took Discrete back in University that advice as very helpful (I got the advice to split up large complex problems into their smallest and simplest cases from a TA at the time.) in proving things you often work yourself up from simple examples to more complex examples generally, but often if you can prove by induction you need only the simplest case (base case) and the abstract case (induction step from n to n+1). Sometimes these abstract cases are hard to spot and they definitely take time, but as you learn more of them over time you’ll find that you can do them a lot easier. My Discrete Math teacher said to learn something in mathematics you have to basically already know it. This was just to say with math there is no metaphorical “royal roads” [1] (short cuts) in mathematics and that things come step by step. You’ll eventually get enough tools in your tool belt to handle abstract thought better and better. [1]: https://en.m.wikipedia.org/wiki/Royal_Road https://en.m.wikipedia.org/wiki/Royal_Road