Old rule: "Measure twice. Saw once." Another old rule: "Believe none of what you hear and half of what you see and still will believe twice too much." I le

Old rule: "Measure twice. Saw once." Another old rule: "Believe none of what you hear and half of what you see and still will believe twice too much." I learned a similar lesson in math: Intuitive descriptions and conceptions and pictures and examples are from really good up to crucial, but they are not sufficient. Instead, make strong efforts to stay really close to carefully stated theorems and proofs. Sure, there are books, lectures, etc. on applied math that try to make the subject easier by omitting the proofs and often even the carefully stated theorems. On further inspection and more learning, what I found was that the with the easier treatments, in practice omitting the theorems and proofs also omitted crucial discipline, care, and checking and brought in too many errors. Sometimes have to work with such "easy" sources and work too fast, but in that case try not to bet more than can afford to lose -- in the sense of the OP, don't take a chance of going to jail.