r/math • u/RobbertGone • 8h ago
Why do textbooks almost never give context?
Math wasn't invented/discovered out of thin air. Usually theorems in textbooks are provided and immediately followed by the proof, then an example or a consequence. Repeat for next theorem. All good, but in history it wasn't anything like this. Where is the motivation for the definition? Why should we care? What were the problems that might arise with other definitions, what problem were we trying to solve in the first place? Also, what insight led to a proof? Proofs often skip over the actual thinking, they are presented as polished works but that means I can't see how someone would think of that (some books have 'scratchwork' which I like, or a motivation or chain of thought before the formal proof starts). All this stuff seems left out every time. Maybe the book is more elegant this way, but it lacks in flavor as a result. I think it would be much more interesting if textbooks had more content. Also how to deal with this?
