Hello, I'm new here and this is the first thing I ever write on this forum, hence the question if this is the wrong place to post anything remains unanswered on my part. I came across this forum doing something on the internet, I can't remember what. I'm certain though that it was related to science, most likely got stuck with homework. Anyway, this question might seem idiotic and I don't really know where or how to start. However, many things are intuitive to me, why the definition of derivative looks like what it looks like, why 2+2=4, why you can add a 5x to the side of the equation that has -5x to make that side equal to 0, and add the 5x to the other side. What my point is that I don't believe that I would ever have come up with it, discovered it, that I had to learn it from someone else. Eventhough I understand it as well as anything else, I couldn't as a caveman have discovered it. Now, I'm alright at maths, I love learning maths and learn it rather quickly. What I want to know is how people on your level of intelligence and ability experience subjects such as maths or physics. Do you read books, go to classes and struggle to comprehend a new concept or have you already in your day dreams come up with a similar idea and just had it confirmed from your teachers? A maths Ph.D. for example, has he gone to classes to learn from others or did he already, eventhough he wasn't sure or had created sufficient proof, understand it from just thinking about it? I apologise for this question, yet I really wish to know how it feels for those who are at your level.