>>12006294I am a different person responding to your math frustrations. It really is true that a proof is not at all the thought process, but having a good teacher and having occasional exposure to a more geometrical works helps a lot. For example, in my first year of college, our linear algebra class was once randomly interrupted by some random person the facultu wanted to walk us through the proof. I remember almost nothing, but the images he was working through stuck with me, and the thought process was there, kind of like the difference between teaching a person how to drive by showing them versus expecting a person to drive just with verbal instructions delivered over phone. In any case, in the years since then, I have come up with funny things on my own just from playing around (math proofs, proof methods, intuitive expansions for physics phenomena even a dog could understand). I think most people do that, and I think school is not a good environment to train you to chill and do that. Occasionally, I wake up from a dream with a fully-formed idea for some neat electromagnet propulsion system and when I work out on paper how to balance the aircraft so it doesn't flip over and stuff, it all just works (of course, I can see this will be ahead of time). Similarly, in rare cases, I prove something obscure and rather uninteresting to others than myself, but then when explaining to others I grab their attention but a terribly strong vision flashes in my eyes and it is a dream - an old dream, 15 years old perhaps, and not part of my mini-lecture but clearly integral to the thought-process that allowed me to solve my problem. They don't teach you this stuff in school, and it really cannot be taught. Your conscious mind is spaghetti. My first math prof explained it this way: don't do all your homework all at once. Look at it a biy, go out and walk, look at trees, play around, feel the wind, smell the scents in the garden, then revisit, rinse and repeat - pic related.
