Any unwillingness to learn mathematics today can greatly restrict your possibilities tomorrow. - Richard Hamming

A long gestation period of intense thinking about the problem may result in a solution, or else the temporary abandonment of the problem. This temporary abandonment is a common feature of many great creative acts. The monomaniacal pursuit often does not work; the temporary dropping of the idea sometimes seems to be essential to let the subconscious find a new approach. Then comes the moment of “insight,” creativity, or whatever you want to call it — you see the solution. Of course, it often happens that you are wrong; a closer examination of the problem shows the solution is faulty, but might be saved by some suitable revision. But maybe the problem needs to be altered to fit the solution! That has happened! More usually it is back to the drawing board, as they say, more mulling things over. The false starts and false solutions often sharpen the next approach you try. You now know how not to do it! You have a smaller number of approaches left to explore. You have a better idea of what will not work and possibly why it will not work.

"From these early attempts to explain things slowly came philosophy as well as our present science. Not that science explains "why" things are as they are - gravitation does not explain why things fall - but science gives so many details of "how" that we have the feeling we understand "why." Let us be clear about this point; it is by the sea of interrelated details that science seems to say "why" the universe is as it is."

The feeling of having free will is deep in us and we are reluctant to give it up for ourselves—but we are often willing to deny it to others!