In a lifetime of many, many independent choices, small and large, a career with a vision will get you a distance proportional to n, while no vision w… - 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.

As a practicing computer veteran, this reviewer has the habit of looking at the hypothesis of a theorem and asking:

All of engineering involves some creativity to cover the parts not known, and almost all of science includes some practical engineering to translate the abstractions into practice.