There are so many ways of being wrong and so few ways of being right that it is much more economical to study successes. - Richard Hamming

I noticed the following facts about people who work with the door open or the door closed. I notice that if you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But 10 years later somehow you don't quite know what problems are worth working on; all the hard work you do is sort of tangential in importance. He who works with the door open gets all kinds of interruptions, but he also occasionally gets clues as to what the world is and what might be important.

The Turing test is a popular approach, but it flies in the face of the standard scientific method, which starts with the easier problems before facing the harder ones. Thus I soon raised the question with myself, “What is the smallest or close to the smallest program I would believe could think?” Clearly, if the program were divided into two parts, then neither piece could think. I tried thinking about it each night as I put my head on the pillow to sleep, and after a year of considering the problem and getting nowhere I decided it was the wrong question! Perhaps “thinking” is not a yes/no thing, but maybe it is a matter of degree.

In the face of almost infinite useful knowledge, we have adopted the strategy of "information regeneration rather than information retrieval." ...most importantly, you should be able to generate the result you need even if no one has ever done it before you—you will not be dependent on the past to have done everything you will ever need in mathematics.