Quote of the page
Irrationally held truths may be more harmful than reasoned errors.
- Thomas Henry Huxley
There is of course no precise procedure that would guarantee creativity. But the following informal procedure is quite useful, and lots of people have working routines which are very similar. It might look very simple, but success does not come from one single application but a repetition of the procedure again and again over a long period of time.
A Hong Kong student once asked the Nobel laureate John Nash for advice on getting ideas for his thesis, and the reply was, "Have you done your reading?"
When we need to come up with an idea to solve a problem, it would be helpful to do some research to see what other people have thought about the topic. If there are already good solutions that can be used, then we don't have to waste our time to reinvent the wheel. But even if the problem has not been solved, we need to find out more about existing approaches and what their limitations are. When you are starting your research, collect as much information as you can, without worrying too much about their relevance.
Some useful things to do:
When you are gathering your data you are doing some preliminary study to learn more about the problem you have to solve. While you are doing this, or after you have collected a lot of material, you need to examine and reflect on what you have, in order to rank the importance of the different pieces of information that you have, and to investigate whether there are special connections between the ideas. Creativity often takes the form of using some idea from one field and apply it to another one.
Very likely we have had experiences where an idea suddenly pops up while we are taking the shower, or after a good night's sleep. When we are sorting out the connections between ideas it is important that we are persistent and spend an extended period of time in order that we keep lots of different ideas in the mind, some of which remain in the background and some of which might enter into unconscious thinking processes. After a period of hardwork it is sometimes necessary to pull back and relax, to do something relaxing and different to stimulate the mind. Or it might perhaps be a case of allowing ourselves to forget about the less important ideas so that the more relevant ones float to the top. But whatever the mechanisms are, it does seem to be important to allow time for ideas to gestate. If we still can't think of anything, then we might have to do more research and think about connections further.
Once we have obtained some ideas that seem to work, we need to examine them carefully to check that they indeed can help solve our problem. We have to think about whether they can be improved further and we need to see how they are to be implemented. Even when they have proved to be successful, we should review the whole process to see how we can do better next time.
Andrew Wiles is famous for proving Fermat's Last Theorem. In this TV interview he talks about his research routine which echoes what has been said in this tutorial:
NOVA: On a day-to-day basis, how did you go about constructing your proof?
Wiles: I used to come up to my study, and start trying to find patterns. I tried doing calculations which explain some little piece of mathematics. I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about. Sometimes that would involve going and looking it up in a book to see how it's done there. Sometimes it was a question of modifying things a bit, doing a little extra calculation. And sometimes I realized that nothing that had ever been done before was any use at all. Then I just had to find something completely new; it's a mystery where that comes from. I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction, I would have the same thing going round and round in my mind. The only way I could relax was when I was with my children. Young children simply aren't interested in Fermat. They just want to hear a story and they're not going to let you do anything else.
NOVA: Usually people work in groups and use each other for support. What did you do when you hit a brick wall?
Wiles: When I got stuck and I didn't know what to do next, I would go out for a walk. I'd often walk down by the lake. Walking has a very good effect in that you're in this state of relaxation, but at the same time you're allowing the sub-conscious to work on you. And often if you have one particular thing buzzing in your mind then you don't need anything to write with or any desk. I'd always have a pencil and paper ready and, if I really had an idea, I'd sit down at a bench and I'd start scribbling away.