| 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. | |
| ### Step 1 - Research | |
| 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: | |
| * Obtain relevant information from the scientific literature or experts. | |
| * Study the history of the problem. | |
| * Do case studies of people who have dealt with similar problems. | |
| * Think about analogous situations. | |
| * Talk to the people who are involved. | |
| ### Step 2 - Explore the connections between ideas | |
| 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. | |
| ### Step 3 - Relax and wait | |
| 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. | |
| ### Step 4 - Apply, review and followup | |
| 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. | |
| ## §1. An example | |
| 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. | |
| > | |
| > From http://www.pbs.org/wgbh/nova/proof/wiles.html (Nov 2000) | |
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