Then I became a mathematician in college. In the maths, it's pretty well accepted that every problem and every proof, except for the most trivial, will take at least two drafts. One for discovery that is exploratory and meandering, and one that drives from the hypothesis to the conclusion like an arrow from Athena's bow. Published proofs are never in raw form, even a single page can hide a year (or several lifetimes) of refinements and incremental improvements on partial results.
Don't be too afraid to scrap your current work and start over, no matter what you're doing. The second round is much faster, and much cleaner. Such an undertaking shouldn't be done lightly, but it's often not as onerous as most people assume it will be.
 Yes, this happened several times. Don't mess with a winning formula.
Especially for students studying proofs, the step from being students to being researchers is greatly impeded by not being able to see how researchers reached the end results they did.
What is useful is contacting people in the community surrounding a particular result, including the person (or people) that proved it. Most are more than willing to share every aspect of the problem and how their solution evolved over the course of time.
- Interruption kills creativity.
- To be creative, you have to create a kind of oasis in your life. Boundaries of space and boundaries of time.
Presumably he means that there's no algorithmic process for getting ideas.
When going into your oasis and taking your time, I'd recommend taking only pen and paper with you.
That said I believe there is a fine line between aping someone and getting inspired by someone, and that is something you have to navigate on your own. I don't know why, but I always think about Steve Jobs ( http://www.youtube.com/watch?v=CW0DUg63lqU) whenever I face something like this. It's like a metric. What can I learn from this which applied to my work makes it great?
"But if you're racing around all day, ticking things off
on lists, looking at your watch, making phone calls,
and generally just keeping all the balls in the air,
you are not going to have any creative ideas."
I find it hilariously ironic that immediately after he
says this, the camera cuts over to two guys in the audience
clicking away on their laptops while ostensibly listening
to Cleese's talk.
I think it releases the mind from trying to remember the ideas in the morning. When I write the ideas down I can review in the morning with the benefit of having a good nights sleep.
You can sometimes get them free at conferences. This one from Amazon works great: http://www.amazon.com/gp/product/B000BUNMU4?ie=UTF8&tag=...
(Also fun, if you think of too many altogether... Complicates the above even further.)
The pen-light idea mentioned elsewhere is a nice addition to the notepad idea.
Most of my solutions so far usually regard trivialities. When a train of thought was genuinely worth finding in the morning, I would usually leave a relevant web search open on my phone (along with all the other things to not forget, or check later. Quite devastating is the browser choked...). Also, the display would be jarringly bright... Although, if it was a compelling enough idea, it would be enough to win me away from sleep.
The Cleese video is down, but many of the other videos, such as Wozniak's, are still up.
EDIT: It appears all the videos on the site are abridged. The Cleese talk on Youtube is probably the same as appeared here before the video was removed.
"If the people in charge are very egotistical then they want to take credit for everything that happens, and they want to feel that they are in control of everything that happens. And that means consciously or unconsciously they will discoourgage creativity in other people."
Full credit to you Mr Cleese.
I wonder where else links were coming from?