I want to share an idea that I’ve built my research career on. It’s essentially a recipe: how to be creative.
The idea is that creativity is a two-step process. Brainstorm, then prune.
The first stage is brainstorming. Open your mind, let your imagination run wild, try everything, chase the slightest thought and just see where it goes. Free write. Doodle. Generate 100 ideas for how to solve a problem. Don’t give any regard to the quality of the ideas, just embrace every idea as beautiful and make as many of them as you can. Be an optimist.
The second stage is pruning. Turn a critical lens to the ideas you made. Explain why they don’t work. Find flaws and holes. Imagine ways you could be wrong. Anticipate failures and then watch them happen. Throw 95 of your 100 ideas into the garbage, and refine the remaining 5 by ironing out their flaws. Be a pessimist.
What’s left after the second stage? Really high quality, original ideas.
Your brain is capable of generating amazing things, but you can’t do it consistently. You have to allow yourself to produce a lot of garbage, and then the amazing new stuff will come out, like a gold nugget buried in the garbage. Your brain just isn’t capable of only producing the gold nugget. You have to do the whole process, or else nothing will come out at all.
I like to think that inside every successful mathematician, there are two mathematicians. They talk, argue, and endlessly build off of each other. The optimist is exuberant, and thinks you’re the greatest thing since sliced bread. The optimist emerges early in a project, helping you get excited and get started. The pessimist, on the other hand, sees problems and flaws with every idea, opportunities for failure, reasons why you’re irrelevant. The pessimist comes out a little later, helping you let go of the ideas that just don’t work. Then the optimist comes back, giving you the energy to work more on the ideas that survived the purge. With each iteration of these stages, your ideas become stronger, tougher, and more powerful.
Of course, you should remember to bring out the pessimist one last time to check mistakes before you post. And the abstract and introduction you should leave to the optimist.