In the last post I talked about how creativity is a two-step process: brainstorming, then pruning. The most creative people seem to have a dual nature. They have a boundless ability to believe in their own stupid ideas, and also a boundless capacity for self-criticism and reflection.
If is is the way that creativity works, then there are two ways you can fail to be creative. (By the way, don’t get down on yourself if you’re not creative — like anything, this is a process and you can grow and learn to do it.)
The first failure happens at the first stage, never believing that you can produce anything. Your ideas are garbage. Why rely on them, when you could turn to so many better ideas that have come before? It’s better to just follow what other people have done, what’s already been tried and tested. While I agree that it’s important to understand and build on the work of earlier mathematicians, it’s equally important to reinvent and reincarnate those ideas by making them your own. To make a deep and meaningful contribution to the research community, you have to break free a little of the old patterns, and find your own approach.
I sometimes see this in graduate students who are afraid to think of the mathematics on their own terms, and want to hold tightly to the way it was done before, or the way the book explains it. I get it, jumping into academia is terrifying, and at least this seems safe. But if you want to be a great mathematician, you have to let go of your fear, take that leap, and try to do things differently.
The second way to fail is at the second stage. You can produce lots of ideas, but you don’t want to criticize them. Everything you produce is amazing! Better than anything that’s come before. This feels good, but ultimately it’s a celebration of mediocrity. If you can’t criticize yourself, you can’t realize your potential.
We try to cultivate high self-esteem in our children, and that’s good, but we attach it to the unrealistic idea that everything we produce is amazing. Sorry, that’s not true. You are always a beautiful, important person, no matter what. And despite that, most of your ideas are crap. This is exactly the way you are meant to be. Embrace the crap, then throw most of it out and save only the good parts.
In mathematics, this lack of self-criticism can lead to embarrassing errors and failed theorems. It also cultivates disregard for existing ideas, because your ideas are so much better! Going too far in this direction makes you into a crackpot. And short of that, it can lead you too far away from other mathematicians. Without their support and criticism, you just can’t get very far.
The takeaway from all this, though, is that it’s actually not hard to be creative. All you have to work on, is being flexible enough to switch between two modes. Let your stupid ideas out, then earnestly evaluate them, then repeat.