Where Good Ideas Come From

It is the long Deepavali weekend, and I finally got some time to catch up on articles I had bookmarked.

One of them, by mathematician Dan Rockmore in The New Yorker, is titled The Myth and Magic of Generating New Ideas. In it, he talks about how new ideas take shape, something I have experienced many times.

The first stage is what mathematicians sometimes call “worrying” a problem.

You stay with it. Read around it. Ask questions. Try different approaches. Get stuck. Come back again. You keep turning the problem over until you understand it deeply enough that it almost lives in your head.

This is the part we rarely see when someone describes a breakthrough.

We hear stories about Henri Poincaré suddenly getting an idea while stepping onto a bus, or mathematician William Hamilton finding the solution to a problem he had pursued for years while walking across a bridge.

What gets forgotten is everything that happened before that moment.

Years of thinking. Studying. Trying. Failing. Thinking again.

Then comes the second stage.

You step away.

Walk. Drive. Swim. Exercise. Do something that occupies you without requiring you to consciously work on the problem.

And sometimes the mind makes a connection that you could not force at the desk.

I have had enough of these moments to know that the idea often arrives when I appear to have stopped working on it.

But the important word is appear.

The break is not a substitute for the work. It becomes useful because the work has already been done.

We like the story of the sudden idea because it sounds magical.

Usually, a lot of ordinary thinking comes before the magic.

So when you have worked deeply on something and still feel stuck, pushing harder is not always the answer.

Sometimes you need to give the mind time to work without your supervision.