The first phase of solving can be described as “worrying” about a problem or idea. It evokes anxiety and gives the impression of productivity.But, overthinking can lead to a dead end. The key to solving the problem is to take a break from worrying. Focus your attention on some other activity. Take a long hike or a long drive, to give your mind the space to have a good idea.

Don't overthink

Big ideas do not come only from leisure. The arduous, mundane work is a vital part of the process. You can't skip the worrying phase. You work, and work, and work some more to get some understanding. The eureka moments will emerge once you have prepared your mind.

Mundane work is necessary

Henri Poincaré, the father of chaos theory and the co-discoverer of special relativity, relates his own discovery. "the idea came to me, without anything in my former thoughts seeming to have paved the way for it.”The Irish mathematician, Sir William Rowan Hamilton, had a similar epiphany while strolling by the Brougham Bridge. He was so delighted that he stopped and carved the defining algebraic equation into the bridge.

Unconscious processing

Ideas come to us when we have a specific problem but we do not focus on solving the problem directly. It’s not at all obvious how to go about thinking up some new twist on these things. A new idea can feel like a remarkable discovery

Where ideas come from

Where do ideas come from? That's a big question. Here's a smaller one: Where do mathematical ideas come from? I've wondered about this from the time I first contemplated being a mathematician until long after I officially became one. My earliest memory of anything like a mathematical idea comes from a childhood walk with my dad.

Don't overthink

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Worrying about the future

Interacting with difficult people

Schedule Time To Worry