[jfv]

Maybe I missed it in this story, but this anecdote about Poincare himself is apropos:

"The famous French mathematician Henri Poincaré was very interested in mathematical creativity. He describes a period of hard and seemingly fruitless effort to solve a problem, from which he took a break to join a geological expedition. As he was stepping on a bus, he made one of the most important breakthroughs of his life. The solution came to him out of nowhere, and was accompanied by a perfect certainty as to its correctness"

(from this blog: https://kjosic.wordpress.com/2012/06/19/creativity-and-waste...)

[JoeAltmaier]

Similar to what Gelman said about what he called the Feynman method: "Step one: write down the problem statement. Step 2: think real hard. Step 3: write down the problem solution."

His point was, I think, that not every scientist can work that way. Some are real treasures, come along one in a generation.

[gwern]

There's a better Feynman method: http://alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-le...

> Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say: "How did he do it? He must be a genius!"

[galdosdi]

That's not the most useful lesson I'd take from that. (That's not a very useful lesson, because I guess if you're not already a Feynman level genius, too bad)

The more useful lesson, useful for anyone, is that sometimes sleeping on it (literally, or just doing a very different activity) helps.

[aoeu345]

It's the seemingly fruitless effort that builds up our familiarity with a problem via intense focus on each small detail. With the clear, detailed problem built up, Poincare could look at it from a distance and see the solution.

[kamaal]

Some other anecdotes:

At seventeen Hussain went on forty-day self-imposed retreat known as a chilla, where a musician practices in isolation until a state is reached in which the music and musician become one. The removal of everyday distractions, combined with single-minded concentration on the practice allows the musician to attain a state of Samadhi or meditative absorption, where one enters into a deeper relationship with one’s own music, and comes in direct contact with the source of music itself. Visions and hallucinations are not uncommon, where one’s musical ancestors may appear and offer encouragement or criticism. What is certain is that the musician makes remarkable progress in his craft. Hussain recalls his first Chilla in Hart’s drumming “I saw things in the music that I had never seen before, new combinations, new patterns”. Six month’s later, against his father’s advice, Zakir was ready to do a second chilla. This time around, the visions were more intense, and Hussain had a premonition that he would soon go to America. From: https://en.wikiquote.org/wiki/Zakir_Hussain_(musician)

Or

“Nobody tells this to people who are beginners, I wish someone told me. All of us who do creative work, we get into it because we have good taste. But there is this gap. For the first couple years you make stuff, it’s just not that good. It’s trying to be good, it has potential, but it’s not. But your taste, the thing that got you into the game, is still killer. And your taste is why your work disappoints you. A lot of people never get past this phase, they quit. Most people I know who do interesting, creative work went through years of this. We know our work doesn’t have this special thing that we want it to have. We all go through this. And if you are just starting out or you are still in this phase, you gotta know its normal and the most important thing you can do is do a lot of work. Put yourself on a deadline so that every week you will finish one story. It is only by going through a volume of work that you will close that gap, and your work will be as good as your ambitions. And I took longer to figure out how to do this than anyone I’ve ever met. It’s gonna take awhile. It’s normal to take awhile. You’ve just gotta fight your way through.” From: http://www.goodreads.com/quotes/309485-nobody-tells-this-to-...

Just presenting a different perspective. Its all too common to look at this idea of brilliant talented scientist to whom 'solutions come out of nowhere'.

The point really is it takes a lot of work to get to a point where you can paint a masterpiece or compose a symphony effortlessly.