Division by Zero | Dave Richeson | Inspiration is for amateursI've actually got that tacked up above my desk at the lab, along with some postcards of Close's portraits.
I found this fantastic quote by the artist Chuck Close. It was his advice for young artists. However, I think that if you replace artist by researcher,* the same advice applies. I would certainly pass this advice along to young mathematicians: just start working, the ideas will come. Conversely, if you don’t put in the time, do not expect that “ah-ha” moment.
I think I saw the quote in Chuck Close: A Portrait in Progress, an hour long biographical film. He's got a fascinating life story, sort of an artist version of Lance Armstrong.
Richeson has an extended version of the quote from Andrew Zuckerman's Wisdom. I wish someone had drilled this into me more firmly before I started my dissertation research.
So here's my advice to grad students who feel at sea: just do something. Pick up a paper and read it. Doesn't matter if it doesn't seem relevant to the specific problem you're stymied by. Just pick it up and read it. It's better than sitting there not knowing how to proceed. Write down some ideas. Even bad ones. Even just a list of problems or questions. Put some thought into something.
I also like the footnote Richeson has:
*The similarity between artist and mathematician was famously pointed out by G. H. Hardy in A Mathematician’s Apology: “A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”That's a great line.
PS I think Sarah Silverman, Chris Hardwick and others discuss this theme in the context of stand up comedy on this episode of The Nerdist. I might be thinking of a different interview, but I think this is the one where they talk about how long it took them all to come to the conclusion that if they wanted to make their acts better they ought to actually sit down and think and write and work, and not just hope for inspiration to deliver new, funnier material.
(That episode was recorded at Gallery 1988, to bring us full circle back to contemporary art.)