I recently came across an article in the New Yorker archives that I greatly enjoyed. It was written by a Dartmouth mathematics professor named Dan Rockmore, and is titled: “The Myth and Magic of Generating New Ideas.” The essay tackles a topic that’s both central to my professional academic life, and wildly misunderstood: what it takes to solve a proof.
To capture the reality of this act, Rockmore tells a story from when he was a young professor. He was working with his colleagues to try to find a more efficient method for solving a large class of wave equations. “We spent every day drawing on blackboards and chasing one wrong idea after another,” he writes. Frustrated, he left the session to go for a run on a tree-lined path. Then it happened.
“As I crested the last hill, I saw it all at once: the key to modifying the algorithm we’d been puzzling over was to flip it around, to run it backward. My hear started racing as I pictured the computational elements strung out in the new opposite order. I sprinted straight home to find a pencil and paper so I could confirm it.”
As Rockmore then elaborates, in popular portrayals of mathematical machinations, the focus is often on this final bit, the eureka moment while jogging through the woods, or John Nash surveying the crowded Princeton bar and figuring out non-cooperative game theory all at once.
But this moment cannot come without the days of frustration at the blackboard. “You can’t really blame the storytellers,” Rockmore writes, “It’s not so exciting to read ‘and then she studied some more.’ But this arduous, mundane work is a key part of the process.”
This absolutely matches my experience as a professional theoretical computer scientist. The top performers in my field are smart, to be sure, but their the real advantage is less some supercharged brain that delivers fully-formed proofs in effortless bursts, than it is a supercharged work ethic: an ability to stick with mastering hard results from the literature; building the mental frameworks, one arduous level after another, on which the eventual insights can then find purchase.
I don’t have a sweeping big think conclusion to draw from these observations. But it seems somehow vaguely true that in an increasingly cognitive world, understanding those who apply their brains at an elite level may end up a worthwhile endeavor.
“Joshua and Ryan have penned an urgent manifesto for the growing movement away from the material and toward the meaningful. An important book for our current moment.”
A great companion to contemplations of living deeper. Check it out…