Study Hacks Blog

On the Myth of Big Ideas

July 16th, 2021 · 6 comments

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.

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Administrative Note:

My longtime friends, The Minimalists, have a new book out this week! It’s titled: Love People, Use Things. Here’s my blurb from the back cover:

“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…

6 thoughts on “On the Myth of Big Ideas

  1. Tried clicking through on the book link, of course it’s an Amazon link, hah! Have the site blocked. Time to go searching. That said, looks intriguing, thanks for sharing it with everyone.

    Also, what you’re saying with sticking with things, I’m seeing this with my children at the moment. Prime ages of one and five; lot of emotions and changes happening every day. But it’s through perseverance and endurance we are seeing changes, not because we are some “expert” “super smart” parents. Maybe I’m drawing the wrong correlation here, but it was encouraging all the same.

  2. rb says:

    I got to sit in on a series of faculty candidate evaluation meetings in the mechanical engineering department at Stanford. Of course, some of the smartest people in the world in their engineering branches were there, including David Kelley, founder of IDEO, et a. And something I observed was that they absolutely confirmed my spiritual teacher’s definition of the qualities required for greatness: jaw-dropping concentration, and very, very big mental energy. I could feel the room reverberating with their magnetism, literally. And so I suspect there are very real limitations to the “elbow grease” formula.

  3. Maitreya says:

    If there is a sensory experience which you want to arise,
    patiently and persistently create the conditions which increase the probability of of the sensory experience.

    If there is a sensory experience which you want to cease,
    patiently and persistently create the conditions which decrease the probability of of the sensory experience.

    In systems theory, this concept is called “emergence”.

    The Buddha called it “dependent origination”.

  4. Jim C. says:

    I think another takeaway is that solving any problems (not just math proofs) requires an attentional focus as noted here, but then also some time away from the problem when your subconscious mind – in its “daydreaming mode” – can work on it, which is often when breakthroughs occur.

    I am curious about your view on this Cal. I listen to your podcast, and you frequently talk about “productive meditation,” which involves bringing your mind back to the problem if it wanders, but I have not heard you talk about this equally-important part of problem-solving, where you need to purposefully make time to let your mind wander…

    1. Ian Howlett says:

      I find that when I need to let my mind wander to work on a problem, it’s sometimes useful to read a book (any topic, I prefer non-fiction).

      Sometimes I find a word or a phrase that suddenly makes something click in my subconscious and gives me the key to unlock the problem.

  5. Maitreya says:

    If there is a sensory experience which you want to arise,
    patiently and persistently create the conditions which increase the probability of the sensory experience.

    If there is a sensory experience which you want to cease,
    patiently and persistently create the conditions which decrease the probability of the sensory experience.

    In systems theory, this concept is called “emergence”.

    The Buddha called it “dependent origination”.

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