There was a stretch, working on computations connected to the corona problem, when I would finish dinner, stay at the table, and not get up for hours. Nothing about the work was mysterious. I had a sense of what to do, I knew it was likely to work, and the computations simply had to be done. So I did them, line after line, until they were sorted out. The focus was unlike almost anything else I can remember from my working life, a strange and complete kind of attention, and it left a lasting impact on me.
Here is the confession. More recently I have been focused on, honestly obsessed with, questions connected to the same problem, and I haven’t been back to that table. Not in that way. The hours are there. The caring is, if anything, greater. The state isn’t.
For a while I took that as a vague bad sign. I now think it means something closer to the opposite. But getting there requires being a little more precise about what was happening at the table.
The state has a name. In the 1960s Mihaly Csikszentmihalyi noticed that the painters he was studying would work with total absorption, ignoring hunger, fatigue, and the clock, and then lose interest in the canvas the moment it was finished. He called the state flow and went on to find it in climbers, surgeons, and chess players. The research behind it is softer than its popularity suggests, but the description is recognizable enough that anyone who has been there knows it on sight: you stop watching yourself work, and time goes somewhere.
More useful than the description is what seems to make it possible. You know what you’re trying to do. You find out right away whether it’s working. And the task needs everything you have, but not more than you have. Too easy and you’re bored; too hard and you’re anxious. Flow lives in the band between, and the band is relative to you. What absorbed you last year might bore you now.
Read that list as a mathematician and notice how badly it describes most of research. At the frontier of an open problem, the goal is clear only at the top level: prove this. The next step usually isn’t. Feedback is slow and ambiguous; you can work for a week without knowing whether you’re closer. And an open problem is, almost by definition, harder than your current skill. That isn’t the flow band. It’s the band above it.
This is why obsession and flow get confused, and shouldn’t. Both involve intense focus. But obsession is what attention does when you care enormously and don’t know what to do next: it circles. Flow needs a next step. The computations at the table had one, every line of the way, and each line either checked or it didn’t.
Where flow does show up in mathematics, I suspect, is in the work around the hardest part: carrying out a computation whose shape you already understand, writing up a proof you finally believe, working through new material. Learning may be the most reliable source of all, because a good textbook is flow that someone else engineered for you. The goals are set, the exercises give feedback, and the difficulty is paced by an author who chose the order. (You can also glide through forty pages feeling absorbed and retain nothing. The flow that builds anything usually has a pencil in it.)
Here’s the part I missed for a long time. Before I got to the table, I had struggled for weeks: with the idea, with the definitions, with what the computations should even be. None of that felt anything like flow. And the problem didn’t get easier during those weeks. I got better. The struggle was my side of the balance moving, slowly, until the problem slid into the band where I could just sit down and compute. I didn’t find the flow state. I moved into it.
That reframes both halves. The struggle isn’t a toll paid before the good part; it’s the mechanism that produces the good part. If you’re a graduate student who has so far only lived in the struggle, with no evidence it leads anywhere, it’s easy to read the absence of flow as a verdict on you. It isn’t one. It came first for me too, not as a matter of reassurance, but as a matter of mechanism. And flow, when it arrives, is more than a pleasant way to work. In a field where feedback is slow and payoffs are uncertain, it may be one of the few direct signals that the uncomfortable work paid off.
I lift weights, and the gym version of this is so familiar I rarely think about it. The set today is tough and might suck, but in six months it will pay dividends. The reps now are not fun; they pay in the future. The difference is that in lifting I have evidence. The program works, and the bar tells me so. In mathematics I have faith. I don’t know that the paper I read or the book I look at will pay off. Most won’t, not in any way I could trace. As with the unasked questions in “The Room Is Busier Than You Are” few essays back, any single instance is worth almost nothing, and the aggregate is everything. What I have faith in is the accumulation, that the work won’t be for naught. The table is one of the rare places that faith gets confirmed.
The gym also carries a warning. Everyone knows the person who benches every session because they’re good at bench, and skips legs. Flow can do that to you. It feels wonderful, so you drift toward work that produces it, which means work matched to skills you already have. The pull is strongest exactly when the stakes feel highest: on a two-year postdoc clock, the executable project is also the safe one. Chased for its own sake, flow is a local optimizer.
You can’t schedule flow directly, but you can stop killing it, and the things that kill it are smaller than people expect.
A fragmented day. One meeting at 11 isn’t one hour lost. It’s the whole morning, because nobody starts a deep computation knowing they’ll have to stop in ninety minutes. The table worked partly because nothing was coming after dinner.
Bouncing between tasks. I know this one from the inside. I have several things going and feel I have to bounce between them to get it all done, and I have to tell myself to complete the task in front of me. Every switch, including the quick check of email or the arXiv, leaves part of your attention behind with the thing you left. Focusing on the one is more productive in the end, even when it doesn’t feel that way.
The unfinished task nagging. Bouncing feels necessary because undone things keep pulling. The cheapest fix I know: before leaving a task, write down exactly where you stopped and what the next step is. Once it’s on paper, your head stops holding it.
Other people’s calendars. If you’re senior, you are scheduling someone else’s 11 a.m., and you will never see what it cost them. When a student tells you a problem has finally turned into something they can just compute, that is the week to cancel the check-in, not keep it.
So I’ve stopped reading the recent absence as a bad sign. Being focused and obsessed without being in flow probably just means I’m in the earlier phase, where the problem hasn’t yet turned into something I can sit down and do. The weeks before the table felt exactly like this. They didn’t feel like progress either.
Whether I get back to the table on this one, I don’t know. That part is faith. But I know what it took last time, and I know the evenings themselves were the easy part. They were made possible by weeks that felt nothing like them.