Edward Hopper, Cape Cod Morning, oil on canvas, 1950
The Knight: As you know, I am afraid of emptiness, desolation and stillness. I cannot bear the silence and isolation.
Death: Emptiness is a mirror turned to your own face.
— Ingmar Bergman’s workbook, April 5, 1955
In the early 2010s, a popular idea was to provide coworking spaces and shared living to people who were building startups. That way the founders would have a thriving social scene of peers to percolate ideas with as they figured out how to build and scale a venture. This was attempted thousands of times by different startup incubators. There are no famous success stories.
In 2015, Sam Altman, who was at the time the president of Y Combinator, a startup accelerator that has helped scale startups collectively worth $600 billion, tweeted in reaction that “not [providing coworking spaces] is part of what makes YC work.” Later, in a 2019 interview with Tyler Cowen, Altman was asked to explain why.
SAM ALTMAN: Good ideas — actually, no, great ideas are fragile. Great ideas are easy to kill. An idea in its larval stage — all the best ideas when I first heard them sound bad. And all of us, myself included, are much more affected by what other people think of us and our ideas than we like to admit.
If you are just four people in your own door, and you have an idea that sounds bad but is great, you can keep that self-delusion going. If you’re in a coworking space, people laugh at you, and no one wants to be the kid picked last at recess. So you change your idea to something that sounds plausible but is never going to matter. It’s true that coworking spaces do kill off the very worst ideas, but a band-pass filter for startups is a terrible thing because they kill off the best ideas, too.
This is an insight that has been repeated by artists, too. Pablo Picasso: “Without great solitude, no serious work is possible.” James Baldwin: “Perhaps the primary distinction of the artist is that he must actively cultivate that state which most men, necessarily, must avoid: the state of being alone.” Bob Dylan: “To be creative you’ve got to be unsociable and tight-assed.”
When expressed in aphorisms like this, you almost get the impression that creativity simply requires that you sit down in a room of your own. In practice, however, what they are referring to as solitude is rather something like “a state of mind.” They are putting themselves in a state where the opinions of others do not bother them and where they reach a heightened sensitivity for the larval ideas and vague questions that arise within them.
To get a more visceral and nuanced understanding of this state, I’ve been reading the working notes of several highly creative individuals. These notes, written not for publication but as an aid in the process of discovery, are, in a way, partial windows into minds who inhabit the solitary creative space which the quotes above point to. In particular, I’ve found the notes of the mathematician Alexander Grothendieck and the film director Ingmar Bergman revealing. They both kept detailed track of their thoughts as they attempted to reach out toward new ideas. Or rather, invited them in. In the notes, they also repeatedly turned their probing thoughts onto themselves, trying to uncover the process that brings the new into the world.
This essay is not a definite description of this creative state, which takes on many shapes; my aim is rather to give a portrait of a few approaches, to point out possibilities.
Part 1: Alexander Grothendieck
It is as if there existed, for what seems like millennia, tracing back to the very origins of mathematics and of other arts and sciences, a sort of “conspiracy of silence” surrounding [the] “unspeakable labors” which precede the birth of each new idea, both big and small[.]
— Alexander Grothendieck, Récoltes et Semailles
In June 1983, Alexander Grothendieck sits down to write the preface to a mathematical manuscript called Pursuing Stacks. He is concerned by what he sees as a tacit disdain for the more “feminine side” of mathematics (which is related to what I’m calling the solitary creative state) in favor of the “hammer and chisel” of the finished theorem. By elevating the finished theorems, he feels that mathematics has been flattened: people only learn how to do the mechanical work of hammering out proofs, they do not know how to enter the dreamlike states where truly original mathematics arises. To counteract this, Grothendieck in the 1980s has decided to write in a new way, detailing how the “work is carried day after day [. . .] including all the mistakes and mess-ups, the frequent look-backs as well as the sudden leaps forward”, as well as “the early steps [. . .] while still on the lookout for [. . .] initial ideas and intuitions—the latter of which often prove to be elusive and escaping the meshes of language.”
This was how he had written Pursuing Stacks, the manuscript at hand, and it was the method he meant to employ in the preface as well. Except here he would be probing not a theorem but his psychology and the very nature of the creative act. He would sit with his mind, observing it as he wrote, until he had been able to put in words what he meant to say. It took him 29 months.
When the preface, known as Récoltes et Semailles, was finished, in October 1986, it numbered, in some accounts, more than 2000 pages. It is in an unnerving piece of writing, seething with pain, curling with insanity at the edges—Grothendieck is convinced that the mathematical community is morally degraded and intent on burying his work, and aligns himself with a series of saints (and the mathematician Riemann) whom he calls les mutants. One of his colleagues, who received a copy over mail, noticed that Grothendieck had written with such force that the letters at times punched holes through the pages. Despite this unhinged quality, or rather because of it, Récoltes et Semailles is a profound portrait of the creative act and the conditions that enable our ability to reach out toward the unknown. (Extracts from it can be read in unauthorized English translations, here and here.)
First contact with the creative state
An important part of the notes has Grothendieck meditating on how he first established contact with the cognitive space needed to do groundbreaking work. This happened in his late teens. It was, he writes, this profound contact with himself which he established between 17 and 20 that later set him apart—he was not as strong a mathematician as his peers when he came to Paris at 20, in 1947. That wasn’t the key to his ability to do great work.
I admired the facility with which [my fellow students] picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle—while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things that I had to learn (so I was assured), things I felt incapable of understanding[.]
Grothendieck was, to be clear, a strong mathematician compared to most anyone, but these peers were the most talented young mathematicians in France, and unlike Grothendieck, who had spent the war in an internment camp at Rieucros, near Mende, they had been placed in the best schools and tutored. They were talented and well-trained. But the point is: being exceptionally talented and trained was, in the long run, not enough to do groundbreaking work because they lacked the capacity to go beyond the context they had been raised in.
In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birth-right, as it was mine: the capacity to be alone.
The capacity to be alone. This was what Grothendieck had developed. In the camp during the war, a fellow prisoner named Maria had taught him that a circle can be defined as all points that are equally far from a point. This clear abstraction attracted him immensely. After the war, having only a limited understanding of high school mathematics, Grothendieck ended up at the University of Montpellier, which was not an important center for mathematics. The teachers disappointed him, as did the textbooks: they couldn’t even provide a decent definition of what they meant when they said length! Instead of attending lectures, he spent the years from 17 to 20 catching up on high school mathematics and working out proper definitions of concepts like arc length and volume. Had he been in a good mathematical institution, he would have known that the problems he was working on had already been solved 30 years earlier. Being isolated from mentors he instead painstakingly reinvent parts of what is known as measurement theory and the Lebesgue integral.
A few years after I finally established contact with the world of mathematics at Paris, I learned, among other things, that the work I’d done in my little niche [. . . had] been long known to the whole world [. . .]. In the eyes of my mentors, to whom I’d described this work, and even showed them the manuscript, I’d simply “wasted my time”, merely doing over again something that was “already known”. But I don't recall feeling any sense of disappointment. [. . .]
The three years of solitary work at Montpellier had not been wasted in the least: that intellectual isolation was what had allowed him to access the cognitive space where new ideas arise. He had made himself at home there.
Without recognizing it, I’d thereby familiarized myself with the conditions of solitude that are essential for the profession of mathematician, something that no-one can teach you. [. . .]
To state it in slightly different terms: in those critical years I learned how to be alone.
[. . .] these three years of work in isolation, when I was thrown onto my own resources, following guidelines which I myself had spontaneously invented, instilled in me a strong degree of confidence, unassuming yet enduring, in my ability to do mathematics, which owes nothing to any consensus or to the fashions which pass as law....
This experience is common in the childhoods of people who go on to do great work, as I have written elsewhere. Nearly everyone who does great work has some episode of early solitary work. As the philosopher Bertrand Russell remarked, the development of gifted and creative individuals, such as Newton or Whitehead, seems to require a period in which there is little or no pressure for conformity, a time in which they can develop and pursue their interests no matter how unusual or bizarre. In so doing, there is often an element of reinventing the already known. Einstein reinvented parts of statistical physics. Pascal, self-teaching mathematics because his father did not approve, rederived several Euclidean proofs. There is also a lot of confusion and pursuit of dead ends. Newton looking for numerical patterns in the Bible, for instance. This might look wasteful if you think what they are doing is research. But it is not if you realize that they are building up their ability to perceive the evolution of their own thought, their capacity for attention.
Questions over answers
One thing that sets these intensely creative individuals apart, as far as I can tell, is that when sitting with their thoughts they are uncommonly willing to linger in confusion. To be curious about that which confuses. Not too rapidly seeking the safety of knowing or the safety of a legible question, but waiting for a more powerful and subtle question to arise from loose and open attention. This patience with confusion makes them good at surfacing new questions. It is this capacity to surface questions that set Grothendieck apart, more so than his capacity to answer them. When he writes that his peers were more brilliant than him, he is referring to their ability to answer questions1. It was just that their questions were unoriginal. As Paul Graham observes:
People show much more originality in solving problems than in deciding which problems to solve. Even the smartest can be surprisingly conservative when deciding what to work on. People who’d never dream of being fashionable in any other way get sucked into working on fashionable problems.
Grothendieck had a talent to notice (and admit!) that he was subtly bewildered and intrigued by things that for others seemed self-evident (what is length?) or already settled (the Lebesgue integral) or downright bizarre (as were many of his meditations on God and dreams). From this arose some truly astonishing questions, surfacing powerful ideas, such as topoi, schemes, and K-theory.
Working with others without losing yourself
So far, we’ve talked about solitary work. But that has its limitations. If you want to do great work you have to interface with others—learn what they have figured out, find collaborators who can extend your vision, and other support. The trick is doing this without losing yourself. What solitude gives you is an opportunity to study what personal curiosity feels like in its undiluted form, free from the interference of other considerations. Being familiar with the character of this feeling makes it easier to recognize if you are reacting to the potential in the work you are doing in a genuinely personal way, or if you are giving in to impulses that will raise your status in the group at the expense of the reach of your work.
After his three years of solitary work, Grothendieck did integrate into the world of mathematics. He learned the tools of the trade, he got up to date on the latest mathematical findings, he found mentors and collaborators—but he was doing that from within his framework. His peers, who had been raised within the system, had not developed this feel for themselves and so were more susceptible to the influence of others. Grothendieck knew what he found interesting and productively confusing because he had spent three years observing his thought and tracing where it wanted to go. He was not at the mercy of the social world he entered; rather, he “used” it to “further his aims.” (I put things in quotation marks here because what he’s doing isn’t exactly this deliberate.) He picked mentors that were aligned with his goals, and peers that unblock his particular genius.
I do not remember a single occasion when I was treated with condescension by one of these men, nor an occasion when my thirst for knowledge, and later, anew, my joy of discovery, was rejected by complacency or by disdain. Had it not been so, I would not have “become a mathematician” as they say—I would have chosen another profession, where I could give my whole strength without having to face scorn. [My emphasis.]
He could interface with the mathematical community with integrity because he had a deep familiarity with his inner space. If he had not known the shape of his interests and aims, he would have been more vulnerable to the standards and norms of the community—at least he seems to think so.