A letter to graduate students, postdocs, and mathematicians at every stage, on obsession, identity, and the problem you cannot let go.
“To the last I grapple with thee; from hell’s heart I stab at thee; for hate’s sake I spit my last breath at thee.” — Herman Melville, Moby-Dick (1851)
Somewhere in your mathematical life, if you are lucky, and I mean that with full ambiguity, you will encounter a problem that refuses to leave you alone. Not a problem you chose, exactly, but one that chose you. A problem whose resistance feels personal. Whose depth keeps revealing new depths. Whose solution, if it exists, seems to promise something beyond a theorem: a kind of vindication, a completion, a proof of something about yourself as much as about mathematics.
Call it your white whale.
Herman Melville gave us the modern shape of this idea in 1851, but the structure is ancient. Ahab’s obsession with Moby Dick echoes Job wrestling with Leviathan, Prometheus chained for reaching too far, Faust trading everything for ultimate knowledge. There is something in human consciousness that generates this dynamic: the overwhelming, ungrasped thing that you cannot stop pursuing, even when, especially when, the pursuit threatens everything else.
Mathematics has its own ecology of white whales. The Riemann Hypothesis. P versus NP. The Langlands program. Goldbach’s conjecture. These are the communal whales, the ones an entire field or generation chases together. But there are also personal ones, quieter ones, problems that matter deeply to a single mathematician or a small community and whose resistance feels no less profound for being less famous.
My white whale has been the Corona problem in several complex variables. The classical case, whether the disk algebra’s maximal ideal space contains the open disk as a dense subset, was settled beautifully by Lennart Carleson in 1962, in a proof that introduced what we now call Carleson measures, a tool of genuine and lasting importance far beyond the original question. The higher-dimensional generalization has resisted for decades. The resistance is not mere technical difficulty. It feels diagnostic, as though it is pointing at something about the geometry of domains in several variables that we do not yet have the language to properly see. That suspicion is what keeps me returning.
The whale is not just difficult. It is ambiguous, and that ambiguity is load-bearing.
What makes a white whale a white whale
Not every hard problem is a white whale. A hard problem with a legible nature is prey you can track, difficult, perhaps dangerous, but you can read the signs, follow the trail, know what you’re after. A white whale is something else. You cannot fully characterize it. You cannot be certain it is even conquerable. In Melville’s telling, what makes Moby Dick terrifying is not his size or his violence but his unreadability, he refuses to mean what Ahab needs him to mean. The whale just is, massively and indifferently.
The great open problems of mathematics have this quality. Is the resistance of the Riemann Hypothesis revealing deep structure, or is it simply hard in the way that many things are simply hard? Is P ≠ NP true because of something profound about computation and logic, or because of a combinatorial accident? We don’t know. And that not-knowing is part of what draws people in. A problem with a clear, legible nature tells you roughly how to approach it. Ambiguity forces you to keep generating new frameworks, new interpretations, new angles of attack, and that generative pressure is why white whales produce so much mathematics through their escapes, not just through their capture.
There are also personal white whales that have nothing to do with fame. A result you have been trying to prove for years that no one else particularly cares about. A conjecture your advisor mentioned once and you have never been able to dislodge from your mind. The obsession can be entirely private. The whale does not need to be famous to be yours.
The career you build in the hunt
This is where the Melville metaphor starts to require careful handling, because Ahab’s story ends in destruction, and the romantic reading of his obsession as heroic is one that Melville himself seems to have written as a warning, not an endorsement. The Pequod goes down. Everyone dies except Ishmael, who survives precisely because he was an observer, not a true believer.
The survivorship bias in mathematical mythology is real and worth naming directly. We tell the stories of Andrew Wiles, who spent seven years in secret on Fermat’s Last Theorem and succeeded. We tell Grigori Perelman’s story, the long solitary pursuit, the Fields Medal declined. We do not tell, because they are not stories in the way we need stories to be, about the mathematicians who made the same bet and lost, who spent a decade or two decades on an unconquered problem and produced nothing that advanced their career, their field, or their own understanding in proportion to the cost. Those people exist. Their silence is the sound of survivorship bias at work.
This does not mean you should not pursue your white whale. It means you should pursue it with some of Ishmael’s awareness alongside Ahab’s fire, because the traits that make someone capable of catching a white whale are the same traits that make pivoting so hard.
The sowing problem
Chasing a white whale is an act of radical long-term sowing. You are planting enormous effort with no guarantee of harvest, possibly for decades. The pivot, stepping back, redirecting, reaping something smaller but real, can feel like betrayal. But it is worth asking: at what point does continued investment stop being sowing and start being a refusal to harvest what you have already grown?
Early in the hunt, you are genuinely building depth, new tools, new intuitions, new connections between areas you would not otherwise have seen. That is rich soil. But the soil does not stay infinitely receptive. At some point the tools you have developed are ready to be used on other problems. The partial results you have gathered are waiting to be published, taught, built upon. The insight you have accumulated about why the problem is hard may be more valuable than a proof would be, if you can articulate it clearly.
Mathematical careers have seasons. Early career is the natural time to sow boldly, the opportunity cost is low, the energy is high, the reputation is not yet staked. The same obsessive focus that is wise sowing at twenty-eight can be genuine recklessness at forty-five, depending on what has been grown and what obligations have accumulated around you. The white whale does not age with you. You have to age with it, and that requires a different kind of awareness than pure obsession allows.
Wiles is instructive here precisely because he was not purely Ahab. His stubbornness was about the destination, not the route. He pivoted within the hunt, abandoning his original approach for Iwasawa theory, then pivoting again when the first proof had a gap. He held the destination with iron will and the method with open hands. That is a subtler relationship with obsession than the myth of the solitary genius usually captures.
What the whale gives even when it escapes
Carleson’s proof of the one-dimensional Corona theorem generated Carleson measures, which have been used across harmonic analysis and complex function theory ever since. The whale escaped, in the sense that the higher-dimensional problem remains open. But the hunt produced mathematics that has outlasted and outgrown any individual attack on the problem. This pattern recurs. The attempt on Fermat’s Last Theorem before Wiles produced entire branches of algebraic number theory. The pursuit of the Riemann Hypothesis has shaped analytic number theory for over a century, regardless of the fact that the hypothesis itself remains unproven.
The whale is generative through its escapes. This is perhaps the most important thing to hold onto when the hunt is long and the prey is elusive: the question of whether you will ever catch it is separate from the question of whether the hunt is worthwhile. These can come apart. They often do.
Finding your whale, or recognizing it when it finds you
If you are still early and not yet sure what your whale is, here is what I have come to think: you probably cannot manufacture it. The white whale arrives through genuine engagement with mathematics, through following your actual curiosity rather than the curriculum of what is prestigious or timely. It tends to announce itself not with excitement but with a kind of low, persistent unease, a problem you keep returning to without fully deciding to, a question that makes you slightly uncomfortable with how much you care about it.
If you are further along and you know what your whale is, the question is how to carry it, how to let it shape your work without letting it capsize it. Hold the destination with commitment and the method with flexibility. Build a portfolio alongside the hunt, not to hedge against failure but because the surrounding work will feed the central obsession in ways that pure focus cannot. Stay close enough to other mathematicians to know what is being developed that might be relevant. The lone-hunter mythology is almost entirely false, even in the cases where it seems most true.
And be willing to ask, periodically and honestly, whether the resistance you are feeling is the productive resistance of a deep problem revealing its structure, or whether it is the problem telling you something about the limits of current mathematics, including your own. These are different kinds of resistance and they call for different responses. Learning to tell them apart is one of the harder skills in a mathematical life, and there is no reliable method for doing it. Experience helps. Other people help more.
Ahab never asked Ishmael what he thought of the whale. That was his first mistake.
Mastodon’s 2004 album Leviathan is a full-length concept record based on Moby-Dick, progressive metal that somehow captures the oceanic scale of this kind of obsession better than most literary criticism manages to. If you have never listened to it while working on something you cannot solve, I recommend the experiment.