48 · The Philosopher's Disease

Feynman called it "the disease of the theoretical physicist" — the tendency to philosophise about physics instead of doing the calculation. He was brutal about it, in himself and others. Hardy wrote in A Mathematician's Apology that the most dangerous phase for a mathematician is when they start writing about mathematics rather than doing it; he saw it as the beginning of decline. Grothendieck — probably the most abstractly gifted mathematician of the twentieth century — eventually abandoned mathematics entirely for philosophy and mysticism. Whether that was transcendence or avoidance is genuinely debated.

The pattern is consistent: the harder the problem in front of you, the more seductive it is to zoom out to the meta level. Building a worldview around mathematics feels like progress. It has the texture of deep work. But it is not the same thing as sitting with a problem you can't solve and refusing to leave until something breaks open. The philosophers of mathematics almost never proved anything. The mathematicians who philosophised — Poincaré, Gödel, Weyl — did so after the work, as a byproduct of it, not instead of it. So yes, it's universal. The difference is whether you catch it.

The clearest voice is Gowers. He wrote explicitly that mathematical culture has a problem with people who are brilliant at talking about mathematics and mediocre at doing it. He's suspicious of grand unified visions and values people who can actually close problems. Tao is the most visible example of the opposite disposition in practice: he almost never philosophises publicly about the nature of mathematics. He just posts work, and even when he talks, he has a strong, radical bias toward concrete, specific examples — partial results, failed approaches, incremental progress. The blog reads like a lab notebook, not a manifesto. Voevodsky said late in his life that he wasted years on approaches that felt profound and went nowhere, and that the most honest thing a mathematician can do is admit when a line of thinking is sterile and stop. Scholze is interesting because he has done genuinely revolutionary abstract work, but in interviews he is almost aggressively concrete — specific objects, specific failures, specific moments of confusion. He doesn't gesture at horizons.

The critique they share, roughly: the feeling of depth is not the same as depth. You can feel like you're thinking at the highest level while actually avoiding the unglamorous thing — being stuck, and staying stuck, until something gives. Gowers put it most bluntly: mathematical talent is mostly the willingness to feel stupid for longer than other people can tolerate.

This lands on me directly. My days can fill with the texture of deep work — journaling about mathematics, planning the study of mathematics, building the philosophy of the fund — while the problem sheet sits unsolved. The correction is always the same: fewer meta-thoughts, more problems. The problem is the teacher. The stuckness is the curriculum.

It's so hard to self-direct, plan, and execute a skill to the level of mastery. But that is the game. No drama, Jamie — just carrying the cross: one problem, then another, then another, then a generalisation, then another. Hundreds and thousands of mathematics problems solved, pattern recognition compounding — same for the code.

You will resolve a problem precisely to the degree you can articulate it. Practice defining, with precision, where and how your thought process failed. That articulation is half the solve.