The grand piano has left the building. A novelist said this once about the feeling that arrives when a book is finished not relief, not satisfaction, but the sense that something enormous has been carried out of the room, and the room is now very quiet.
This is how I feel now. I should be honest that this feeling has nothing to do with anything else happening in the world. It arrives every time. So much investment goes into a project that when it ends, there is no energy left to begin the next one for some time, and for a while, the desk is a strange place to sit. I have felt it after every paper. I will feel it again. It is ordinary weather of work. But this time it happened to coincide with something else, and I have been trying to keep the two apart, because they are not the same, and confusing them would make both less true.
In July, I wrote about why I pursue mathematics, and I ended with a kind of peace. I borrowed it from Transformers, the idea of a mystical bond between man and machine, and that we would coexist. I meant it. I wrote that the pursuit does not stop; it is only carried further with us. Then, a few weeks later, two long-standing questions in my own corner of mathematics were answered by a machine; the neighborhood I have lived in for years. The peace I made in July was real, but it was cheaper than I thought.
Here is what I have arrived at instead, and it is less comfortable. There will be proofs everywhere and an abundance of them. Only the understanding will dwindle. I want to be careful about this sentence, because it is the one that actually frightens me, and it frightens me for a reason I set down in July without knowing what I was setting down. When I asked why I pursued mathematics, my answer was not that I wanted results. It was that there is a great joy in just understanding in coming to a correct conclusion after a great deal of thought and ordeal.
That is the thing under threat. Not the standing of the field. The ordeal and what it produces in the person who goes through it. I relate it to what has happened to cricket. The five-day game was a game of time, patience, and perseverance, and then a shorter format arrived, and time went out of the sport. Mathematics has always been a game of time. What happens to it when time is no longer required?
I do not know. I have stopped trying to predict any of this; I have realized that prediction here is futile. But I notice that the question is not really about machines. It is about whether understanding survives the abundance of answers, and that question would exist even if the answers came from anywhere else.
One thing I want to say plainly, because I have seen it argued the other way and I have argued it the other way myself. This is not a democratization. It is tempting to say that anyone can now produce a paper, that the guardians of the great journals matter less, that the gate has come off its hinges. There is something in that. The purpose was always to pursue and to understand; publication came afterward and was never the goal, and anything that loosens the grip of the second on the first is worth having.
But look at who solved these problems. Not a kid with a laptop. A laboratory, with computing and access that most of the profession will never see. If the tools that now move mathematics are concentrated in a handful of institutions, then what has happened is not a widening but a narrowing, and it will show up first in exactly the places that were already thin the smaller departments, the poorer countries, the people working alone. I am in a comfortable position by most measures, and I still felt the distance this month. The concerns being raised about equity are serious, and I do not think we should let the language of the liberation paper over them.
So what remains?
Five years ago, I wrote about the Ents. Merry asks Treebeard: ” But you are a part of this world, are you not? The Ents in their entmoot decide to sit out the war, and in all their wisdom, they miss one simple thing the fight finds you anyway, however carefully you have arranged your forest. I wrote then that Frodo’s part was to carry the ring and Sam’s was to stand beside his friend, that neither fought at Pelennor, and that Aragorn bowed to them regardless. There are no great or small actions. There are only actions. Choose to act, and do it well. It is perhaps the answer, and it is a better one than any I have managed since.
Everything I have been asking these last weeks has been a question about size. Will the departments survive? Will the journals matter? Will my work count for anything, set against what a machine can now do in an afternoon? Every one of those is the question of whether my action is large enough, and I have already answered that (for myself). I believe we must answer in our own ways.
It also warns me off the easy exit. The instinct, when the war in your own domain looks unwinnable, is to leave the forest to say that theory has had its day and we should turn to problems that feel more urgent. Perhaps we should turn to some of them. But if the turning is a retreat rather than a conviction, then it is the entmoot, and my earlier self already objected.
It is evening again, and I am in the same café, though the light is going earlier now than it did in July. The trams are yellow and red as they always are. I will finish this coffee and walk. The tools will keep improving, and I will use them; I have already used them, and they have been most useful not for producing answers but for showing me where a wall was, faster than I would have found it alone. That is not nothing. That may be the shape of it.
But the ordeal is still mine to go through, and the understanding on the other side of it is still the only thing I have ever actually wanted from this.
There are no great or small actions. There are only actions.
Why do we do anything? Because we cannot simply live.
Crossposted from my blog.
Received 14 September 2026.
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