The Branch and the Wish

When I was young, I learned about the great Sanskrit poet and playwright Kālidāsa, the author of Śakuntalā and other works whose beauty has survived across centuries. But the story I remember most about him is about a man sitting on a tree branch and cutting the very branch on which he sits. It was usually told as a joke about stupidity, but I could never hear it only that way. The man was absorbed in the motion of the blade, unable to see the branch beneath him. He was not failing at the task. He was doing exactly what he had set out to do, letting the task fill the whole field of attention.

Mathematics has always needed proof. Without it, a claim remains too dependent on the person who made it. Proof allows an insight to be checked by others, long after the circumstances of its discovery have disappeared. It is one of the most beautiful inventions of human thought.

But I have begun to wonder whether, over the centuries, something else happened alongside this beauty. Once results entered the record, they could be counted. From there it became easier to compare them, and eventually, to reward them. The proof became the paper, the paper became the record, and the record became a career. The long apprenticeship, the failed attempts, the slow building of taste, the willingness to remain inside a problem before it became an answer—all of this remained essential to mathematics, but it became harder to see. What counted was the result. The publishable theorem became the visible unit of mathematical work, and everything before it began to look like time waiting to be justified.

This was not a decision. It was the kind of drift institutions produce when they need visible objects to compare, and proof and paper were the visible objects mathematics had to offer. The mathematician became someone who produces results, the career became the accumulation of those results, and the field became, at least in its public face, the sum of its papers. The more visible the proof became,…