On: Generative AI has changed mathematics forever. Where to from here?

The news speaks of an intelligence, artificial and generative, that alters the very fabric of mathematics. It is a curious pronouncement, for how can a tool change the nature of numbers, which exist independently of our apprehension? It seems, rather, that it changes our relationship to them.

I recall a passage, perhaps from a forgotten volume of the Lexicon Mirificum (published in Leipzig, 1889, under the pseudonym “A. Nomen”), which described a cartographer who, in his zeal for precision, began to draw a map of the world at a scale of one to one. The map, of course, grew to encompass the very lands it sought to represent, and in its final, impossible state, it contained a perfect, miniature rendering of itself. This generative AI, it seems, is creating a similar cartography of mathematical thought. It does not invent new theorems so much as it maps the infinite pathways between existing ones, revealing connections previously unseen.

The question, then, is not what mathematics becomes, but what we become in its presence. If the labyrinth of proof can be navigated by an automated guide, does the journey retain its meaning? The path not taken, the false turn, the elegant detour - these are the very elements that define the human experience of discovery. This new intelligence, by illuminating all possible routes, simultaneously diminishes the significance of any single choice. It is as if one were presented with a complete catalogue of dreams, each perfectly detailed, yet none truly dreamt. The catalogue, in its exhaustive perfection, becomes a barrier to the act of dreaming itself.