Has Modern Algebraic Geometry Become Too Focused on Generalization? Will AI Change That?

It has been decades since derived algebraic geometry and spectral algebraic geometry began to develop into major areas of modern mathematics. I believe these theories are genuinely powerful and have led to important insights, particularly in deformation theory, intersection theory, and moduli problems.

However, I have become increasingly skeptical of a certain trend in mathematical research: generalization for the sake of generalization.

A considerable amount of research seems devoted to extending established theorems into increasingly abstract settings—derived schemes, spectral stacks, and so on. While these extensions can be technically impressive, it is not always clear what new mathematical understanding they provide.

Of course, generalization is essential to mathematics. Many of the most important breakthroughs came from finding the right level of abstraction. But I think there is a meaningful distinction between generalizations that reveal new structures or solve previously inaccessible problems and those that primarily reproduce known results in a more sophisticated language.

This raises a question: Are we sometimes rewarding technical generality more than mathematical insight?

The rapid development of large language models makes this question particularly interesting. If AI systems become increasingly capable of handling sophisticated abstract mathematics, systematically translating proofs, and extending existing results to more general settings, much of this work could eventually become automated.

Perhaps this will push mathematicians toward deeper questions, genuinely new ideas, and applications that were previously out of reach.

Or perhaps AI will have the opposite effect, making it easier than ever to produce technically valid but conceptually incremental research.

Will AI bring an end to the era of overgeneralization, or will it accelerate it?