Greg Egan's description of how mathematics evolves into "truth mining" in his novel Diaspora is seeming more and more prescient. It essentially describes what mathematics would look like after formalization records all theorems discovered so far in a huge, collective database and proof assistants can instantly work out the details of a given proof. What remains of mathematics? According to Egan, visualization, intuition, and insight.

One of the most fruitful approaches in mathematics is to flip back and forth between geometric and algebraic views of a problem. I think this works so well because these are actually handled by two different parts of the brain on a physical level; spatial reasoning is separate from language processing. Cytoarchitecture shows these regions have different "textures;" the local details of the way neurons are wired together are simply different in these different regions of the brain, in the same way a CNN and a transformer have different topologies. Thus, by flipping problems from geometry to algebra and vice versa, we're able to bring an entirely different cognitive style to bear on a problem. For example, the proof of Monge's Theorem by moving to 3D and visualizing not three circles, but three spheres sitting on a table with a book on top of them and then pointing out that the intersection of two planes is a line. What is pages of unintuitive symbol pushing turns into something a child can understand. Going the other way, things like the angle addition formulas or the quadratic formula, which are quite hard to prove geometrically, become quite simple if you use a little algebra.

Current-gen LLMs are still relatively weak at visual reasoning; see the Vision Language Models are Blind paper, for example, or the ARC-AGI benchmark. So that's one way humans can stay ahead of the agents, at least for now.