I've noticed something puzzling and exciting when I work with abstract algebra and models. In physics, we have the notion of supercriticality, i.e., when you follow the liquid-gas coexistence curve as temperature and pressure increase, you reach a critical point beyond which matter enters this weird state where it is neither a gas nor a liquid. The distinction between the phases disappears, and it's hard to tell what you're looking at. I want to say that I've recently experienced this phenomenon a lot in the AIxMaths space, in the region where we consider highly abstract notions from universal algebra. At some point, the level of abstraction becomes so high that you end up talking about objects that are not intuitive to people at all. Every insight in this space comes basically from text, and no human can claim to be superior to LLMs in terms of originality, creativity, etc. Because everything at this level of abstraction is based on text. The new notions, ideas, and progress basically come from text processing, and to admire new theorems, you have to get used to them. This is something I see personally when I work with semigroups, loops, and other arcane objects using models. One can prompt agents to make synthetic discoveries, and they are capable of original ideas, new insights, etc., because all of this is based on pure text. Even the legendary Irving Kaplansky, when asked what he pictured when thinking about algebraic rings, reportedly said, "I see the letter R." And I think this is much deeper than one might think. Because at some level of abstraction, we enter a supercritical zone of symbolic thinking, and at this level none of our intuitions has a natural background. Every insight is superhuman, alien, and artificial. It's a no-man's land, and everything there is hard-earned. And LLMs are fast and capable. I'm learning now that, once guided well, they can make artificial discoveries. More to report soon. Stay tuned!