Training AI to invent in alien simulated worlds

I argue that AI should be trained to discover and invent in simulated worlds whose laws, their alien physics, lie outside human comprehension. Such worlds are fully verifiable for the people who build them, yet look like an obscure mess from the inside, which makes them a test and training ground for fluid intelligence. Books and papers record where discoveries ended up, not the dead ends on the way there. Learning to find laws, and to turn them into inventions, in worlds that no literature describes may teach AI that path-finding. I define what I mean by incomprehensible, propose a curriculum that gives agents powerful tools and then takes them away, describe an invention ladder in which agents build instruments to reach other layers of a world, argue that such worlds give a second purpose to pure mathematics, and answer the main objections. Early experiments with Claude agents suggest that current models can find a foothold in these worlds, which is what reinforcement learning would need.