This isn’t the most philosophically sophisticated idea, but basically the idea that the universe was created by “something” that desired a certain evolution of the universe. This as opposed to the most popular idea that the universe just sprang into existence randomly.
Basically proof of some sort of god. I wish I found STEM interesting, but the main pseudo-intellectual interests I have that bounce around my head are existential questions. I think answering existential questions would be what I would be most excited about an ASI coming into existence for. I think most people’s most burning question if they were talking to a superintelligence wouldn’t be “is the Riemann Hypothesis true?” I think it would be “is there a god? What was it thinking when it made the universe this way?”
Not a real superintelligence because it can’t even understand the spirit of my question.