“will the first animals that take over the world be able to solve the Riemann hypothesis”, and the answer is no because humans intelligence, while general, is still pointed more at civilisation-building-style tasks than mathematics.
Pardon the semantics, but I think the question you want to use here is “will the first animals that take over the world have already solved the Riemann hypothesis”. IMO humans do have the ability (“can”) to solve the Riemann hypothesis, and the point you’re making is just about the ordering in which we’ve done things.
I’m not sure this is the most useful way to think about it, either, because it includes the possibility that we didn’t solve the Riemann hypothesis first just because we weren’t really interested in it, not because of any kind of inherent difficulty to the problem or our suitability to solving it earlier. I think you’d want to consider:
alternative histories where solving the Riemann hypothesis was a (or the) main goal for humanity, and
alternative histories where world takeover was a (or the) main goal for humanity (our own actual history might be close enough)
and ask if we solve the Riemann hypothesis at earlier average times in worlds like 1 than we take over the world in worlds like 2.
We might also be able to imagine species that could take over the world but seem to have no hope of ever solving the Riemann hypothesis, and I think we want to distinguish that from just happening to not solve it first. Depending on what you mean by “taking over the world”, other animals may have done so before us, too, e.g. arthropods. Or even plants or other forms of life more or before any group of animals, even all animals combined.
Pardon the semantics, but I think the question you want to use here is “will the first animals that take over the world have already solved the Riemann hypothesis”. IMO humans do have the ability (“can”) to solve the Riemann hypothesis, and the point you’re making is just about the ordering in which we’ve done things.
Yes, sorry, you’re right; edited.
I’m not sure this is the most useful way to think about it, either, because it includes the possibility that we didn’t solve the Riemann hypothesis first just because we weren’t really interested in it, not because of any kind of inherent difficulty to the problem or our suitability to solving it earlier. I think you’d want to consider:
alternative histories where solving the Riemann hypothesis was a (or the) main goal for humanity, and
alternative histories where world takeover was a (or the) main goal for humanity (our own actual history might be close enough)
and ask if we solve the Riemann hypothesis at earlier average times in worlds like 1 than we take over the world in worlds like 2.
We might also be able to imagine species that could take over the world but seem to have no hope of ever solving the Riemann hypothesis, and I think we want to distinguish that from just happening to not solve it first. Depending on what you mean by “taking over the world”, other animals may have done so before us, too, e.g. arthropods. Or even plants or other forms of life more or before any group of animals, even all animals combined.