Eh, not so sure about any of this. There's also the possibility that math gets so easy that AI can figure out proofs of just about anything we could think to ask, in milliseconds, for a penny. In such a case, there's really no need that I can think of for university math departments; math as a discipline would be relegated to hobbyists, and that'd likely trickle down through pure science and engineering as well.
Then as far as king makers and economies, I don't think AI would have as drastic an effect as all that. The real world is messy and there are too many unknowns to control for. A super-AI can be useful if you want to be king, but it's not going to make anyone's ascension unassailable. Nash equilibria are probabilistic, so all a super AI can do is increase your odds.
So if we assume the king thing isn't going to happen, then what? My guess is that the world keeps on moving in roughly the same way it would without AI. AI will be just another resource, and sure it may disrupt some industries, but generally we'll adapt. Competition will still require hiring of people to do the things that AI can't, and if somehow that still leads to large declines in employment, then reasonable democracies will enact programs that accommodate for that. Given the efficiencies that AI creates, such programs should be feasible.
It's plausible that some democracies could fail to establish such protections and become oligarchies or serfdoms, but it seems unlikely to be widespread. Like I said, AI can't really be a kingmaker, so states that fail like this would likely either be temporary or lead to a revolution (or series of them) that eventually re-establishes a more robust democracy.
Then as far as king makers and economies, I don't think AI would have as drastic an effect as all that. The real world is messy and there are too many unknowns to control for. A super-AI can be useful if you want to be king, but it's not going to make anyone's ascension unassailable. Nash equilibria are probabilistic, so all a super AI can do is increase your odds.
So if we assume the king thing isn't going to happen, then what? My guess is that the world keeps on moving in roughly the same way it would without AI. AI will be just another resource, and sure it may disrupt some industries, but generally we'll adapt. Competition will still require hiring of people to do the things that AI can't, and if somehow that still leads to large declines in employment, then reasonable democracies will enact programs that accommodate for that. Given the efficiencies that AI creates, such programs should be feasible.
It's plausible that some democracies could fail to establish such protections and become oligarchies or serfdoms, but it seems unlikely to be widespread. Like I said, AI can't really be a kingmaker, so states that fail like this would likely either be temporary or lead to a revolution (or series of them) that eventually re-establishes a more robust democracy.