The other option you don't mention is "algorithms can solve it, but they do something different to what humans do". That's what happened with Go and Chess, for

The other option you don't mention is "algorithms can solve it, but they do something different to what humans do". That's what happened with Go and Chess, for example. I agree with you that people don't consider intelligence as fundamentally algorithmic. But I think the appeal of algorithmic intelligence comes from the fact that a lot of intelligent behaviours (strategic thinking, decomposing a problem into subproblems, planning) are (or at least feel) algorithmic.