I'm not sure what you mean by a "fixed program". Is a statistical clustering algorithm not a "fixed program"? Even the human brain is running some "fixed program", as we cannot reprogram our brains to efficiently run general sorting algorithms on "bare neurons".
> "general problem solving ability" seems about right for some value of "general"
It may be more useful than nothing at all, but I don't see how it conveys too much information. Clearly, a universal Turing machine has a "general problem solving ability" for much more general values of "general". So I'm not sure how much information "general problem solving" conveys. More importantly, why do we even need a definition? Statistical learning is very effective at solving some useful problems. Why do we need to philosophize about the relationship between those algorithms and human intelligence before we have more data?
Having said that - I'm always bemused that AI is supposed to compete with a hypothetical single human brain, and that the Turing Test is supposed to prove we have AI when we can build a brain that appears human.
Learning is a social activity, not an individual one. Individual brains are useless without social training and access to culture.
And some humans are actually quite stupid.
A machine that passes the Turning Test for a hypothetical middle-of-the-bell curve human isn't so interesting a thing.
If I had to build an AI, I would like to "train it" by pitching it against other AIs. Imagine an open AI network where bots will learn by challenging each others. Does such a thing exist?
Until we know what intelligence is, I'm not sure we could classify something as being distinct from human intelligence. If AI is any computational model that can learn (i.e., adapt its parameters as a response to inputs to solve various problems), then evolution would qualify as well (well, maybe it is).
But currently, "AI" is a marketing or science-fiction term, not anything we define even remotely rigorously. If we use the Turing test as a definition to AI (i.e., intelligence is the quality of an agent that is indistinguishable from a person through communication), we are not much closer today than we were forty years ago.
Science fiction can inspire science, but using sci-fi terms as if they were scientific terms is confusing, and I think we should similarly leave marketing terms to marketers (over the past decades, marketers have assigned the name AI to very different algorithms solving very different problems).
Many such things exist and have existed for years, just google it.
Also google AGI (artificial general intelligence) or see the videos I linked to on youtube in this thread.
Really the questions you are asking are sort of interesting but it indicates that you are completely unfamiliar with the decades of AI and AGI research that have been done.
Now wait a second. I would say humans are better at solving some problems directly and computers programmed by humans are better at solving other problems.
However, a computer with a single, fixed program alone will choke completely at some problems and humans are far more robust at finding a solution or at least "dealing" with any problem whatsoever one throws at them.
In the end, you're right that we don't know what intelligence is. And so just about any description is going to be somewhat tautological but "general problem solving ability" seems relatively less tautological than other concepts - ie, "general problem solving ability" seems about right for some value of "general" which we'll have to determine as we go along.