Even worse, we have some strong theoretical results suggesting that none of the techniques we have developed so far can ever lead to AGI, and that refers very much to machine learning primarily.
I'm talking about the work that was done on inductive inference, and then PAC-learning, in decades past (starting in the 1960's). There are many negative results and very few positive ones.
I wouldn't say I've reviewed the bibliography extensively (it's a huge area spanning a couple of fields), but from the little I've read I'm getting the feeling that, if you want to be able to learn any function in polynomial time, with a polynomial number of training examples, and with arbitrary error, you're basically stuck with the easiest classes of concept to learn. And if you want to learn specific distributions or representations (like DFAs or PCFGs) then you can just forget about it.
Which reminds me of something that Andrew Ng has said, about how recent results in machine learning and deep learning only reached the "low hanging fruit" and further progress is going to be much harder. No references to all this- I'll dig 'em up if required.