Well, we get from simple algorithms to general AI the same way evolution got from small individual blobs of protoplasm to Albert Einstein. The question then is, how do we program something potentially a lot smarter than us to always do 'the right thing'.

The singularity stuff is unconvincing though, I very much doubt we will achieve human level general AI in my children's lifetime. We still don't really have even a very high level idea how to even architect something like that. If you can't decompose a problem down into individual sub-problems you do have a way to solve, there's no basis for making an estimate.

It is possible that these problems are related though. Once we're smart enough to know how to design an intelligent being, maybe we will figure out how to program it intelligently. It's can't be a given though.