Take just about anything from the reinforcement learning for ai agents domain - I'm particular to neuroevolution examples. Here's a simple one:
https://www.youtube.com/watch?v=Cb4LAT3cJfM
No behaviors preprogrammed just a simple simulation environment with environmental constraints.
> Humans are certainly not "hardwired" to prove mathematical statements, yet they do.
Umm... yeah we are? We're just chemical reactions and physics, there is no escaping that. Are we extremely sophisticated and complex, absolutely but that doesn't make us nondeterministic in any meaningful or special way.
> it's clear that the human mind has a property that the current generation of AI agents does not emulate at all
Certainly but it is a matter of degree, not a matter of possessing an ill-defined concept like "consciousness" which is what I was responding to (Unless we want to call "consciousness" an emergent phenomena arising from complexity -I'm fine with that - but the word is loaded with plenty of other connotations so I find its use counterproductive personally).