In transhumanism it refers to self-improving machines which again can not be constructed by definition. Every machine will still have a constraint defined by the parameters it is programmed even if it is able to construct copies of itself and use stochastic processes to fine-tune the parameters.
I'm no expert but it seems to me that you're talking about twentieth century style AI. Nowadays computing engineers for AI use genetic algorithms, artificial neural networks and stuff like that. They don't program the behavior of the machine. Moreover, your brain also has "parameters": the maximum number of neurons, the physical laws they obey, and so on. A computer might actually have more degrees of freedom than your brain can ever have.
Again a machine is by definition lifeless. Discussing a hypothetical scenario where we could
enable life makes no sense since we have no idea how it could be accomplished.
Genetic algorithms and artificial networks are exactly what falls under computer science as the subject of "AI" they are exactly the mathematical processes I was referring to.