It's the exponent problem though: if it can actually engage in abstract mathematical reasoning, then it's a machine which doesn't need to sleep able to come up with new independent ideas potentially.
It's the rudiments of being able to develop and reason about computation, which means it's the rudiments of self-modification and improvement. Which is basically the holy grail of AI: a program which can iteratively improve itself to create better AIs and suddenly we're off to the races.
This is before getting into other interesting parameters, like how the scale and components of computer technology have a physical reality, and we've had experiences in the lab of genetic algorithms developing novel "cheat" strategies which exploit the physical characteristics of their hardware.
It's the rudiments of being able to develop and reason about computation, which means it's the rudiments of self-modification and improvement. Which is basically the holy grail of AI: a program which can iteratively improve itself to create better AIs and suddenly we're off to the races.
This is before getting into other interesting parameters, like how the scale and components of computer technology have a physical reality, and we've had experiences in the lab of genetic algorithms developing novel "cheat" strategies which exploit the physical characteristics of their hardware.