Err... what does doing math have to do with it? If I have a good (human) assistant, I can ask him or her to find me all the Y Combinator articles and it just works. I don't need to write some formal mathematical description of the task.
It's true that it's all math/physics/chemistry underneath, due to how the brain works, but in practice we never worry about that, just as an engineer doesn't generally consider quantum and relativistic effects when he's designing a bridge, or an outfielder doesn't scribble down a bunch of differential equations before catching a fly ball.
Sure, any standard computer is equivalent to a bounded Turing machine, but Turing machines are a real pain in the ass to program.
Mathematical purity is one thing. Getting your work done is quite another.
It's true that it's all math/physics/chemistry underneath, due to how the brain works, but in practice we never worry about that, just as an engineer doesn't generally consider quantum and relativistic effects when he's designing a bridge, or an outfielder doesn't scribble down a bunch of differential equations before catching a fly ball.
Sure, any standard computer is equivalent to a bounded Turing machine, but Turing machines are a real pain in the ass to program.
Mathematical purity is one thing. Getting your work done is quite another.
Over-mathematization is what killed AI (IMO).