If you built a complex series of gears that took input, revolved through different sets of millions of gears, and produced meaningful output, I would consider that a form of intelligence.
So with unlimited budget and time, can you write something complex enough to seem intelligent? I think so. Is what you wrote actually intelligent? No idea, and I think that’s more philosophy than I’m interested in.
General purpose solving functions will only get better with time and already solve more than we can write solvers for by hand. I don’t suspect there’s a limit here, assuming we can keep improving in ways to scale its compute and scale the function goals.