Well, let me describe the sort of architecture I have in mind.

The AI has a "knowledge base", which is some sort of database containing everything it knows. The knowledge base includes a set of heuristics. The AI also has a "thought heap", which is a set of all the things it plans to think about, ordered by how promising the thoughts seem to be. Each thought is just a heuristic, maybe with some parameters. The AI works by taking a thought from the heap and doing whatever it says, repeatedly.

Heuristics would be restricted, though. They would be things like "try to figure out whether or not this number is irrational", or "think about examples". You couldn't say, "make two more copies of this heuristic", or "change your supergoal to something random". You could say "simulate what would happen if you changed your supergoal to something random", but heuristics like this wouldn't necessarily be harmful, because the AI wouldn't blindly copy the results of the simulation; it would just think about them.

It seems plausible to me that an AI could take off simply by having correct reasoning methods written into it from the start, and by collecting data about what questions are good to ask.