Can undecidability theorems be detected by a machine?
Humans have found undecidability theorems. There is no reason known why an artificial intelligence cannot be built that matches what humans can do intelligence wise (although what is currently fashionable seems to be just pattern matching on a massive scale, which is not going to get you very far), therefore there is no reason known why an artificial intelligence, that is a machine, cannot find undecidability theorems.