Joel David Hamkins
I have often mentioned that there is a certain threshold of maturity in mathematics, which is the boundary between knowing whether you have a proof or not and not knowing. Below the threshold, students will put up garbage, hoping to succeed, but unsure whether they have succeeded. Above the threshold, students will abstain to offer an argument when what they have doesn't actually work. To my way of thinking, this is the threshold of Actually Being a Mathematician. And in my experience, AI doesn't yet meet it. Too often it confidently serves up garbage.