> It is developing new methods and deepening understanding to drive useful applications.
Knowing that a solution exists is not an impediment to deepening your understanding of a problem.
For example: Knowing that there is a proof of Pythagoras’ theorem is not an impediment to thousands (millions?) of geometry students developing the intuition that comes from drawing the famous diagram where the number of squares visually add up to one another.
What about the existence of an AI-generated proof prevents a mathematician from working through the problem on their own to deepen their understanding, as if the proof didn’t exist in the first place?
Knowing that a solution exists is not an impediment to deepening your understanding of a problem.
For example: Knowing that there is a proof of Pythagoras’ theorem is not an impediment to thousands (millions?) of geometry students developing the intuition that comes from drawing the famous diagram where the number of squares visually add up to one another.
What about the existence of an AI-generated proof prevents a mathematician from working through the problem on their own to deepen their understanding, as if the proof didn’t exist in the first place?
That’s what is hard to understand.