If you're after new methods. Then new methods is the goal, the answer to the question is not the goal then. The animated response indicates the answer wasn't just a byproduct.
There is still something to glean from the answer. You have a further constraint. Otherwise whatever "new method" proposed may as well be hallucination, potentially taking you in the wrong direction away from the answer.
This line of thought is not unique, stonemasons made obsolete by uniform brickword suddenly were "worried about the art and preserving traditions".
You’ve provided a bunch of cliches but not really anything substantial against my primary point: that in math the “how” is often much more important than the “what”, but in AI-generated proofs the “what” is the goal and the “how” is sent whizzing by on the terminal while you press enter.
If you're after new methods. Then new methods is the goal, the answer to the question is not the goal then. The animated response indicates the answer wasn't just a byproduct.
There is still something to glean from the answer. You have a further constraint. Otherwise whatever "new method" proposed may as well be hallucination, potentially taking you in the wrong direction away from the answer.
This line of thought is not unique, stonemasons made obsolete by uniform brickword suddenly were "worried about the art and preserving traditions".