Much of this goes way above my head, but I found it interesting nonetheless. Q I had was why textbooks would need to be re-written? From your account it doesn't seem like results are upended, but rather confirmed?

I suppose when people do re-write the textbooks they'll say "this is confirmed now" not "if this conjecture is true...", but usually re-writing the textbooks would imply that things have been shown to be false?

May have misunderstood. Thank you for the post though, it was very interesting to someone who doesn't know much about the topic.

In a way I'm not entirely sure if proving the conjecture or posing it is the most important part here. It used to not matter much because proving results dependent on a connecture and making progress towards solving it were considered mostly equivalent.

But the distinction is going to become relevant very soon if many conjectures can be resolved (albeit in inscrutable fashion) by throwing raw computational resources at it.