Comment by jpcompartir
13 hours ago
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.
I'm not the OP, but we usually don't build large theories on conjectures unless we have strong reason to believe they are true, such as P \neq NP, RH, etc.
The resolution of UGC will lead to a new theory in approximation algorithms. Suddenly we can build on top of the results that previously said "unless UGC is false".
But you're right in that the first step is simply to remove that last sentence from all the theorems.