For one, it doesn’t seem like AI is good enough at this point to really “go deep” compared to very good mathematicians, but is good at covering a lot of ground, so counterexamples + finding clever constructions based on existing techniques are comparatively easier (compared to e.g. doing theory building).
For another, I think “almost all” is heavily overstating it: E.g. the double cycle conjecture was resolved positively by extending existing constructions. So if you look at the top 3 most visible results you have 2⁄3 counterexamples. If you go to top 12, this goes down to 4⁄12 (as judged by the AI).
Also, some counterexamples are different than others: In the Jacobian conjecture case, this seems to be “just” writing down the right object (presumably based on extensive search and smart guessing); for the unit distance conjecture, the counterexample is obtained by leveraging deep theoretical connections to produce an object with exactly the right structure needed to refute the conjecture.
For one, it doesn’t seem like AI is good enough at this point to really “go deep” compared to very good mathematicians, but is good at covering a lot of ground, so counterexamples + finding clever constructions based on existing techniques are comparatively easier (compared to e.g. doing theory building).
For another, I think “almost all” is heavily overstating it: E.g. the double cycle conjecture was resolved positively by extending existing constructions. So if you look at the top 3 most visible results you have 2⁄3 counterexamples. If you go to top 12, this goes down to 4⁄12 (as judged by the AI).
Also, some counterexamples are different than others: In the Jacobian conjecture case, this seems to be “just” writing down the right object (presumably based on extensive search and smart guessing); for the unit distance conjecture, the counterexample is obtained by leveraging deep theoretical connections to produce an object with exactly the right structure needed to refute the conjecture.