I think this is quite plausible. Also see toner’s comment in the other direction though. Both probabilities are somewhat high because there are lots of easy IMO problems. Like you, I think “hardest problem” is quite a bit harder than a gold, though it seems you think the gap is larger (and most likely it sounds like you put a much higher probability on an IMO gold overall).
Overall I think that AI can solve most geometry problems and 3-variable inequalities for free, and many functional equations and diophantine equations seem easy. And I think the easiest problems are also likely to be soluble. In some years this might let it get a gold (e.g. 2015 is a good year), but typically I think it’s still going to be left with problems that are out of reach.
I would put a lower probability for “hardest problem” if we were actually able to hand-pick a really hard problem; the main risk is that sometimes the hardest problem defined in this way will also be bashable for one reason or another.
I think this is quite plausible. Also see toner’s comment in the other direction though. Both probabilities are somewhat high because there are lots of easy IMO problems. Like you, I think “hardest problem” is quite a bit harder than a gold, though it seems you think the gap is larger (and most likely it sounds like you put a much higher probability on an IMO gold overall).
Overall I think that AI can solve most geometry problems and 3-variable inequalities for free, and many functional equations and diophantine equations seem easy. And I think the easiest problems are also likely to be soluble. In some years this might let it get a gold (e.g. 2015 is a good year), but typically I think it’s still going to be left with problems that are out of reach.
I would put a lower probability for “hardest problem” if we were actually able to hand-pick a really hard problem; the main risk is that sometimes the hardest problem defined in this way will also be bashable for one reason or another.