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They don't need to win IMO, they need to get a gold medal. I got a gold medal at IMO solving 4 out of 6 problems

I don't want to speculate, but it's not inconceivable that this will be achieved by AI within the future lifetime of XTX

Well there's a $1m prize for the Riemann hypothesis. Now this is bigger. Which do you think will fall first?

What is AMC AIME, USAMO ?

They're the feeder contests in the U.S. that determine who gets to represent the U.S. in the IMO.

AMC = multiple choice test, open to all grade school students.

AIME = open response test, all answers are numerical, open to students who score high enough on AMC only.

USAMO = USA Math Olympiad. IMO-style proof problems. Open only to top N scorers on AMC and AIME.