https://artofproblemsolving.com/community/u48336h3265944p30032043

]]>you give examples of moderately elite outcomes (USAJMO HM or mid level MOP) so it’s not surprising some of the marginal (i.e. lucky) cases of this would not qualify the next year. The topic of discussion was mainly about realistic IMO candidates being filtered out by AMC and AIME, and as people said above the second is rare and the first is pretty hard to imagine as AMC12 is trivial for them. Maybe there are some deep but really slow thinkers, but the IMO and Putnam are also speed contests to a substantial extent (based on more advanced material of course).

Of course olympiad level geometry helps on the AIME. To assert otherwise is ridiculous. All the little tricks that help with proofs come up as time savers in numerical problems of the AIME type. Deeper knowledge and problem solving experience accelerate work on simpler problems.

]]>There are numerous people who have scored highly on the USA(J)MO one year, getting USAJMO HM or even qualifying for Red MOP, but they fail to make USAJMO the next year or USAMO in any of their later years (11th/12th grade) in high school. Many were definitely at the level of blue MOP or TST group contention. I personally know several of them.

One of these people who I know pointed out that the skillset for solving olympiad problems is often quite different from the skillset for computational problems, especially the AMC where competitors are at a much bigger time crunch. For example, solving olympiad geometry problems really does not help very much with solving AMC or AIME type geometry problems. In olympiad geometry, there is an emphasis on much more advanced and varied techniques (such as barycentric coordinates and projective geometry, inversion, etc.) while AMC/AIME geometry is much more “bashy” and uses things like dropping uninteresting perpendiculars, assigning variables, doing trig, etc. On the other hand, the synthetic geometry in olympiads is often very different. As one of my MOP friends noted, doing a lot of olympiad geometry can actually hurt your ability to solve AMC/AIME type geometry problems.

The other problem is that with AMC/AIME type problems (especially AMC), it is always easy to make simple mistakes under the time pressure. No amount of olympiad experience can really help you with that. You have to prepare specifically for this. Being good at olympiads does not necessarily mean that you are good at solving these types of computational problems very quickly and accurately. These days, the cutoff for USAMO qualification is usually in the high 230s, and one needs a good AMC 12 score 126+ and a high 11+ on AIME to comfortably qualify for USAMO, which is no easy task, even if you’re very good at solving olympiad problems.

]]>This. The number of people with the brilliance and hundreds and thousands of hours of dedication necessary to be IMO high performers who can’t get past an easy math IQ test is zero basically. The fact that you only have a handful of examples (of people who didn’t even qualify for the IMO, much less place) “over the years” shows your point is off-base.

Americans care less about the IMO compared to other countries for the same reason Soviets cared more about chess than all but one American named Bobby: opportunity. There are a lot more profitable and interesting ways to ply that math G and being a USAMO qualifier repeatedly or especially placing is usually enough to get one into MIT etc. and open the doors to these.

The easiest way to solve the concerns about occasional slippage or time spent studying for the AIME is give one “AIME point” for every USAMO problem solved the prior year. That handles most of the concerns about budding IMO stars missing future USAMOs.

“It is also important to note that the purpose of the AMC/AIME/USAMO is not just to select the most promising IMO team–I don’t think one could justify all the resources devoted to it, if that were the only purpose, but also to engage and inspire a large number of young students to develop mathematically.”

Also this. These tests are among the only reliable ways for students to stand out and get into Caltech and MIT to pursue lots of non-math subjects that require high math ability.

Calculus BC and the SAT are a joke and have way too low a ceiling, and the AMC/AIME are performing a crucial sorting function for all the future physicists, computer scientists, and engineers out there. This is more valuable to the US and its GDP than slightly better sorting for the one or two people who have the math IQ necessary to prove anything new these days. Those people are truly a different breed, and will find their way to a math Ph.D. with or without a cute little competition along the way.

]]>Game over.

]]>The problem that the AIME does create for the US IMO team is that students who are potential IMO material but aren’t naturally good at the AIME have to spend extra time in their training for the sole purpose of getting past this one strange exam. This reduces the time they can spend preparing for the proof-based olympiads.

A more serious problem, for selecting an IMO team, is that the USAMO itself can be flaky. It is not unusual for IMO-worthy students (especially 12th graders) to be stopped at the USAMO because they had a bad day, or misread one problem.

]]>