AIME higher
Year after year, a large number of Uni students take the American Mathematics Contests. Some even prepare for it, and everyone is eager to check their answers after the test to see if they’ve qualified for the next round, the American Invitational Mathematics Exam. A good 10 or so always advance.
But then, it seems that everyone gives up. In the last two years, I haven’t seen anyone make a serious effort to do well on the AIME, even though it is one of the most mathematically rewarding contests in existence. I suspect that the typical mindset walking into the testing room goes something like this:
I’ve already qualified for the AIME. There’s no chance I can qualify for the USA Mathematical Olympiad, so I’m just going to grind out a few answers by brute force and enjoy my half day off from school.
To be sure, the AIME is a hard test. It usually takes eight or nine out of 15 questions to qualify for the USAMO. The national average score is consistently less than three. However, the fact that several Uni students can get a score of four or more tells me the USAMO might not be as far off as people think.
Another reason the AIME gets overlooked is that the Illinois Council of Teachers of Mathematics contests happen at around the same time. Practicing for the ICTM is more appealing because it could translate into a recognizable award rather than simply a numerical score.
Unfortunately, students who brush off the AIME are missing an important opportunity. The AIME is discouraging because, unlike other contests, it often takes 20 minutes or longer to solve a single problem. But this is precisely why it is also extremely valuable.
Most people are accustomed to giving up or seeking help within 10 minutes of getting stuck on a problem. They don’t realize that learning is not a passive activity. The teacher gives you the theorems and techniques — you have to figure out the motivations and fundamental ideas that lie beneath them.
The AIME is an excellent way to build up the necessary skills to understand math at a deeper level, because its difficulty lies just beyond the comfort zone. In the course of tackling truly challenging problems, you accumulate your own insights and think about things in ways that make more sense to you. You empower yourself to learn new material without getting bogged down by countless formulas, because you see that most of them are simple extensions of a few core theorems.
Thus, beyond qualifying for the USAMO, Uni students have a lot to benefit from setting some higher goals for the AIME. Many people are taught what they know. I encourage them to switch to the active voice and to learn.
— Alex Zhai