Evan Chen is a mathematician (PhD in number theory, MIT) and one of the most influential figures in the American competitive math landscape. A former International Mathematical Olympiad (IMO) gold medalist, he has served as assistant academic director for the Math Olympiad Program, as Editor-in-Chief of the USA Math Olympiad (USAMO), and on the USA delegation to the IMO. He is the author of three textbooks (the first of which, Euclidean Geometry in Mathematical Olympiads, he penned while still in high school) and makes numerous resources available on his website, web.evanchen.cc.
Charting the Course is a series from Education Progress featuring pro-excellence education commentary, news, and policy analysis.
In the old days, the road to the United States team at the International Math Olympiad (IMO) started with the American High School Mathematics Exam. Back in the 1980s, this exam was taken by around 400,000 students every year, roughly 2–3% of all US high school students.1 Fast-forward to today: the starting exam, renamed the American Mathematics Competition (or “AMC”), now has two dates and two divisions. With four different entry points instead of just one, one would expect an even broader reach.
But reality looks completely different. In 2025, the total number of students across all four exams was under 100,000 — less than a quarter of the raw count 40 years ago, and well below 1% of high schoolers.2 And that’s double-counting the students who participated on both dates; if one counts the number of distinct students, the numbers are worse.
Given how often the United States scores highly in the International Math Olympiad, the quiet implosion of the American competition system might seem surprising. How did things end up this way? How can the United States continue to bring back gold medals3 from the International Math Olympiad every year even as the base competition system is crumbling?
What are math competitions for anyway?
To understand how the landscape has gotten this way, it’ll help to step back and ask what its North Star is. Why do we have math competitions at all? What’s the point of all this? When people think of the International Math Olympiad, the thing they know right away is that the problems are difficult. When the United States created a documentary about its 2006 IMO team, they named it Hard Problems: The Road to the World’s Toughest Math Contest. And in recent years, AI companies have treated success on the IMO as a grand target. Given this narrative, it’s easy to get the impression that the IMO is meant to identify mathematical talent, and the sheer difficulty ensures only the best students stand out.
But that perception is wrong. Math contests aren’t merely exams to measure talent. They create talent.
The beauty contest
How can an exam create talent? To give you an idea, it might help to have an insider retelling of how IMO problems are selected.
Each year, the IMO forms a Jury with one representative from each country. The host country (in a laborious, months-long process of reading hundreds of proposals) presents the Jury a shortlist of about 30 problems. For every shortlisted problem, each Jury member submits two ratings. One rating is difficulty. But the other rating is arguably more important: how beautiful the problem is. A problem can be “acceptable,” “nice,” or “excellent.”
For someone who’s never seen a math contest problem before, this might seem bizarre. You know what it means for a problem to be easy or hard. But what could it mean for a problem to be “nice”? Maybe it teaches you something you didn’t know; maybe its statement immediately piques your curiosity. Maybe its answer is totally different from what you expect. Maybe its solution blows your mind. At minimum, it should be a problem that a contestant would want to work on. The most colorful quote I’ve seen comes from a competition called the Putnam:
It used to be said that a Broadway musical was a success if the audience left the theater whistling the tunes. I want to see contestants leave the Putnam whistling the problems. They should be vivid and striking enough to be shared with roommates and teachers.
For a real example, here is a problem shortlisted for the 2018 IMO.4 The solution is much too difficult to discuss in this post, but I hope its beauty will still nerd-snipe some of you.
A tennis tournament has N players in it. The organizing committee needs to schedule the matches for the tournament so that every two players play once, with one match played each day. Each player arrives to the tournament site the day of their first match, and departs the day of their last match. For each day a player is present on-site, the committee has to pay 1 coin to the hotel. When the organizers design the schedule, what’s the minimum possible hotel cost?
If you felt the itch to find an answer5 yourself, you understand the engine for creating talent with a test. Scratching the itch means sizing up the problem and choosing an approach, not just rehearsing the steps in the lesson of the week. “Teaching to the test” is rightfully viewed with suspicion in mainstream education when the tests are merely supposed to measure (often inaccurately) the learning that happened elsewhere.
But math competitions are different: the exam is the product.
The central guiding tenet of the math competition movement is this: if you pour your heart into designing instructive, interesting math problems, then the students studying those problems develop interest and learn an immense amount.6 The best problem-setters treat their problems with the same kind of care that choreographers, film producers, or game developers all do: experiences for a human audience to enjoy. Thus, top-tier math competitions almost always publish all their past problems and solutions, actively encouraging students to try them.7 (It’s the opposite of the classroom teacher who hides past years’ final exams out of fear students will study them.)
On a more practical note, there is one big real-world advantage to this approach: it’s cheap. If you wanted to build a system that engages millions of students per year, the per-student price tag had better be low. An annual contest can do that for just a few dollars per student engaged. And with the Internet, the cost of hosting an archive of past problems online is close to zero.
How are things falling short in reality?
So how did things end up the way they are today? If the problems on the IMO are so great, why has the audience vanished?
The overarching story here is something that won’t be unfamiliar to many readers: advanced education has long moved away from public schools. If you are interested in math above your grade level (or just outside the standard curriculum), you study it after school, not during it.
The AMC, which is supposed to be the entry point and many steps removed from the IMO, is suffering the same story. On one extreme, there are still pockets of students who are really familiar with all the competitions and study in their own free time (or during their normal math class when the teacher isn’t looking). The internet makes this straightforward: all the past problems are online, as are abundant study resources. Perhaps in response to increasing preparation from well-connected students, the AMC difficulty has crept up over time. I’ve even heard the modern AMC described as an “arms race over speed.” This arms race has produced something worse: a cheating problem so severe that it’s made news. A community happy to share its past problems now has people leaking upcoming ones. These are directions I worry about.
But what happens to everyone else? As math competitions grow increasingly disconnected from what’s actually taught in schools, the competitions turn into a niche activity insulated from outsiders. Although the AMC is supposed to be the first exposure for students coming from a normal high-school background, it’s now inaccessible to them: the AMC has earned a reputation as an exam designed only for geniuses. As for the schools, I think the late Dr. Kent Merryfield describes it best:
I was a 10th grader in 1969, in Oklahoma. It was a pretty strong high school in a community that valued education, and in which a significant number of parents (including mine) were engineers or scientists — but it wasn’t fundamentally all that unusual a place. At some point in the school year, I was just told that on such-and-such a day I was supposed to take some test, which turned out to be the AHSME. It was school business, and it was just something that was done. This was before there was any follow-on — no AIME, no USAMO, no U.S. participation in the IMO. But hey, when I got the highest score in my school as a 10th grader I thought it was a pretty big deal.
That’s what’s missing in what I see around me — the idea that “you will take the AMC” being ordinary school business at any more than a handful of places […]. There are many schools where the AMC is only offered because some long-veteran teacher has always done it and insists on it. Three years after that teacher retires, not only will the school no longer participate, but no one will remember that the school ever participated. Perhaps there’s enough life in a non-school model — but I have trouble seeing how that can be large enough or inclusive enough.
This is why the top students might appear unaffected despite the dramatic shrinking of total AMC participants. The quality of contest problems is no worse than 40 years ago; if anything, the problem designers today are even more capable.8 So the students who find the world of math contests and fall in love with it can still get something out of it.9 But today most schools have no idea what the AMC is. And unless the AMC can find a way to become relevant to schools again, it’s likely to stay that way.
Where could we go?
One could imagine driving math contest participation back up by marketing them as a reliable standardized test of math talent. I’m more cynical about this approach. The kind of things one would need to make an elite college entrance exam often conflict with the goal of designing problems that are interesting, creative, and insight-causing. And even if it could be done, there is something unsavory to me about turning what should be a fun and educational event into a high-stakes environment. One past director of the AMC describes it this way: “to do so would ‘bureaucrat-ize’ what is now a good mathematical experience and kill it.”
In my utopia, the goal is to have many different on-ramps into math, one of which is a healthy competition series, with students free to choose between whichever ones fit them the best. The math circle movement, for example, is another such road. I share the general view that anyone claiming they have the sole answer to math education is likely to be mistaken. I certainly don’t want to sell anyone that bridge.
What I’m concerned about is that in practice, the US doesn’t actually have many avenues for advanced math at all. The math contest system historically had one of the largest reaches, since it scaled cheaply to many students. And now that system is dying too.
See e.g., https://pubs.nctm.org/view/journals/mt/75/7/article-p548.xml: "In 1982 it was taken by over 418 000 students in 6623 schools in North America alone.”
One can pull this report from the MAA’s own website https://maa.edvistas.com/eduview/report.aspx?view=1561&mode=6, where the 10A, 10B, 12A, 12B had 31600, 25204, 20429, 16433 students respectively. This is in spite of the advertisement on https://maa.org/student-programs/amc/ that claims 300,000 students; this figure includes both students taking the middle-school AMC 8 and a substantial number of students outside the United States.
Generally, using the IMO as a ruler for the whole country is misleading because the IMO only measures the strength of 6 top contestants. Truthfully, what often happens today is that the top 10 or 20 USA candidates have fairly similar ability levels; certainly within variance of the sports cliché “on any given day.” This means IMO results cannot reliably detect the size of the talent pool for a country as large as the US. Hence, even if the contest system is missing lots of “hidden gems” such as in Kent Merryfield’s story below, it will not reflect in IMO results.
I picked an example of a difficult problem where the statement is still immediately accessible to anyone. A typical problem at the IMO might require more mathematical background in order to understand or appreciate the statement and solution; there is definitely a bit of acquired taste sometimes too. That said, the amount of background needed is typically overestimated. For a rough point of comparison, it should be possible to explain the statement and solution of an IMO problem to an undergraduate math major.
You can also find the solution at under C5 of the IMO 2018 shortlist. The C5 version makes the problem easier by specifying $N$ is even, but the Remark outlines the adaptation to $N$ odd.
For many in the math competition community, creating and nurturing interest in math is at least as or even more important than creating and nurturing talent. But the two go hand-in-hand: more interested students spend more time learning and practicing in ways conducive to building talent.
Except the AMC does not maintain their own official archives. The de facto public archive is hosted by a third party, the Art of Problem Solving website (aops.com). From an international point-of-view, this is unusual; most countries maintain official archives of their own national contest. As they should.
For readers with some math background, here is a bit more nuance. In general, as you advance to later rounds of math competitions, the amount of assumed background knowledge increases, the time limits change from minutes to hours, and real proofs are demanded (rather than just a numerical answer). For a problem-setter, that gives you way more power to design a learning experience. So it's actually the latest stages of the competition (like the IMO) which have the best problems showcased. Whereas on the other extreme, the entry-level AMC has a large speed component that is often rightly criticized, and its format as a multiple-choice exam is a major weakness in its design. This means the best pedagogical value is disproportionately concentrated on the most advanced stages of the competition series.
Unfortunately, it's not all moonlight and roses for the top students today either. The cheating issue has severely poisoned the atmosphere, where there are so many cheaters that honest students now seriously struggle to advance to later rounds of the competition. This also needs to be dealt with for the AMC to have a chance of recovering.
These competitions are a wonderful experience for participants, who represent their country at the highest level. Apart from the irreplaceable intellectual challenge, students I’ve taken to the IOL - Computational Linguistics - on two occasions have made terrific lasting friendships. There’s no other experience like it.
Thank you for writing this, particularly about the lack of access to the AMCs in rural areas. Parents often need to fight or drive long distances to find a seat for their students. Meanwhile, the MAA seems to have an ambivalence about the AMC that is mystifying, about such a valuable undertaking in a world with rampant grade inflation.
The MAA may disagree, but the AMC is in fact a college admissions test. Currently CalTech and MIT ask specifically for AMC scores (though they are not required for admission).
I've heard about cheating at the highest levels, but there's no need to cheat, when the MAA takes a hands off approach in the name of avoiding "bureaucratization." Students can report on college applications any reasonable score they want, and there is no way to verify, there is no official score reporting, no way to determine who qualified for AIME and who did not.
I've heard insiders describe the MAA as a "ghost ship." At so many levels they don't seem to care about this most historic and beloved exam.