Well it certainly got me to study harder, and I probably wouldn't have made it without last year's expansion with my 3.5 stupid mistakes on the AIME.

As much as I supported the first two expansions, and as much as I probably will support a few more to come (possibly), there's always a limit on stuff. When there are 800, 1000, 1500, people taking the USAMO, much more prestige is lost (500 is actually a good number, in my opinion), and there are going to be alot more people sitting there clueless when they actually take the USAMO, which can be discouraging. Though I may be wrong about that.

I still think that if someone can make the USAMO with a score of 5, then it's way too low of a cutoff. I think that 400 would be a better number than 500, but oh well.

This year I prepared almost exclusively for AIME, and went from 0 on AIME last year to an 8 this year (well I didn't take AIME last year, but I wouldn't have gotten more than 1 or 2), so it's certainly possible to make USAMO comfortably with only a year of hardcore practice.

The local prestige factor might be good for some, but I also think that many times local people don't have a sense of how significant USAMO qualification is. I would say that the USAMO is too different and people are probably not going to view it much differently from an AMC perfect score.

Furthermore, sometimes these people who have only one or two other USAMO qualifiers in the area are already sort of disconnected with the local math community by being significantly more advanced than their peers. Personally I doubt that first time USAMO qualifiers from a small place will become motivated as a result of their immediate peers, but perhaps it will get them to go beyond the probably uninteresting local math contests. However, if somebody has qualified for USAMO, maybe it will encourage others to try for it.

So do you plan to have another expansion next year, or will you leave it at 500 for now?

(Personally, I think the number of qualifiers should be kept at 500 for a while. No matter what, only people with a reasonable expectation of actually earning points on the USAMO should qualify. Another expansion would mostly let in people who don't have that expectation. Of course, there are exceptions, but not enough to make it worthwhile, I think.)

The important thing that Richard is saying (correct me if I'm wrong) is that the idea of the expansion is not to "dumb down" the difficulty of making USAMO, but rather to sponsor an increase of interest in competetive math and problem solving in general. They want to advertise the WAY OF LIFE that it offers, not necessarily the difficulty. I didn't make USAMO this year by 2 AIME questions, and yes, it frustates me, but I also will continue to remain interested in math whereas my friend, who missed by 48 index points, decided to drop out of our math club. That's why the expansions are a good idea: you can keep people like that coming back for more interesting problems.

As it stands now, I'm going to try to get him to come to ARML and we'll see how it goes from there.

I agree with Mr. Rusczyk. Qualification for the USAMO can indeed motivate people to study math more. In addition, it can motivate people around them. Furthermore, many people who qualify may try to prepare seriously, if only a little bit, which can make a difference for that person.

But there has to be a point where having many people who just can't do USAMO math take the USAMO gets kind of pointless and even potentially harmful. I would support a separate awards system for people who do well on the AMC/AIME but not well enough to qualify for the USAMO, but in the end, the USAMO isn't just a recognition of math ability, it's also an actual test. I don't like the idea of giving such an unusual, specialized test to just anybody. (Besides, any more expansions and certain regions, such as the one where I live, would see a significant drop in LOCAL prestige...)

At this point, there are no plans (that I know of) to expand the USAMO pool further in the near future. However, it's my hope that it will be necessary and desirable to do so in 5-15 years, due to an increase in ability and preparation among the top few thousand students in the US. This may be a pipe dream, but it's a pipe dream worth pursuing, I think.

Prestige is a function of both awareness and difficulty. Right now, I don't think the number of USAMO qualifiers significantly impacts prestige in most communities. Other than those who score highly on the AIME, a few math club sponsors and some mathematicians, very few people really know anything about the USAMO. The vast majority of high school math teachers in the US wouldn't be able to identify the USAMO as a proof-oriented contest for high school students.

Building awareness is much more important to increasing prestige than restricting the number of qualifiers. Many schools with very good math students don't even bother to participate in math contests.

You'll know that you've succeeded when students, parents, and school administrators assess the quality of math programs by performance on the AMC and other math contests. A few people already do this but not nearly enough to make an impact on math education at 99.9% of schools.

Last year, Newsweek rated schools based on the number of AP exams attempted/passed per student. I usually don't pay much attention to these ratings but our local school administrators did. Policies that previously kept students out of AP classes were dropped. Capable freshmen and sophomores are now encouraged to take the more challenging AP courses. Imagine the difference in math education that might be possible if good school scores on the AMC/AIME contests were considered as important as the Newsweek rating.

One way to make this happen is to publicize school performance on the contests. The school honor rolls and merit rolls published on the web by the AMC this year are a good start. Most of these schools already have excellent reputations in their regions. This idea should be extended to include "state" rolls so that the top 30% of schools in each state are ranked and recognized. Harold Reiter publishes such rankings for NC at http://www.math.uncc.edu/~hbreiter/AHSME/amc12index.htm. It would be more effective if these school results were compiled centrally (at MAA's site) for each state so that web searchers would be more likely to turn up the lists. The MAA has the potential to drive over 100,000 contestants and parents each year to its contest site. If enough of these folks looked at the relative performance of their local and state schools on the contests, the impact on math education would be substantial.

The more people that ask a school administrator "how did your school do last year on math contests?" at open houses and other forums, the more schools will pay attention. If it becomes clear that top math students are selecting schools based on the quality of math teams, you could expect real changes in how top math students are educated. The changes would happen even faster if community leaders believed that having schools with excellent math reputations were a requirement for attracting and retaining doctors, scientists and other desirable professionals.