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As someone who will almost certainly travel down that road that you did not, I am curious about your last sentence. What's there to be impatient about with respect to academia? I suppose that my impatience makes it impossible for me not to go into academia -- I need to learn everything, and it can't wait another 10 minutes to do so.

I was at the conference as well. I'm just a college student and not one who's done spectacularly well on contests or anything like that, but I'll put in my two cents.

My understanding was that the MSRI's interest in grade school enrichment IS largely the prospect of nurturing future mathematicans. It's arguable that the organization should be more interested in general outreach activities independently of whether it helps the field itself, but given that the organization is heavily grounded in research math such an interest is perhaps not surprising.

On a related note, I think that there is something to be said for activities more closely associated with research math than contest math being beneficial to all sorts of people. There's definitely a lot more to math than being given a series of problem to the effect of "Suppose A satisfies X, Y and Z , prove that ....." and solving it. Sure, that type of thing can involve an immense amount of sophisticated thinking, but there are vast expanses of mathematical territory that aren't touched by solving such problems.

I'm thinking of things like realizing the need for greater rigor in a holistic sense ala Real Analysis. (For example, noticing that while at first it might seem like it's okay to prove the Cauchy Schwartz inequality in n dimensions by saying that dot product is product of magnitudes times cosine of included angle, with some thought realizing that such a proof presumes a notion of angle in n dimensional space which turns out to need to be defined in terms of dot product and that the justification for angle being well defined IS the Cauchy Schwartz inequality, and that while it at first seems like it might be possible to patch the issue up by projecting the plane with the two vectors onto R^2 the issue is more messy than it might seem at first because such an attempt uses the idea of an angle preserving transformation which is impossible to define without a notion of angle to begin with).

The other thing that I was thinking of was the development of aesthetic preference for certain problems and ideas over others. Some of the ideas present in the contest problem lore are more interesting than others. Of course, everyone has the opportunity to think about his or her preferences, but when you train for an olympiad you have to know X and you have to know Y and you have to know Z and you have to have a lot of practice with problems of all types, etc. There's not necessarily a lot of time to stop and think about if and why a certain problem is interesting and how the result might be generalized. It's not discouraged and does take place, but it's not explictly encouraged either.

Doing research like activity in which one poses her own questions, creates her own definitions, decides which questions are fundamental and which are just curiousities, etc. is qualitatively different from olympiad problem solving. I think that there is something of value to this other side of math that most high schoolers don't get to see. Of course, doing research can be slow and perhaps less thrilling, but I think that it would be good if more people could at least be exposed to the concept in a user friendly context. Part of the reason for this is aesthetic - there are matters of much interest in all different parts of math.

Moreover, I don't think that it's at all clear that the pure problem solving part is really the part that is applicable to industry jobs and real world problems. On the contrary, I think that crossover intellectual training gained from math is gleaned from all aspects of math; perhaps not in a direct and obvious way but in the long run.

I think that some people the conference were coming at least in part from the point of view that I expressed above, would be curious as to your response.

My comment about patience was simply one of personal preference - I lack the patience for long-term research. I'm not saying such research is without value, just that it is not part of my personality. On the other side of the coin, those who wish to know for the sake of knowing and are willing to spend years in order to know, do indeed have the patience I lack to pursue research. I'm more interested in doing and creating, and don't have the patience to view a 15-year project in that time horizon. Complex, don't you worry, you are going to be a fantastic contributor to academia. You are impatient to know. I am impatient to do, to produce tangible results that affect others in the short-term. Therefore, you will be very happy in research academia. I, however, will find my home elsewhere.

My comments regarding the point of mathematics competitions and problem solving were not intended to say that producing mathematicians is not a lofty goal; they are intended to say that it is not the only goal. Further, I don't think producing mathematicians is even the most important goal of these contests, which was distinctly the attitude of some of the conference attendees. (In fact, I don't think it's even an important goal - the world is not hurting for lack of mathematicians.)

As for problem-solving skills being applicable to real world problems and industry, we may have to agree to disagree. I find fundamental problem-solving skills far more applicable to what I do now, and what I did at DE Shaw, than I do/did any higher mathematics. Most people, even those in technical jobs, use little higher mathematics. They solve problems all the time. This may, however, be a semantic disagreement - you may be defining 'mathematics' as I define 'problem solving', and you may be defining 'problem solving' as 'contests'.

I do, of course, agree that there's much more room for more interesting contests, and exploration as you suggest. Finding and defining the interesting problems is extremely important. If extracurricular programs could address this more completely (and not just to those who have access to a professor or parent to help them, as is the current case for the most part), this would be fantastic. But I will note that while there's not much time during contests to stop and think why one thing leads to another, all successful problem solvers will probably tell you that they did indeed wonder this, and addressed it after the contest (or better yet, before it). That's life - in many disciplines, you do have to make decisions and then ruminate later about how to handle them if they come up again.

As for research being less thrilling, that's in the eye of the beholder. This really is a matter of personal preference. Complex, for example, will find it far more interesting than building educational resources or trading bonds, both of which I found eminently more interesting than research. Like I feel about airplane pilots, judges, policemen, and a host of other professions, I'm glad there are researchers, I'm simply not one of them.