Thomas Jefferson HSST in VA produced 14 qualifiers this year, almost as many as Exeter (8) and Princeton (8) combined. 
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Of course they do - compete for NSF grants, compete for NIH grants , etc. Academia is one giant pie-eating contest, and the reward is - more pie (or pi, in the case of mathematicians)
(Since irony doesnāt travel well on the Internet, yes, I know the quoted comment was a jokeā¦)
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My kiddo is already well launched, a Senior level engineer at 25 with a patent already under his belt. 
However, many of the majors that use math do not require the level of math skill that would win medals at top level math competitions. Winning medals at top level math competitions may be an indicator that one may be able to become a top level mathematician, but is not necessary to be a statistician, engineer, computer scientist, or āordinaryā mathematician.
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That is true. But for every student that reaches the top level of math competitions there are thousands that donāt and stop at the level of math skills that are required. 
But, as I have already said, I never encountered anybody at a disadvantage because they knew too much.
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No engineer need prove that 1+1=2. There are maths that are complex, yet completely irrelevant to many practical endeavors.
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Interesting example, but everyone knows football exists, most high schools offer football, and over 1 million high school students play football, so it is not exactly a niche pursuit.
Water polo might be a more apt example. It is a niche sport played by relatively few kids in a handful of states, and a relatively small number of high schools seem to be producing quite a lot of the players at the best colleges for water polo. For example, looking at the rosters from five top boys programs (Princeton, Stanford, Harvard, UCLA, Cal), the same schools come up again and again. The first high school I checked had 10 kids playing for these just these five schools.
@tarator Iām not suggesting schools quit considering competitions or ECās all together. It was merely a thought experiment, to try to understand the impact that potential
college admissions has on such thing. We disagree on the impact it would have.
Likewise we disagree on whether all this extra math better qualifies these kids for college. No use continuing to rehash it.
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Does it hurt them if they know why 1+1=2?
So why are you suggesting the colleges stop considering these competitions? Arenāt they ECs?
Knowing more is not a disadvantage in and of itself.
However, if the time spent learning more math could be used for learning or doing something else, then it becomes a matter of whether learning more math versus learning or doing something else is more worthwhile. For example, would someone considering a future career in engineering find doing math or robotics competitions more worthwhile, if both were available to choose from? (assuming that the student has the basics in math, completing precalculus or calculus in high school)
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Let me guess . . . big water polo region? fencing? equestrian?
(I remember when I first heard they had fencing in college. I was incredulous. You donāt need to go to college to learn how to build and fix fence. had I heard about water polo, Iād probably have wondered how the horses didnāt drown.)
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Both are really interconnected. How does anybody know that they want to pursue engineering if they havenāt tried it first?
Thatās why I always encouraged my kids to try as many activities as they can, provided that they stick with them for at least few months.
That is at least part of the reason why robotics competitions, PLTW engineering courses in high school, etc. exist. In other words, to give high school students a taste of what engineering is like before they commit to it (either when applying to college or early in college when they have to start taking the major requirements and prerequisites).
Should a student who is good at math, but not showing any indication of elite level skills (e.g. Fields Medal potential) and not set on majoring in math, spend their time in math competitions, or exploring various professions like engineering through robotics etcā¦?
These are qualifiers, not winners. The winners for this year are listed here:
Thereāre 2 winners from Princeton International School of Mathematics and Science and 1 winner from Exeter. No winner is from TJ.
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I would say that it depends on their preferences. My kids chose robotics (and ISEF), but some of their friends chose pure math/computer science. Both are valid choices and much better than playing video games.
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Again, Iām not suggesting that. But I donāt think that such competitions should automatically punch the tickets of a large share of the STEM students at these schools either, for reasons Iāve repeatedly explained. And, as I have explained, I have epistemological concerns about the sportification of education, but Iāve explained that as well.
All that said, Iām glad you got a lot out of these competitions.
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I gave an estimate how many students is the ālarge shareā. Is few hundred THAT large?
Oh, absolutely not. Your post intimated though that all maths are on the same continuum. They really arenāt. You can have mastery in one branch and minimal facility in another.
Yea, none of those either. 
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Interestingly, there are 2 from Oregon, both homeschooled. I guess it goes to show, if one is in the know, motivated and their kiddo has the horsepower, it can be made to happen.
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