How do top scorers on tests fail to gain admission to top schools?

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Some of their members have concluded that bright, mathematically-inclined students can generally qualify for AIME “on their own,” but that doing well enough on the AIME to qualify for the USAMO is highly correlated with having a good teacher. . . . and hence the workshops.

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<p>I think this is a generally correct statement. In some local cases I know, the good teacher appears to be a parent with Ph.D. qualifications in a quantitative discipline. </p>

<p>About your comment on admission committees, I know specifically that Harvard, MIT, and Stanford invite members of the mathematics faculty to look at applications submitted by would-be math majors. I rather imagine that the same thing happens at Princeton and perhaps a few other peer universities.</p>