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<p>Yes, we have. You spend enough years in academic programs and elite universities and you meet enough to make judgements.</p>
<p>Here’s what you are missing. Let me try to use a sports analogy because, for some reason, people don’t seem it odd to rank people on upside and performance at age 18. Bo Jackson and Lebron James were both can’t misses for recruiting in college by holistic measures. The same thing is true for math and science. The whole premise of recruiting at top schools is based on the ability to distinguish among the top 10,000 candidates in terms of athletic talent and ability. And yeah, some schools recruit for their own system, but I don’t care what system you have, Lebron James is going to be your best pick. </p>
<p>I remember when Lebron James came out of high school. He was heralded as a combination of Magic Johnson and Michael Jordan. Some sportswriters said, however, “How can you know how good he is playing against slow high school players.” To which Lebron replied that they aren’t giving high school players enough credit, particularly the AAU competitions, which, like magnet schools do for academics, allowed for direct comparison of the talented athletes across the country. He had played against many blue chip athletes in barnstorming tours already, many of which were a couple of years away from the NBA.</p>
<p>Now you point out, rightly, that there are great talents that haven’t distinguished themselves. What about Tom Brady, for instance, who wasn’t recruited heavily in college? Well, the point is that Lebron James is good enough that you can be sure that he is in the top 1500 (the approximate # of people admitted at the top colleges). So it really doesn’t matter that there is someone like Tom Brady out there (assuming you could even identify him, which is another problem.) No matter how it shakes out, Lebron James is a rational pick to take in your first 1500 picks. It’s not likely that 1500 underdogs are going to surpass him. And even if you say you need different sports, Lebron still ends up as one of your top 1500 picks if you are choosing for talent. </p>
<p>And yes, there are people who are that good in math and science. I’ll just cite just one example. The year I graduated there was a guy who won a gold medal in the math olympics and won the westinghouse (now intel) with a math project. Professors said that his work was not only an original contribution that required tremendous talent, but that he was different from other prodigies that come along every few years in that it looked like it came from a mature mathematician. He was skilled at a professional level at several subdisciplines of mathematics, and was able to use them all rather than relying on one strength as even professors sometimes do. He is now a prof at Harvard. </p>
<p>And more relevant to everyone else, there are people at different levels between your median valedictorian and the mathematician I just spoke of.</p>