<p>“An excellent math teacher has to be able to motivate and drive some of the most talented math students on the planet. At Williams, the school is more concerned about providing each student with a basic understanding in math and science, as part of a broad liberal arts education, not turning out Putnam Fellows. An excellent math teacher at Williams may be one who helps students with no a priori interest or strong background in math achieve a reasonably solid foundation. The objectives are simply not the same.”</p>
<p>While i agree that many of the most gifted math students will end up at schools like Harvard, Princeton, and MIT, and indeed, they might not find a sufficient challenge at schools that could not provide very top math faculty, the Putnam prize participants only represent a relatively small number of math students. And this is true even at Harvard, Princeton, and MIT. They are the exception, not the rule. I would argue that students majoring in math at a number of different schools can receive a math education as good as the typical math student at Harvard. (Does this apply to every math student at another school? Of course not, but if you’re talking about an honors student at a public university or a strong student at an LAC, e.g., St. Olaf, I would maintain that it does apply. In fact, if you’re simply good in math, but not at the Putnam level, maybe you’d be more likely to complete a math major at a lower-ranked school because you wouldn’t select yourself out of the field out of concern that you’d never measure up to the best.)</p>