I agree with Dmouth. It’s easy to be humble and gracious when you are so enormously brilliant. But would you continue to be of the same viewpoint if suddenly–due to stroke or some other freak trauma to your higher cognitive processes as the result of an accident (i.e., automobile collision?)–you suffer severe brain damage which, after weeks or months of recovery, you no longer have access to your 230 ratio IQ and your doctors and experts now estimate that you effectively function at an average adult IQ of 115 (the mean of all college graduates in this country). So what now? Will you be able to perform as a mathematician as you have before this tragedy? I really doubt it. But most of all, would you still believe and stand by the false hope that you are feeding most of your readers here? Don’t get us wrong. We don’t doubt your well-meaning message that just about anyone who can graduate from a four-year college can become a mathematician if they worked hard at it. But statistically almost none of them will be able to perform at the level you have as a mathematician, and I get the feeling that your audience here all secretly dream of becoming another “Terence Tao, prodigy” because–honestly–who wants to get into any field or calling (like mathematics) just to be mediocre at it, or, in other words, unremarkable and undistinguished at it? It seems to me that most students who enter into a highly creative and potentially rewarding field like mathematics do so in order to make a significant contribution, that is, to distinguish themselves from their peers and also make a name for themselves as a professional mathematician–as you have so outstandingly done. Unless I am patently wrong, that is the exception…and not the rule. Not everyone can be you, or, for example, a Grigori Perelman, the guy who solved the Poincare Conjecture. Whatever that elusive quality we call “genius” is or however it’s defined you either have it or you don’t. And people like you–and Grigori Perelman–have it. The rest of us do not, so we have to struggle diligently and apply ourselves and compensate for it in other ways–but no matter what no amount of hard work or genuine passion can make up for the difference and allow us to catch up to your level of super-profound, mathematical ability which we average human beings call “genius” for lack of a better word, as we don’t share your rarefied cognitive “frame-of-reference,” as most of us are statistically closer to the mean of the Bell Curve in terms of native ability. When you have outlier ability it is much easier to do outlier work (as a mathematician).
This is starting to get longer than I intended, so I will end on this point. Take, for example, Carl Gauss, “The Prince of Mathematicians,” the greatest mathematician since antiquity. As a professor at the University of Göttingen he rarely, if ever, taught classes to the students because his gargantuan brilliance could not tolerate the extreme boredom and ennui that overtook him every time he had to endure teaching students of almost no math ability or perceptible promise at all. Consequently, he avoided teaching maths to students altogether. However, there were some exceptions for those who showed mathematical talent and/or promise. One of these was Bernhard Riemann, a student who fulfilled his doctoral thesis under Gauss. It is noteworthy that Gauss was only too happy to give his student Bernhard Riemann the time of day because he immediately recognized this young man’s genius for mathematics and his exceptional promise as a mathematician. (Gauss was not disappointed by his likewise brilliant student. As a result, we today owe Riemann a debt for the legacy of the Riemann Hypothesis, arguably the most famous unsolved problem in number theory.)

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