I once read a very interesting, barely-upvoted reddit post titled "I suck at Brazilian Jiu-Jitsu". It was written by a black belt, himself a formidable combatant and instructor, who no one would accuse of "sucking at BJJ". His rationale was that compared to world champion BJJ athletes, he was barely a blip on the radar of the sport itself. Although he had achieved significant mastery relative to the everyman, or even the average advanced practitioner, he was still woefully far off from the true limits of the sport.<p>This can a tremendously valuable mindset to take up in mathematics; especially when one is a student learning under the factory model of modern school, where one is evaluated relative to their peers and the institution itself, rather than relative to the limits of what is possible. Countless "gifted and talented" students have been done a tremendous disservice by being informed at a young age by the system that they are "good at math" or "good at English" because they show relative aptitude in memorizing and regurgitating simplified models of advanced material.<p>Terry Tao is lucky to be so smart that he was already somewhat well-known and successful by the time he learned the truth that these administered tests of ability are arbitrary; it would be tremendously helpful for modern students to learn the same, much earlier.
This is something that afflicts a lot of younger, talented students. I was able to breeze through K-8 without studying, then attended a challenging high school where I went from a straight A student to a B/C student. It took me at least two years to realize that I could no longer succeed by simply showing up. Fortunately, this was great preparation for college. I saw many straight-A high school devastated after their first round of college engineering exams.<p>I think this is an unfortunate consequence of our education system at-scale. It's difficult for advanced students to be properly challenged until they reach a certain reckoning point, which for Terence was impressively during his grad school exams.
Reminds me of a friend from high school who was one of the smartest people I've ever known. In multivariable calculus we weren't required to do the HW if we didn't want to. He never did homework and never studied outside of paying attention in class and still got 100s on all the quizes/exams. He went to MIT and failed most of his classes his first semester there. He'd never had to study before so he didn't know how. Like Terence Tao though he's doing fine now.
This essay also appears in a book called "Living Proof: Stories of Resilience Along the Mathematical Journey" put together by the AMS and MAA recently. Its a collection of essays kind of like this about near (or actual) mathematical failures and what happened afterward. The whole thing is here [1]. Most of the essays are from pretty "normal" mathematicians rather than super-duper stars like Tao.<p>[1] <a href="https://www.maa.org/sites/default/files/pdf/ebooks/pdf/LivingProof_WEB.pdf" rel="nofollow">https://www.maa.org/sites/default/files/pdf/ebooks/pdf/Livin...</a>
Here’s the summary that Tao wrote at the time, for future Princeton grad students: <a href="https://web.math.princeton.edu/generals/tao_terence" rel="nofollow">https://web.math.princeton.edu/generals/tao_terence</a><p>Other students: <a href="https://web.math.princeton.edu/generals/" rel="nofollow">https://web.math.princeton.edu/generals/</a>
I sometimes feel very uncomfortable reading such stories, especially when the person in the story is a legendary mathematician. It is as if my mediocrity is afraid of their excellence.<p>Maybe this is why we have so few Terry Taos and Ed Wittens, idolatry aside, there is a kind of fear that lurks inside of most people. Realising which the average joe distances himself more instead of striving to attain his full potential.