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.

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.

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 a great post, and I think you often tend to see that kind of humility in top competitors -- especially athletes. I remember a guy in my social circle back at UCLA was an Olympic discus thrower: extremely talented, hard-working, gifted, and intimidating. One of the most humble, respectful, and down-to-earth people. He spoke with great reverence of the sport and his competitors and teammates. My sister's boyfriend was an Olympic-level swimmer and he has the same exact attitude.

From my own experience playing Counter-Strike at world-class levels, I found that, generally speaking, the best players were the most humble and down-to-earth; the ones that talked shit were not only bad teammates, but sub-par players in general. These days, I'm much better than the average Joe at first-person-shooters, but I always point out that I'm actually pretty bad: I'd get easily beaten even by mid-tier semi-pro teams. Interestingly, this is a side-effect of our human brain not quite grasping exponential growth (or log scales). Going from the 95th to the 96th percentile is much harder than going from the 50th to the 85th.

On the other hand I've just been watching the last dance on Netflix and Jordan talked shit non-stop :)

Hah, when you're the 1% of the 1%, you might be allowed to do that ;)

Not when he started.

Why do you think this correlation between top-tier skill and humility exists?

I'd say there's several factors working in the same direction

At the very top levels, everyone has very close to the same level of preparation in terms of physical training, equipment, and mental preparation. A lot of the result comes down to your mental edge on a particular day, and some luck. The mental edge is the most fickle and difficult part of the skill set, yet it is virtually everything at the top. So, everyone recognizes that they may have an on or an off day.

Recognition that just in general, a position at the top is fragile, and it is not about your previous result, but your next result, which is uncertain.

Recognition that your competitors are also extremely good and prepared, and respect for them also leads to humility.

Then, even if they've got multiple world championship seasons under their belt, they see the context of the other greats in their sport (or similar in their field).

The post-qualifying and post-race interviews in Formula 1 auto racing often provide great examples. The top qualifiers will almost always say something like: "we qualified well, we think we're prepared, and hope for a good result tomorrow.". And after winning the race, it's about the team effort and the way things fell into place to make the win. I can't recall hearing anything resembling trash-talk in that environment.

I think that those highly skilled communities tend to be very small and very tight-knit. So there's quite a bit of self-selection that happens: no one wants to train with someone that constantly talks trash or complains.

Is it even possible to achieve top-tier skill without humility? To improve in the skill, you first need to know and accept that there is an improvement to be had, i.e. that you haven't already mastered it.

It may be that those who would trash talk or incessantly complain aren't focusing as much on how they can improve their performance?

I think our system has to stop this. Instead of appraisals that indicate fake proficiency, if they truly wanted to encourage, they could show the next higher level and gently ask us to pursue the path until we are bored. Instead they slam the top students with not just the title 'genius', but also the burden and self-doubt that comes along with it -- which only amplifies later as we move up the ladder.

I agree. Once, I read a piece that alleged "you're not a true intellectual until you've contributed an original thought to the existing paradigm". No one at school had ever said anything of the sort; as we all knew, true intellectuals got incredible grades and were lauded by the system as genius PhDs.

I don't know how to stop these appraisals of fake proficiency without dismantling the entire school system. There are so many students today that feel the burden of "being smart" and strive to prove it to everyone who's watching, who don't realize that they're not actually that smart, and that most people who are watching don't particularly care.

That last paragraph hits home. I was always ‘good at school’ (even though I spent a lot of effort studying to maintain that status), up until I got to my PhD program and I couldn’t just ‘regurgitate simple models’ and succeed anymore. I got my PhD in the end, but I’m not as successful as many of my peers have been. Acceptance that I am not an elite scientist and committing to the work anyways was the thing I learned in grad school that has helped me in industry so far.

Obtaining a PhD seems like the academic equivalent of growing and harvesting a crop, or creating a profitable business. It's so insane that students can make it all the way to hundreds of thousands of dollars in debt and dozens of years of hard study before anyone actually requires them to produce something original that yields additional value.

Well you have to learn the skills to produce the cash crop.. that's what takes a long time. The adage that overnight success takes 10 years. Well that applies to everyone, including academics.

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.

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.

similarly, I was able to go through k-8 with no effort outside of paying attention during class. high school was more or less the same, not to mention interests can easily wander during those years. in college I quickly discovered I could get more or less straight Bs with almost zero effort and figured the effort needed for the last 1 point in GPA was far too "expensive" relative to the first 3 so I coasted.

never having explicitly failed during those years ill admit my level of "grit" is lacking. after a decade and variety of circumstances i sit here, mid 30s, saddled with a ton of student debt and no career. in the grand scheme i have definitely failed; if this reckoning point (realization) had been reached as early as mr. tao perhaps there would be time to turn things around.

If you turn the boat around in the next 5 years, you will hopefully have another 30 years of a flourishing career, more than the entire career of some prodigies who perished young. This assumes a projected retirement of 70 years old. What is particularly exciting is that new industries are starting to form, and any one of us can be pioneers in those industries (fintech, VR, AR, AI, automated vehicles, drones, robotic process automation, Edge Cloud, etc...).

Your comment and the parent's comment both resonated with me, as someone who also finds himself "stuck".

What do you suggest that someone do in this situation--one where they want to reset their career, carve out a new one, etc.?

I'm in the same boat (except I wasn't "stuck," I was climbing, but I wanted to do something else), and my post articulates logic that I am using myself :) I recently cold-messaged someone in a startup in one of those industries, and they were surprisingly willing to carve out an opportunity for me. He's the person who would be my boss and just needs to get approval from the CEO. Even if that doesn't work out, I've learned the following lesson in various ways over the past few months: just applying to jobs isn't enough if you don't have specific applicable experience. That should be common sense, but somehow I had fooled myself into thinking otherwise before. Career switching is a complete grind. That's why it's so important to join a growing industry, do great work, and hopefully never have to switch again.

I welcome comments from someone who successfully reset their career after at least 5-10 years of working.

Thanks for the response. The story about cold-emailing your future boss (hopefully!) is very cool.

And I agree completely regarding applying to jobs. I've sent out some applications recently but it feels like I'm sending them into a black hole of complete radio silence. Part of me thinks that I should go back to school to do a complete career reset, but my academic performance was abysmal during undergrad...lots to think about! Thanks again for the response.

same - done with applying. has only consumed a massive amount of time with no results. perhaps im just from the island of misfit candidates but shifting focus for now to work on a reset as you mention. feel like im just too stale to continue that path. diving into perhaps some of the things @keenmaster mentioned, perhaps working on some certifications. either way, opportunity ebbs and flows (imo) just need to be better prepared to take advantage.

best regards to both of you (and anyone else reading feeling similar circumstances).

thank you for the perspective and you're right (imo) - survive and adapt. your suggestions sound like a great starting point.

This was my experience as well. When I see geniuses that coast through everything thrown at them, I wonder if I have any advantage over them in the future, having struggled before, or they're just so smart that nothing touches them.

I'm sure it depends on the challenge. Most folks that I'd consider geniuses just relentlessly pursue the things they're interested in. Depending on the topic, this gives them enough ability to get by the basic concepts tested in school. And then later in life, a good career if they're lucky (definitely lucked out being interested in computers).

I think these people are still working hard in a sense, they just have a low tolerance for work that doesn't interest them.

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.

If we live long enough, we all find our limits. Learning to work within those limits and succeed in spite of them seems like one of the great leveling-ups of life.

Strictly speaking, I don't think that's true if you're the smartest person in the world.

John von Neumann springs to mind, who did his mathematics PhD at the same time as his chemical engineering degree, with a friend of his commenting that Evidently a Ph.D. thesis and examination did not constitute an appreciable effort. [0]

To my knowledge he never really failed at any of his intellectual pursuits, but I could be mistaken.

[0] https://en.wikipedia.org/wiki/John_von_Neumann#University_st...

Well said

You had multivariable calculus in high school? Was it some kind of special programme?

It was an advanced class for kids who'd done single-variable calculus early.

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.

[1] https://www.maa.org/sites/default/files/pdf/ebooks/pdf/Livin...

Here’s the summary that Tao wrote at the time, for future Princeton grad students: https://web.math.princeton.edu/generals/tao_terence

Other students: https://web.math.princeton.edu/generals/

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.

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.