I was introduced to this reality quite early, when I was invited to our national mathematics summer school (at a younger age than most of the group), where I met the brilliant Terry Tao as a nine year old. I didn't know he would one day be regarded as the GOAT mathematician, so believing that he represented the bar I had to reach (and underestimating myself as my achievements were solely from my own efforts), I reassessed my ambitions to become a maths academic and allowed my parents to usher me into a different career pathway.
That is quite the story! I think something similar did happen to me, although at a much lower level. I thought a gifted math student should be able to clear the national mathematics Olympiad with zero coaching. I barely studied for it specifically, and hoped my intuition would carry me through. I was 14 and could only do 1.5 problems out of 6.
i) Every individual is the best judge of his/her success.
What about when your very own judgment of success tells you you haven't succeeded? I feel like being told all my life I had potential -- the Olympiad coach said I could make it to the IMO although I didn't quite believe him, etc. -- makes it hard for me to appreciate small wins which "anyone can do" when I do them in a fraction of the time or effort. But there is this gulf between being say a data analyst and a mathematician which is as wide as the ocean, and I may know that the latter is out of reach, for example. I say this having seen mathematicians up close -- the good ones could grok the entire data science syllabus in a week. They were studying graduate level math in their second year of college.
ii) Productive work, 'making a difference', should be highly valued, perhaps even more than being at the top of a field if you've had to climb on a lot of people to reach the top.
Also, I don't feel like I'm making a difference, or ever will. Being in the corporate world is generally like being a small replaceable cog in a giant contraption which will move forward with or without you.
iii) If you teach and mentor others, you can enjoy their successes as yours too.
I feel like everyone's talent is their own, and teaching only seems to make a difference of about 20% at most. The rest is on the student. I see this quite clearly, over and over again. So, it feels like a stretch to take credit for a student's achievement because I know it's mostly on them. This again derives from personal experience -- people think I must have had a great educational background, but for the most part I had zero enrichment outside of class, and still somehow managed to stumble into a top rated math program. 99% of people could not do that even with years of instruction given what I now know about IQ.
Edit: I did study for it. It's just that the questions were direct applications of principles I knew such as Euler's equation or Vieta's relations etc. where a smart student could come up with a solution without specific training, and I lucked out that day.
