Thank you, let's see. One part is probably that I was brought up to admire great scientists—my dad gave me popular science books by Stephen Hawking ("The Universe in a Nutshell" in particular) at a young age, and some Feynman books, and such. (I remember "Black Holes, Wormholes, and Time Machines" by Jim al-Khalili from the library.) For a long time I figured I should become such a scientist myself.
Another is probably high self-opinion and wanting to prove I was the best. In elementary school, I entered the chess club; there was a five-week tournament (one game per week), and I studied chess books my mom gave me and by the end of the tournament was the strongest player in the school. (I only tied for first place in that tournament, but I had improved enough by the end that I believe I won all subsequent rematches against the guy I lost my first game to.) Upon entering middle school, I took a Mathcounts test to determine who would be on the school team, and I got the highest score in the school (which was actually kind of a fluke, because I had a friend who generally outperformed me at arithmetic-based contests and did so at the actual Mathcounts events—but I tended to beat him at proof contests later on). I did lots of math contests, and generally did "rather well". The pinnacle of that was qualifying for the math olympiad camp in 9th grade, from which the U.S. International Math Olympiad team is selected (although people below 12th grade have a lower bar, and aren't in the running for the team unless they've met the higher bar; my achievement isn't that impressive). So my self-opinion had some justification.
Regarding calculus textbooks, in the summer after 7th grade I went to one of my sisters and said, "You know, I've heard of this thing called calculus, but I don't know what it is"; she gave me my oldest sister's calculus textbook (Ostebee and Zorn), and I read through chapters, and did problems out of the the chapters until I figured I understood it, and moved onto the next chapter. (I didn't go through all the chapters—towards the end it did multidimensional stuff that just got boring.) With this as my sole calculus education, I later chose to take a calculus round of a math contest, and got a "decent" score (IIRC it might have been in the top 10%). :-)
So, for quite a long time, I wasn't actually sure that I'd ever met anyone who was smarter than me. (My abovementioned friend was certainly close, and was better at some things.) At the math olympiad camp, I did meet people who were clearly significantly better than me at math contests. I figured that a certain amount of that was due to drilling, which was something I didn't do (I mean, I went to math club and did whatever they put in front of me, but I didn't practice contests at home), which gave me a way to suspect that I might still be at least as smart as them. :-) I knew this was a self-serving line of thought, but I figured that, as long as I knew it was specious, it was harmless to indulge it and let it motivate me. I think Colin Percival is the clearest example of someone reasonably close to my age that I'd have to bow down to. (Though even then, if my education had been properly arranged, instead of wasting most of my K-10 years... Well, that is an experiment I hope to carry out multiple times in the next generation.)
The olympiad camp actually gave worksheets that they recommended we do throughout the year. I did not want to pursue that, or pure math in general (although I thought I was good, I didn't think I had a good chance of, say, proving the Riemann hypothesis, and anything less than that didn't seem worth it), and refocused on computer science. (I also had discovered Paul Graham's essays around 8th grade, Scheme in 9th grade, and took an AP CS class in 10th grade, whose curriculum included SICP—yeah, that teacher was pretty cool.) After leaving school, I did over 100 Project Euler problems, and did other "programming for math" stuff, although I drifted towards pure programming stuff (implementing languages, specifically).
Now, don't get me wrong. I'm not some kind of work-maniac like Isaac Newton. I've spent plenty of time playing computer games, and still do. But I have some reflexes that have served me well. (1) Whatever you're doing, do it well. If you're doing it well, see if you can do it even better. (2) Keep an eye out for opportunities to practice your skills. When I got irritated at repetitive Youtube comments, I used curl/egrep/sed/sort/uniq to count how many of them matched a particular format. When I felt frustrated about limitations in EV Nova or Civilization II or other games, I did some work towards reimplementing them myself—which, in the case of EV Nova, led me down a rabbit hole of researching real-time garbage collection, which occupied my productive efforts for some years. When I set an alarm clock, it is a shell command of the following form:
~> sleep (math "3600 * 8 - 600"); pelimusa
where "pelimusa" is a command that sets the computer volume (in case I muted it) and then plays a song[1] in a loop until I control-C it. (3) You
should know how to do everything. If there's something you don't know how to do, it should irritate you a little or hurt your pride. (4) Don't do unnecessarily stupid things. Being smart means you can do
very stupid things (which other people wouldn't even try, or think to try), and if this actually leads you to cause permanent damage to yourself or other terrible outcomes, then you really weren't smart in the ways that mattered, which is unacceptable.
I was in the weeds of implementing my idealized real-time GC in x64 assembly (which may have been a bad idea, but I had my reasons, and I didn't have anyone whose opinion I trusted advising me against it; at least I learned a lot), and eventually my family started putting pressure on me to start earning money. So I did. I got a referral to Google—which turned me down, by the way, which... lowered my opinion of them :-P—and then to a few other places. I've been working at a medium-sized Silicon Valley tech company since then.
Today, in my job, the things that motivate me are pride, curiosity, and lolz. Pride could be summarized as proving to myself that I'm the best (however I might choose to define it), and that those who have invested in me made the right choice. Curiosity is self-explanatory. Lolz is when I use absurd means (like overwriting executables in /usr, or piping "yes" into installation programs, or running "kill -STOP; kill -CONT" in a loop to slow down a program) because they're actually a very effective and quick path to what I want.
Beyond my job, I want to fix things for future generations, perhaps to prove that I'm right that there was a better way. John Holt tried to reform school, ran into the cancer (as well as the astonishingly common view that children are no damn good), and concluded you had to work outside school. Seems about right to me.
Civilization II has taught me that exponential growth is the most powerful strategy ever. If I can create several people like me, each of whom creates several more, and so on, then that can achieve a lot more than I might do myself. (I am being 70% serious.) Even if they're not as smart, raising them properly (i.e. no goddamn school, plus find them some cognitive peers, and generally have an intellectually rich household) may more than make up for that: the improved education and non-isolation (my social development was certainly hampered by growing up 99% around kids I couldn't relate to, which may have made the difference in my squandering some opportunities) and possibly improved motivation (having 6+ hours a day forcibly wasted is very demotivating). In the worst case, they'll still carry my genes and can try again with the next generation.
I encourage smart and motivated people to try this too. At some point we may figure out how to directly increase intelligence (that would be one of the projects I would hope a kid of mine tackles); for now, the most obviously workable approach is to find a suitable genius (with no severe mental health or personality issues) who is willing to give you their genetic material. That may take the form of marrying them, if you're lucky. Once you have the kids (plural; one of the easiest ways to have peers is to have them at home, although you can't guarantee they'll be friends), the default approach of unschooling seems best: buy good books and intellectually stimulating toys, help them meet friends, maybe experiment with 1:1 tutoring if you have the resources and they like it, support them in activities they seem interested in, but fundamentally just make sure they are fed and watered and loved, and trust to their natural curiosity and to luck. (There is going to be a large luck component. Another reason to have multiple kids.)
[1] https://www.youtube.com/watch?v=XKs5mkEpWuU