My brother was a mathematical protege. You know those kids who teach themselves to read as babies, and by the time anyone thinks to ask them to look at a letter flash card they’re already reading chapter books? He was the mathematical equivalent. He looked at problems and just knew what the answer was. Sometime in elementary school he took at IQ test (a real one, administered by trained professionals) and scored perfect on the math section. Meanwhile, I remember math as the only subject in elementary school I was bad at (it wasn’t- I also struggled with whatever foreign language they pretended to teach us that year. But it was the only subject I was bad at that my parents cared about).
By age 18, I had finished three semesters of calculus and another of differential equations at community college, and I went on to take more when I matriculated at college for real. I was very into computational biology, which involves very high level calculus. My brother got to pre-calc, maybe calculus, at high school, and never took any in college. His first stumbling block was teachers that marked him off for not showing his work, even though his answer was correct. They never understood that for him, there was no intermediate step. The second stumbling block was when he met problems hard enough he stopped seeing the answer. When I faced the same level of problems, I had toolkit of how to approach problems and derive answers, painfully derived from all the other, easier problems I’d seen but couldn’t solve. He had nothing. And so I eventually went much further in math. Originally it was just because my parents insisted on a math class every semester and I wasn’t going to rock the not-going-to-high-school boat, but I eventually came to enjoy it because it was so easy and everyone else found it so hard. I got a severe case of mono while taking differential equations and still got an A+, because the class simply wasn’t hard enough to measure the change.
I saw a miniature version of this playing Portal 2 with a friend (we were playing co-op after we’d each finished the individual campaign). At lower levels he saw the solution before I’d even oriented myself in the room. At higher levels he’d sit there stuck while I said things like “that’s the only piece of portalable wall, and clearly we need to use that wall paint for something, so let’s portal the paint over to there and see what happens.” Translation for those of you who haven’t played Portal: we have a bunch of parts, they can only connect in so many ways, let’s connect some likely looking ones and see what presents itself.
I have several points I want to make about this. First, I think we as a society tend to conflate the following: initial skill at a subject, speed of learning a subject, ceiling of ability in a subject. My brother’s and friend’s initial abilities were higher than mine, but their ceilings appeared to be lower, in part because my initial skill level led me to develop skills we weren’t directly measuring.
The second one is more personal, more speculative, and will require more stories. In a nutshell, I think math was the only thing I ever learned how to learn.
I mentioned I also struggled with languages. When I struggled with math my parents put me down and painstakingly walked me through my homework until I got it right. When I struggled with Spanish they said “yup, foreign languages are hard.” I loved and love reading and writing, but when I started to get graded for them, and felt the grades were more about ability to fit the teacher’s conceptions than anything I enjoyed about reading or writing, I swore off all but the most mandatory English classes, and more generally anything “subjective.” I fell in love with behavioral biology at age 12 and took a staggering number of mandatory prerequisites in order to pursue it (seven semesters of chemistry, two of physics, plus all the biology you have to take before they let you get to behavioral*.) But I don’t feel like I ever mastered any of the parts except those I was interested in. I have this nasty tendency to just skim textbooks and fill in the complicated parts from context. This worked way better than it has any right to- I graduated cum laude from Cornell University with a double major in computer science and biology- but not well enough. I could have done better. Not necessarily on anything Cornell was measuring, but better nonetheless.
I was originally considering math for my second major at Cornell. That died my first semester, when I was suddenly taught theory by people hired for their research rather than applications taught by people hired for their teaching. Suddenly class was nothing but proofs, and I hated them. Except that my eventual second major, computer science, also required proofs. I hated them there too, for one semester, but they started to grow on me the second, and I went on to take multiple 600 level theory classes. I loved the little logic puzzles.
I’ve been scared about nursing school because it’s a lot of physiology, which I did everything I could to avoid when I was studying biology. I know I find it more interesting now than I did then, but that’s because everything I’ve done since is researching my own medical problems, at my own pace. How will I handle having to learn what other people tell me to, on a timetable they set?
My first solution was a combination of denial, Trying Really Hard, and cramming all the knowledge I could into my head ahead of time. This was not going to work. But this kind of learning is a learnable skill, and that skill is something I can learn ahead of of time.