Hi,
Today I’d like to tell you about the time I decided I wasn’t good enough to be a mathematician.
I was always pretty good at math. How good? It’s hard to say. But in 7th grade I joined an accelerated math program. We finished the usual 5 years of high school math in 3 years, and then we all started taking standard university math classes together as a group. Everyone else in the program started in 8th grade, so I was a year younger than the other students.
For context, this was in Israel, so the math curriculum was rather more advanced than in the US. And the classes we eventually took at university were math for mathematicians: building up everything from basic axioms.
I always did pretty well, and I thought I was doing pretty well, until two things happened. First, we were joined by a new student who was years ahead of the rest of us: I’d find a proof that took 20 steps, and he’d come up a with simpler proof in just 4 steps. I couldn’t figure out how he did it.
A year or two later I also started having trouble keeping everything in my head. By that point I was almost up to 20th-century math, and there was lots of background material: solutions could involve math I’d learned three years before. I’d started forgetting things that far back, so I had an increasingly hard time keeping up.
I concluded that while I was, obviously, better than average at math, I wasn’t good enough to be a mathematician. And that was OK, I wasn’t really interested in becoming one. More broadly, I believed that mathematical ability was a talent: some have more, some have less.
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These days, I’m not so sure: I tend to think “natural talent” has much less to do with ability than things like practice and motivation.
Let’s consider my story a different way: I wasn’t interested in being a mathematician, and much of my time was spent doing other things. I was going to high school, nominally studying other subjects, and later I was also taking computer science classes at university. I was also working as a programmer, admittedly not a very good one.
If I’d wanted to be a mathematician, I might have done things differently. I would have spent much more of my intellectual capacity focusing on learning math, instead of all the other things I did. When I’d forgotten old material I would have reviewed it. If I’d not found the simplest proof I would have taken the time to understand it, and then practiced applying that new technique.
But I didn’t do any of this; I did my homework, and that’s it. So was the problem lack of talent, or lack of motivation and therefore lack of effort?
More generally: I believe you can learn almost anything you want to. I don’t mean you can learn anything easily: depending on what it is, it may take years of effort, and of practicing the right way. Learning from the best teachers will certainly speed things up, and you will have an easier time getting started on some skills than on others. But it can be done.
For more details I recommend the book Peak: Secrets from the New Science of Expertise, by Anders Ericsson and Robert Pool; your local library likely has a copy. Ericsson is a psychologist who has spent decades studying expertise: how one becomes an expert. If you’ve heard of “deliberate practice” then that is a concept that came out of his research. For some of the practical implications of this research, as applied to programming, watch Kathy Sierra’s talk Making Badass Developers.
Don’t make my mistake: don’t be taken in by the myth of talent. Practice the right way, and you will be able to learn whatever you wish to. Eventually.
Until next time,
-Itamar
Every week I write an email explaining one of my mistakes—as a programmer, as an employee, sometimes just as a person—and what you can learn from it. I’ve been writing software for more than 20 years, so there’s plenty of past mistakes, and of course I keep making new ones.
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