Here’s how to become a math whiz:
Keep working on your problem set after you get stuck.
Don’t just sit and stare at it: think hard; until you’re exhausted; then come back the next day and try again. This will be uncomfortable, but that discomfort is the feeling of your brain stretching to accommodate new abilities.
This advice came to mind recently when I received an e-mail from a high school senior. “Yesterday, I was accepted to MIT,” he began. “I’m ecstatic, but on the other hand, I’m a little nervous…I was hoping you could give me some tips.”
I explained that I had been studying theoretical computer science and mathematics at a high-level for the past decade, much of it spent right here at MIT. Over these years, one conclusion has become increasingly clear: the more hard focus you dedicate to a technical subject — be it computer science, chemistry, or physics — the better you get.
Junior graduate students think senior graduate students are smarter, but they’re not: they simply have more practice.
Senior graduate students think junior professors are smarter, but they’re not: they simply have more practice.
And so on.
When I arrived at Dartmouth, to name another example, I didn’t consider myself good at math. I had taken AB calculus during high school (not BC), and had scored a 4 on the AP exam (not a 5). By my sophomore year of college, however, I had made a name for myself by snagging the highest grade out of 70 students in an advanced discrete mathematics class. What happened in between? A lot of hard focus.
Eventually, this all becomes clear, but for an incoming freshman, it’s not intuitive. When you struggle with a calculus problem set while a classmate knocks it out in an hour, it’s easy to start to thinking that you’re just not a “math person.”
But this isn’t about natural aptitude, it’s about practice. That other student has more practice. You can catch-up, but you have to put in the hours, which brings me back to my original advice: keep working even after you get stuck.
That’s where you make up ground.