Mathematician David Bessis has written a book about what we do when we do mathematics. It’s one of the best books I’ve read recently. One the second page, Bessis writes,
“I have no special talent. I am only passionately curious.” When I was fifteen, I hated this quote from Einstein. To me it sounded phony, insincere, like a supermodel saying that what really counts is inner beauty. Do we really need to hear this stuff? The main message of this book, however, is to take Einstein’s words seriously.
I’m not a mathematician, but even so what Bessis writes aligns with my experience. He argues that the brains of great mathematicians aren’t different from ours. Like for other activities, natural aptitude like intelligence plays a role, but not as much as people assume. Instead, mathematics is a skill like others in that it can be acquired. The difference is that unlike other skills, mathematics can’t be learned by imitating others, since it’s a purely mental skill. Reading math textbooks isn’t helpful because, at least for the novice, they don’t convey the thinking behind the notation.
Mathematics is an intuitive activity. When we learn math, we train our intuitions. Logic doesn’t help doing math, but it helps grounding our intuition and figuring our when it went wrong. Bessis, tongue-in-cheek, calls this system 3, contrasting it with systems 1 and 2 as defined by Daniel Kahneman.
System 3 is an assortment of introspection and meditation techniques aimed at establishing a dialogue between intuition and rationality […] when I got in the habit of lending an ear to the dissonance between my intuition and logic, I put system 3 at the center of my strategy for learning math.
Bessis’ book, while it’s about mathematics, is applicable to all of thinking, or at least all of scientific thinking. It’s a kind of book that, maybe for the first time, accessibly defines what mathematics really is. It may also, if read by 14 or 16-year-olds, give them a better start in mathematics than any amount of tuition could.
Bessis’ blog can be found here.
Nehaveigur 