What is wrong with the way most of us are introduced to math?
The way mathematics is taught is akin to an art class in which students are only taught how to paint a fence and are never shown the paintings of the great masters. When, later on in life, the subject of mathematics comes up, most people wave their hands and say, “Oh no, I don’t want to hear about this, I was so bad at math.” What they are really saying is, “I was bad at painting the fence.”
So what is it really like to be a mathematician?
You don’t discover something beautiful every day. Most of the time, you work on something for weeks or months, only to realize that it doesn’t work. But you never give up, you go back and try to analyze the data that you have, and try to see the analogies and connections to try to come up with a new hypothesis. Then you try to test that.
What is the ultimate goal of all these efforts?
Another analogy is solving a jigsaw puzzle. Imagine that somebody gives you a puzzle, but they don’t give you the box, just the pieces. You take those different pieces and try to put them together to create something of value, something beautiful and powerful. You can think of mathematics as the grand project of building this enormous jigsaw puzzle, with different groups of people working on different parts. Then, every once in a while, somebody finds a bridge between two parts, a way to assemble pieces together so that big chunks of the puzzle connect.