Intellectual Trespassing book recommendations
1. What Are the Arts and Sciences?: A Guide for the Curious by Dan Rockmore
Mathematics is many things. All of you have worked with numbers and played with shapes — and I hope you have enjoyed those activities! When you are adding, subtracting, multiplying, and even dividing (!) numbers, you are using mathematics. When you are confronted with shapes and try to describe them, you are thinking about mathematics. When you are glimpsing and wondering and seeing patterns in your playing and working with numbers and shapes, you are doing mathematics.
You see, mathematics is more than just working out lots of particular problems and getting good at arithmetic or recognizing shapes. Mathematics as a subject studies numbers and shapes like they were animals in the jungle or stars in the sky. Numbers can relate to one another in the same way animals relate to one another in the wild or astronomical objects relate to each other in space. Numbers have patterns of behavior and obey laws. Shapes have properties that distinguish them from one another in the way that a salamander is different from a newt or a frog (even though they are all amphibians) or the way that a planet is different from a comet that is different from a meteor that is different from a star. To “do mathematics” is to study these mathematical “things” and all of their properties and relationships.
2. The Poetry and Music of Science: Comparing Creativity in Science and Art by Tom McLeish
Related:
My earliest memory of anything like a mathematical idea comes from a childhood walk with my dad. We left the house and made our way toward downtown Metuchen, the tiny town in central Jersey where I grew up, to a little luncheonette called the Corner Confectionery. I can still picture it: the rack of newspapers, magazines, and comic books; the ice-cream treats in the back corner; the long counter with stools, where I used to sit and spin until I was told to stop. It was about a mile-long walk, reserved for special occasions. On that bright fall morning, we strolled up Spring Street — a beautiful street lined with huge oak trees — and talked about fractions, though I wouldn’t have known to call them that. We were puzzling over — or, rather, I was puzzling over — how to fairly divide a pie (probably one of the Corner Confectionery’s apple pies). My dad, a mathematical physicist, a man with an active mind, but one of few words, was a gentle guide, letting me think through things on my own.
We took our time walking, and we also took our time thinking and talking about the basic properties of numbers. In my head, it was easy to cut the pie in half, and then in half again, and again: two, four, or eight pieces. But, somewhere near Main Street, I got stuck on how to reliably create three, five, or six pieces. I started thinking about making bigger numbers out of smaller numbers. This leisurely walk through the neighborhood soon led me to the exciting idea that twelve was a great number. Twelve could be divided by one, two, three, four, and six. That’s a lot of numbers! If I had a pie cut into twelve pieces, it would be easy to divvy up dessert for many different-sized groups of friends. By the time we crossed the railroad tracks and arrived at the door of the Confectionery, I thought that I had made a remarkable discovery: Everyone! Stop! We need to think about the world in terms of twelves!
— A mathematician on how to get the mind into motion.