The Myth and Magic of Generating New Ideas

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 whe...

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 puzzli...

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...

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!...

Ten or so years later, when I was a college freshman, I would learn that I had stumbled upon an instance of what is called an abundant number, a phenomenon first studied by the ancient Greeks. ...

As odd as it might sound, I've never been particularly confident of my mathematical abilities. I don't mean the arithmetic part, the part that people usually associate with being a mathematicia...

Mathematical objects are big ideas about algebra, geometry, and logic, about the properties and definitions of numbers. It's not at all obvious how to go about thinking up some new twist on the...

Where do ideas come from? That’s a big question. Here’s a smaller one: Where do mathematical ideas come from? I’ve wondered about this from the time I first contemplated being a mathematici...

Where do ideas come from? That’s a big question. Here’s a smaller one: Where do mathematical ideas come from? I’ve wondered about this from the time I first contemplated being a mathematician until...

 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 ...

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...

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 ...