Ideas from books, articles & podcasts.
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).
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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 long after I officially became one.
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 gr...
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 ...
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 long after I officially became one. My earliest memory of anything like a mathematical idea comes f...
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How do Eureka moments happen? They do feel contingent & magical, arising in consciousness on their own. But looking at the history of breakthrough ideas there seem to be a rough 2-phase process:
Ideas come to us when we have a specific problem but we do not focus on solving the problem directly.
It’s not at all obvious how to go about thinking up some new twist on these things. A new idea can feel like a remarkable discovery
There is a lot of math behind how the Golden Ratio is calculated. But designers, artists, and photographers aren’t usually high-level mathematicians. To benefit the algebraically disinclined, let’s keep it simple.
The Ratio is approximately 1.618 to 1. It’s approximate bec...
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