Crazy as it sounds, over the next several weeks I'm going to try to do something close to that. I'll be writing about the elements of mathematics, from pre-school to grad school, for anyone out there who'd like to have a second chance at the subject -- but this time from an adult perspective. It's not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it's so enthralling to those who get it. ... The creative process here is the same as the one that gave us numbers in the first place. Just as numbers are a shortcut for counting by ones, addition is a shortcut for counting by any amount. This is how mathematics grows. The right abstraction leads to new insight, and new power. ... Yet despite this infinite vista, there are always constraints on our creativity. We can decide what we mean by things like 6 and +, but once we do, the results of equations like 6 + 6 are beyond our control. In mathematics, we'll see in the coming weeks, our freedom lies in the questions we ask -- and in how we pursue them -- but not in the answers awaiting us.
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The creative process here is the same as the one that gave us numbers in the first place. Just as numbers are a shortcut for counting by ones, addition is a shortcut for counting by any amount. This is how mathematics grows. The right abstraction leads to new insight, and new power.
Yet despite this infinite vista, there are always constraints on our creativity. We can decide what we mean by things like 6 and +, but once we do, the results of equations like 6 + 6 are beyond our control. In mathematics, we'll see in the coming weeks, our freedom lies in the questions we ask -- and in how we pursue them -- but not in the answers awaiting us.
