The Joy Of X: A Guided Tour of Math, from One to Infinity

by Steven H. Strogatz

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.

math always involves both invention and discovery: we invent the concepts but discover their consequences. As we’ll see in the coming chapters, in mathematics our freedom lies in the questions we ask—and in how we pursue them—but not in the answers awaiting us.

The silver lining is that even wrong answers can be educational . . . as long as you realize they’re wrong.

Mathematicians and conspiracy theorists have this much in common: we’re suspicious of coincidences—especially convenient ones. There are no accidents. Things happen for a reason. While this mindset may be just a touch paranoid when applied to real life, it’s a perfectly sane way to think about math.

Whenever a state of featureless equilibrium loses stability—for whatever reason, and by whatever physical, biological, or chemical process—the pattern that appears first is a sine wave, or a combination of them.