8 Quotes by Steven H. Strogatz

Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy -- it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.

Simulation is no substitute for math – it could never provide a proof – but if Peskin’s conjecture was false, this approach would save me a lot of time by revealing a counterexample. This sort of evidence is extremely valuable in math. When you’re trying to prove something, it helps to know it’s true. That gives you the confidence you need to keep searching for a rigorous proof. Programming.

Those of us who teach math should try to turn this bug into a feature. We should be up front about the fact that word problems force us to make simplifying assumptions. That’s a valuable skill – it’s called mathematical modeling.

When a guitar string is plucked or when children jiggle a jump rope, the shape that appears is a sine wave. The ripples on a pond, the ridges of sand dunes, the stripes of a zebra – all are manifestations of nature’s most basic mechanism of pattern formation: the emergence of sinusoidal structure from a background of bland uniformity.

To shed light on any continuous shape, object, motion, process, or phenomenon – no matter how wild and complicated it may appear – reimagine it as an infinite series of simpler parts, analyze those, and then add the results back together to make sense of the original whole.

To grasp how different a million is from a billion, think about it like this: A million seconds is a little under two weeks; a billion seconds is about thirty-two years.

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And because the PageRanks are defined as proportions, they have to add up to 1 when summed over the whole network. This conservation law suggests another, perhaps more palpable, way to visualize PageRank. Picture it as a fluid, a watery substance that flows through the network, draining away from bad pages and pooling at good ones. The algorithm seeks to determine how this fluid distributes itself across the network in the long run.