1. "It's a curious thing about human psychology that if you don't have the right mental framework, you sometimes can't see what's right in front of your face."

Steven H. Strogatz, Chaos
2. "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."

Steven H. Strogatz, The Joy of x: A Guided Tour of Math
3. "let’s begin with the word vector. It comes from the Latin root vehere, to carry, which also gives us words like vehicle and conveyor belt. To an epidemiologist, a vector is the carrier of a pathogen, like the mosquito that conveys malaria to your bloodstream. To a mathematician, a vector (at least in its simplest form) is a step that carries you from one place to another."

Steven H. Strogatz, The Joy of x: A Guided Tour of Math
4. "In the early part of the ninth century, Muhammad ibn Musa alKhwarizmi, a mathematician working in Baghdad, wrote a seminal textbook in which he highlighted the usefulness of restoring a quantity being subtracted (like 2, above) by adding it to the other side of an equation. He called this process aljabr (Arabic for restoring), which later morphed into algebra. Then, long after his death, he hit the etymological jackpot again. His own name, alKhwarizmi, lives on today in the word algorithm."

Steven H. Strogatz, The Joy of x: A Guided Tour of Math
5. "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."

Steven H. Strogatz, The Joy of x: A Guided Tour of Math
6. "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."

Steven H. Strogatz, The Joy of x: A Guided Tour of Math
7. "(Actually, languages can be very tricky in this respect. The eminent linguistic philosopher J. L. Austin of Oxford once gave a lecture in which he asserted that there are many languages in which a double negative makes a positive but none in which a double positive makes a negative—to which the Columbia philosopher Sidney Morgenbesser, sitting in the audience, sarcastically replied, Yeah, yeah."

Steven H. Strogatz, The Joy of x: A Guided Tour of Math
8. "Nature—cue the theme from The Twilight Zone—somehow knows calculus."

Steven H. Strogatz, The Joy of x: A Guided Tour of Math
9. "I have a friend who gets a tremendous kick out of science, even though he’s an artist."

Steven H. Strogatz, The Joy of x: A Guided Tour of Math
10. "Yet in another way, calculus is fundamentally naive, almost childish in its optimism. Experience teaches us that change can be sudden, discontinuous, and wrenching. Calculus draws its power by refusing to see that. It insists on a world without accidents, where one thing leads logically to another. Give me the initial conditions and the law of motion, and with calculus I can predict the future  or better yet, reconstruct the past. I wish I could do that now."

Steven H. Strogatz, The Calculus of Friendship: What a Teacher and a Student Learned about Life While Corresponding about Math