How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

Without the rigorous structure that math provides, common sense can lead you astray.

formal mathematics without common sense—without the constant interplay between abstract reasoning and our intuitions about quantity, time, space, motion, behavior, and uncertainty—would just be a sterile exercise in rule-following and bookkeeping.

as long as you believe there’s such a thing as too much welfare state and such a thing as too little, you know the linear picture is wrong.

Nonlinear thinking means which way you should go depends on where you already are.

When Reagan cut taxes after he was elected, the result was less tax revenue, not more.

government’s diminished ability to spend means it constructs less infrastructure, regulates fraud less stringently, and generally does less of the work that enables free enterprise to thrive.

Improbable things happen a lot.

what is improbable is probable.”

“I had failed as a writer because I had nothing important to say,

human beings are quick to perceive patterns where they don’t exist and to overestimate their strength where they do.

Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.

Keep this in mind when you’re told that two phenomena in nature or society were found to be uncorrelated. It doesn’t mean there’s no relationship, only that there’s no relationship of the sort that correlation is designed to detect.

“Many people seem to want to cut down the forest but to keep the trees.”

Americans think the programs that benefit them personally are the ones that must, at all costs, be preserved.

expected value is additive,

American people think each government program is worthy of continued funding, but that doesn’t mean they think all government programs are worthy of continued funding.