Counterexample Quotes & Sayings

They don't know they have expectations, but I show them by counterexample what their expectations were. — John Darnielle

We ... have to open our mouths and bear testimony. — Henry B. Eyring

Until we fully understand what turned two brothers who allegedly perpetrated the Boston Marathon bombings into murderers, it is hard to make any policy recommendation other than this: We need to redouble our efforts to make America stronger and healthier so it remains a vibrant counterexample to whatever bigoted ideology may have gripped these young men ... And the best place to start is with a carbon tax. — Thomas Friedman

I developed a crazy face rash after I got engaged to a guy I must have known somewhere I should not marry. I hadn't articulated this to myself, so my face told the world instead. — Heidi Julavits

I have been clinically depressed for most of my life. I once used drugs to fix it. Then I stopped. I stopped because I decided they were making me stupid, and I'd rather be miserable than stupid. I am what I am. — Neal Stephenson

Art is an investigation. — Twyla Tharp

That's the problem with false proofs of true theorems; it's not easy to produce a counterexample. — Jeffrey Shallit

A failed structure provides a counterexample to a hypothesis and shows us incontrovertibly what cannot be done, while a structure that stands without incident often conceals whatever lessons or caveats it might hold for the next generation of engineers. — Henry Petroski

It's been fascinating watching all those pictures of me with a lot more hair Jeremy, and looking very young. And we've all got things we've said, twenty, thirty years ago, indeed the whole world has changed since then. — Peter Hain

However the machine would permit us to test the hypothesis for any special value of n. We could carry out such tests for a sequence of consecutive values n=2,3,.. up to, say, n=100. If the result of at least one test were negative, the hypothesis would prove to be false; otherwise our confidence in the hypothesis would increase, and we should feel encouraged to attempt establishing the hypothesis, instead of trying to construct a counterexample. — Alfred Tarski

Incidentally, when we're faced with a "prove or disprove," we're usually better off trying first to disprove with a counterexample, for two reasons: A disproof is potentially easier (we need just one counterexample); and nitpicking arouses our creative juices. Even if the given assertion is true, our search for a counterexample often leads to a proof, as soon as we see why a counterexample is impossible. Besides, it's healthy to be skeptical. — Ronald Graham