A Quote by Ronald Graham

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

Quote Topics

Assertion Besides Better Better Off Creative Creative Juices Easier Even Faced First Given Healthy Impossible Juices Just Just One Leads Need Off Often Our Potentially Proof Prove Reasons Search See Skeptical Soon True Trying Two Why

Quote Author

Ronald Graham
American - Mathematician
Born: October 31, 1935

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

Jeffrey Shallit

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

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

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

Given a conjecture, the best thing is to prove it. The second best thing is to disprove it. The third best thing is to prove that it is not possible to disprove it, since it will tell you not to waste your time trying to disprove it. That's what Gödel did for the Continuum Hypothesis.

Saharon Shelah

The Consequentialist trinity is typically regarded in this way: Bentham is crude, Mill's writings are full of howlers and inconsistencies, and Sidgwick was too smart to fully embrace Consequentialism. All of these great traditions in moral philosophy express strands of our moral consciousness and they should all be treated as research programs rather than as fully determinate views that can be leveled by a counterexample or by a clever argument.

Dale Jamieson

We cannot, of course, disprove God, just as we can't disprove Thor, fairies, leprechauns, and the Flying Spaghetti Monster. But, like those other fantasies that we can't disprove, we can say that God is very, very improbable.

Richard Dawkins

If one were to claim that the U.S. occupation forces in Iraq have been provided with "keys to heaven" by the Pentagon, would that need historical research to be disproved or would you just say, "That's just propaganda"? Indeed, how can you disprove the claim that U.S. soldiers have such keys? Or why should you disprove such ridiculous claims? It is the accusers who must provide the evidence.

Mohammad Marandi

We cannot, of course, disprove God, just as we can't disprove Thor, fairies, leprechauns and the Flying Spaghetti Monster.

Richard Dawkins

Everyone - male and female - is biased. But no one wants to admit it, so our brains search for examples that disprove the accusation.

Nell Scovell

In order to disprove the assertion that all crows are black, one white crow is sufficient.

William James

Faced with having to change our views or prove that there is no need to do so, most of us immediately get busy on the proof.

John Kenneth Galbraith

Go and try to disprove death. Death will disprove you, and that's all!

Ivan Turgenev

It is often said that education and training are the keys to the future. They are, but a key can be turned in two directions. Turn it one way and you lock resources away, even from those they belong to. Turn it the other way and you release resources and give people back to themselves. To realize our true creative potential-in our organizations, in our schools and in our communities-we need to think differently about ourselves and to act differently towards each other. We must learn to be creative.