A Quote by Jeffrey Shallit

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

Jeffrey Shallit

Quote Topics

Easy False Problem Produce The Problem With Theorems True

Quote Author

Jeffrey Shallit
Scientist
Born: October 17, 1957

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

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.

Adrien-Marie Legendre

God has the Big Book, the beautiful proofs of mathematical theorems are listed here.

Paul Erdos

If only I had the Theorems! Then I should find the proofs easily enough.

Bernhard Riemann

Without computers we will be stuck only proving theorems that have short proofs.

Kenneth Appel

There are no hard distinctions between what is real and what is unreal, nor between what is true and what is false. A thing is not necessarily either true or false; it can be both true and false.

Harold Pinter

Paul Erdos has a theory that God has a book containing all the theorems of mathematics with their absolutely most beautiful proofs, and when he wants to express particular appreciation of a proof he exclaims, "This is from the book!"

Ross Honsberger

Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations.

Imre Lakatos

Either Christianity is true or it's false. If you bet that it's true, and you believe in God and submit to Him, then if it IS true, you've gained God, heaven, and everything else. If it's false, you've lost nothing, but you've had a good life marked by peace and the illusion that ultimately, everything makes sense. If you bet that Christianity is not true, and it's false, you've lost nothing. But if you bet that it's false, and it turns out to be true, you've lost everything and you get to spend eternity in hell.

Blaise Pascal

Fiction can produce truth, and truth can be false. What does it mean to say that it's true that, what, two out of six people in this city are starving? That's true, but that is only true because the conditions we live under are completely wrong - that should not be true, and it is. And in something like Sarah Polley's film, her fictions deliver so much truth. The retellings and the simulations and the theatrical aspects are what deliver all the truth.

How to Dress Well

To me, the problem with the president is that he takes very authoritarian actions in terms of attacking democratic institutions and then just uttering a large number of false and misleading statements that then make it hard sometimes for the people to know what is true and what is false.

Ted Lieu

He, who knows how to distinguish between true and false, must have an adequate idea of true and false.

Baruch Spinoza

What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. Roughly speaking, people know that it deals with numbers, figures, with relations, operations, and that its formal procedures involving axioms, proofs, lemmas, theorems have not changed since the time of Archimedes.

Stanislaw Ulam

To be able to discern that what is true is true, and that what is false is false,--this is the mark and character of intelligence.

Ralph Waldo Emerson

All religions, plainly and simply, cannot be true. Some beliefs are false, and we know them to be false. So it does no good to put a halo on the notion of tolerance as if everything could be equally true. To deem all beliefs equally true is sheer nonsense for the simple reason that to deny that statement would also, then, be true. But if the denial of the statement is also true, then all religions are not true.