Quotes About Logic

A basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe doesn't object.

A mathematician is always asking, "What assumptions are you making? And are they justified?

Dividing one number by another is mere computation ; knowing what to divide by what is mathematics.

Mathematics is the extension of common sense by other means.

It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth, unless the truth is a hypothesis it didn't occur to you to consider.

When you reason correctly, as Silver does, you find that you always think you're right, but you don't think you're always right.

Mathematicians can be persnickety about logical niceties. We're the kind of people who think it's funny, when asked, "Do you want soup or salad with that?" to reply, "Yes.

Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world. Math is a science of not being wrong about things, its techniques and habits hammered out by centuries of hard work and argument. With the tools of mathematics in hand, you can understand the world in a deeper, sounder, and more meaningful way.

The ultimate reason for teaching kids to write a proof is not that the world is full of proofs. It's that the world is full of non-proofs , and grown-ups need to know the difference. It's hard to settle for a non-proof once you've really familiarized yourself with the genuine article.

Math gives us a way of being unsure in a principled way: not just throwing up our hands and saying "huh," but rather making a firm assertion: "I'm not sure, this is why I'm not sure, and this is roughly how not-sure I am." Or even more: "I'm unsure, and you should be too.

In 1931, Kurt Godel proved in his famous second incompleteness theorem that there could be no finitary proof of the consistency of arithmetic. He had killed Hilbert's program with a single stroke. So should you be worried that all of mathematics might collapse tomorrow afternoon? For what it's worth, I'm not. I do believe in infinite sets, and I find the proofs of consistency that use infinite sets to be convincing enough to let me sleep at night.

0.33333. . . . .= 1/3. Multiply both sides by 3 and you'll see 0.99999. . . .= 3/3= 1.

Mathematics is common sense.

To do mathematics is to be, at once, touched by fire and bound by reason.

the mathematical approach is a formalized version of our natural mental reckonings, an extension of common sense by other means.

It comes back to his math-trained habits of thought. A mathematician is always asking, "What assumptions are you making?

Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense—or deciding whether the method is the right one to use in the first place—requires a guiding human hand.

Math is a science of not being wrong about things,

numerically flavored advice.

All mathematical writing is creative writing.

Math is a science of not being wrong about things, its techniques and habits hammered out by centuries of hard work and argument.

when you're working hard on a theorem you should try to prove it by day and disprove it by night.

If you have before you a square whose side has length X, its area is X times X—indeed, that's why we call the operation of multiplying a number by itself squaring!

La idea del principio en Leibniz ? la evolución de la teoría deductiva.