Quotes About Analysis

Knowledge must pass through many stages of analysis—a multitude of transformations—before it becomes, let us say, commonplace.

PERFECT ORDER BEFORE YOU CRITICIZE

Almost all ideas are wrong. It doesn't matter if they are your ideas or someone else's ideas. Your job is to assume that they are probably wrong, and then to assault them with every thing you have in your arsenal, and see if they can survive.

En términos estadísticos, los niños de dos años son las personas más violentas que existen.

Beware of intellectuals who make monotheism out of their theories of motivation.

before a problem can be solved it must be formulated precisely.

It sounds great, let me think about it …" or "Let me do a bit more research and I'll call you back.

First, you're identifying their needs—and not just their core need but also any secondary needs or 'problems' they might have.

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. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel.

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

Mathematics is the extension of common sense by other means.

Cauchy was not interested in the needs of engineers. Cauchy was interested in the truth.

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.

There is real danger that, by strengthening our abilities to analyze some questions mathematically, we acquire a general confidence in our beliefs, which extends unjustifiably to those things we're still wrong about.

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.

If you've ever run an experiment, you know scientific truth doesn't pop out of the clouds blowing a flaming trumpet at you. Data is messy, and inference is hard.

He was unsweaty, undusty, and unbloody, but he was right. He was a critic who counted.

In modern terms we would say that the more strongly correlated the measurements, the less information, in Shannon's precise sense, a Bertillon card conveys.

If you decide what color jelly beans to eat based just on the papers that get published, you're making the same mistake the army made when they counted the bullet holes on the planes that came back from Germany.

Assessing the scale of the p-hacking problem is not so easy—

That's how the Law of Large Numbers works: not by balancing out what's already happened, but by diluting what's already happened with new data, until the past is so proportionally negligible that it can safely be forgotten.

Data is messy, and inference is hard.

The significance test is the detective, not the judge.

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. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel.