Quotes

Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.

I have made this longer than usual because I have not had time to make it shorter.

Don’t worry about people stealing your idea. If it’s any good, you’ll have to force it down their throats.

I’m tired of trying to do something worthwhile for the human race, they simply don’t want to change!

Copying bad design is not good design.

All generalizations are false, including this one.

Even if everyone agrees, everyone can be wrong.

[in response to the book “Hundred Authors Against Einstein] Why a hundred? If I were wrong, one would have been enough.

Mathematics is one of the few disciplines that teaches us about the power of thought as distinct from the power of authority.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

This common and unfortunate fact of the lack of an adequate presentation of basic ideas and motivations of almost any mathematical theory is, probably, due to the binary nature of mathematical perception: either you have no inkling of an idea or, once you have understood it, this very idea appears so embarrassingly obvious that you feel reluctant to say it aloud; moreover, once your mind switches from the state of darkness to the light, all memory of the dark state is erased and it becomes impossible to conceive the existence of another mind for which the idea appears nonobvious.

Since when did a mathematician need any tools but his own head? Pythagoras had done well enough with a stick and a stretch of sand.

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

Mathematicians do not study objects, but relations between objects. Thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.

We often hear that mathematics consists mainly of proving theorems. Is a writer's job mainly that of writing sentences?

Mathematics is no more computation than typing is literature.

One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject, its symbolism and formality, its baffling terminology, its apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were to be summed up as ‘a lot of tadpoles drawn on a row of lines’; but that's all that the untrained eye can see in a page of sheet music… In the same way, the symbolism of mathematics is merely its coded form, not its substance.

The only way to learn mathematics is to do mathematics.

A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one.

Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.

If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.

Life is good for only two things, discovering mathematics and teaching mathematics.

The wonderful thing about formal mathematical proof is that it eliminates the use of intuition in an argument. And the trouble with formal mathematical proof is that it eliminates the use of intuition in an argument.

People think of axioms as laws you have to follow, or true things you have to assume, and I think neither of these perspectives is correct. It's more accurate to think of axioms as a way to agree that we're talking about the same thing.

Perhaps the purpose of categorical algebra is to show that which is trivial is trivially trivial.

[after hearing that a student had dropped out to study poetry] Good, he did not have enough imagination to become a mathematician.

Physics is like sex. Sure, it may give some practical results, but that’s not why we do it.

Lots of people don’t care about programming languages, possibly because they think that all languages are the same, or they don’t want help from their patient and careful friends, or have never used an optimizing compiler for a high-level language, or they suspect that programming is mostly about taping together programs that other people wrote. I am fairly certain that I have more fun programming than these people, which makes me sad.

So, accept the traps of the language as a fact of life, and just avoid them? No, that doesn’t fly with me. Programming languages aren’t Forces of Nature, they are human artefacts. They can be corrected.

Do not tell me that “good developers can write good code in any language”, or bad developers blah blah. That doesn’t mean anything. A good carpenter can drive in a nail with either a rock or a hammer, but how many carpenters do you see bashing stuff with rocks? Part of what makes a good developer is the ability to choose the tools that work best.

A complex system that works has evolved from a simple system that worked. A complex system built from scratch won’t work.

With a sufficient number of users of an API, it does not matter what you promise in the contract: all observable behaviors of your system will be depended on by somebody.

The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.

Object-oriented design is the Roman numerals of computing.

Any sufficiently complicated C or Fortran program contains an ad hoc, informally-specified, bug-ridden, slow implementation of half of Common Lisp.

Any organization that designs a system (defined broadly) will produce a design whose structure is a copy of the organization's communication structure.

On two occasions I have been asked, — “Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?” In one case a member of the Upper, and in the other a member of the Lower, House put this question. I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

Anyone who insists that Free Software is anti-capitalist and anti-commercial, is deeply misunderstanding it. Free Software creates a level playing field in the market for software vendors. There is nearly perfect freedom of movement from one vendor to another. It creates nearly the economist’s ideal perfectly competitive market. This is capitalism in its purest form.

Playing a game is the voluntary attempt to overcome unnecessary obstacles.

Basically AI is the exact opposite of compression. We take what should be a few bullet points, turn it into some overly wordy bullshit with AI, then the recipient uses AI to turn that wordy bullshit back into a few bullet points.

If we don’t believe in freedom of expression for people we despise, we don’t believe in it at all.

Moderation is when you take down material because the recipient doesn’t want to see it. Censorship is when you take down content because you don’t want the recipient to see it, regardless of how the recipient feels about it. If people think censorship is sometimes justified, they should argue that, and not muddle the picture with moderation.

My philosophy on anything like this, whether it happens to align with my beliefs or not, is that the truth shouldn’t fear scrutiny. If a company, government, or person decides to show how right they are by banning dissent then it should be a red flag even if you agree with them on the actual issue. I’m all for self moderation tools so people don’t have to see anything they don’t want to but I don’t need anyone deciding what opinions are ‘correct’ enough for me to see.

I disapprove of what you say, but I will defend to the death your right to say it.

To determine the true rulers of any society, all you must do is ask yourself this question: Who is it that I am not permitted to criticize?

The people who offend you with truth do not hate you. The people who comfort you with lies hate you. And if you prefer a comfortable lie over an offensive truth—you hate yourself.

I like offending people, because I think people who get offended should be offended.

We are all atheists about most of the gods that humanity has ever believed in. Some of us just go one god further.

The Bible is only missing two words in order to be true: There is at most one God.

The God of the Old Testament is arguably the most unpleasant character in all fiction: jealous and proud of it; a petty, unjust, unforgiving control-freak; a vindictive, bloodthirsty ethnic cleanser; a misogynistic, homophobic, racist, infanticidal, genocidal, filicidal, pestilential, megalomaniacal, sadomasochistic, capriciously malevolent bully.

I’m going to place a doggie biscuit in my backyard and forbid my dog from eating it. When turn my back and he eats it, I’ll kick him out and hold every other dog I ever have accountable for the actions of the first dog. And then I’ll punish the dogs eternally for the things deem to be bad, even though willed them to do it in the first place.

But Marge, what if we chose the wrong religion? Each week we just make God madder and madder.

What I cannot create, I do not understand.

Reading, after a certain age, diverts the mind too much from its creative pursuits. Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.

Arguing that you don’t care about the right to privacy because you have nothing to hide is no different than saying you don’t care about free speech because you have nothing to say.

Quidquid latine dictum sit, altum videtur.