Donald Knuth Quotes

Science is what we understand well enough to explain to a computer; art is everything else.

The computer scientist Donald Knuth was struck that “AI has by now succeeded in doing essentially everything that requires ‘thinking’ but has failed to do most of what people and animals do ‘without thinking’—that, somehow, is much harder!

The best programs are written so that computing machines can perform them quickly and so that human beings can understand them clearly. A programmer is ideally an essayist who works with traditional aesthetic and literary forms as well as mathematical concepts, to communicate the way that an algorithm works and to convince a reader that the results will be correct.

An algorithm must be seen to be believed.

Premature optimization is the root of all evil.

Beware of bugs in the above code; I have only proved it correct, not tried it.

Programs are meant to be read by humans and only incidentally for computers to execute.

The language in which we express our ideas has a strong influence on our thought processes.

Nearly every example of faulty reasoning that has been published is accompanied by the phrase "of course" or its equivalent.

Overstimulation has been the real drawback. I need to find ways to stop thinking about analysis of algorithms, in order to do various other things that human beings ought to do.

Programming is the art of telling another human being what one wants the computer to do.

Premature optimization is the root of all evil.

If you optimize everything, you will always be unhappy.

We should continually be striving to transform every art into a science: in the process, we advance the art.

Everyday life is like programming, I guess. If you love something you can put beauty into it.

People think that computer science is the art of geniuses but the actual reality is the opposite, just many people doing things that build on each other, like a wall of mini stones.

In fact, my experiences as I was writing the 3:16 book weren't that different from writing computer books, although I wasn't using integral signs as much.

Instead of concentrating just on finding good answers to questions, it's more important to learn how to find good questions!

A person’s success in life is determined by having a high minimum, not a high maximum. If you can do something really well but there are other things at which you’re failing, the latter will hold you back. But if almost everything you do is up there, then you’ve got a good life. And so I try to learn how to get through things that others find unpleasant.

It’s very important to be able to get inside of somebody else’s way of thinking, to decode their vocabulary, their notation. If you can understand something about the way they thought and the way they made a discovery, then that helps you make your own discoveries.

Everyday life is like programming, I guess.If you love something you can put beauty on it.

Everyday life is like programming, I guess. If you love something you can put beauty on it.

I'm trying to get to the bottom of things

I'm trying to get to the bottom of things.

An algorithm must be seen to be believed

A brute-force solution that works is better than an elegant solution that doesn't work. It can take a long time to get an elegant solution to work. In describing the history of searching algorithms, for example, Donald Knuth pointed out that even though the first description of a binary search algorithm was published in 1946, it took another 16 years for someone to publish an algorithm that correctly searched lists of all sizes (Knuth 1998). A binary search is more elegant, but a brute-force, sequential search is often sufficient. When in doubt, use brute force. — Butler Lampson

The five stages of model development. —Donald Knuth, Stanford computer scientist Knuth discovered that computer program development goes through five stages. These steps also apply to building models, and I rigorously adhere to them in my consulting work. 1. Decide what you want the model to do. 2. Decide how to build the model. 3. Build the model. 4. Debug the model. 5. Trash stages 1 through 4 and start again, now that you know what you really wanted in the first place. Once you realize that step 5 is inevitable, you become more willing to discard bad models early rather than continually to patch them up. In fact, I recommend getting to step 5 many times by building an evolving set of prototypes. This is consistent with an emerging style of system development known as Extreme Programming.2 To get a large model to work you must start with a small model that works, not a large model that doesn’t work. —Alan Manne, Stanford energy economist

The language in which we express our ideas has a strong influence on our thought processes.

From now on whenever I read a math book, I'm going to try to figure out by myself how everything was done, before looking at the solution. Even if I don't figure it out, I think I'll be able to see the beauty of a proof then.

Nearly every example of faulty reasoning that has been published is accompanied by the phrase "of course" or its equivalent.

premature optimization is the root of all evil. —Donald E. Knuth [

B: True. I've got this mad urge to get up before a class and present our results: Theorem, proof, lemma, remark. I'd make it so slick nobody would be able to guess how we did it, and everyone would be so impressed.

B: True. I've got this made urge to get up before a class and present our results: Theorem, proof, lemma, remark. I'd make it so slick nobody would be able to guess how we did it, and everyone would be

The most important thing in the programming language is the name. A language will not succeed without a good name. I have recently invented a very good name and now I am looking for a suitable language.

If you find that you're spending almost all your time on theory, start turning some attention to practical things; it will improve your theories. If you find that you're spending almost all your time on practice, start turning some attention to theoretical things; it will improve your practice.

People who discover the power and beauty of high-level, abstract ideas often make the mistake of believing that concrete ideas at lower levels are worthless and might as well be forgotten. On the contrary, the best computer scientists are thoroughly grounded in basic concepts of how computers actually work. The essence of computer science is an ability to understand many levels of abstraction simultaneously.

So I went to Case, and the Dean of Case says to us, says, it’s a all men’s school, says, “Men, look at, look to the person on your left, and the person on your right. One of you isn’t going to be here next year; one of you is going to fail.” So I get to Case, and again I’m studying all the time, working really hard on my classes, and so for that I had to be kind of a machine. I, the calculus book that I had, in high school we — in high school, as I said, our math program wasn’t much, and I had never heard of calculus until I got to college. But the calculus book that we had was great, and in the back of the book there were supplementary problems that weren’t, you know, that weren’t assigned by the teacher. The teacher would assign, so this was a famous calculus text by a man named George Thomas, and I mention it especially because it was one of the first books published by Addison-Wesley, and I loved this calculus book so much that later I chose Addison-Wesley to be the publisher of my own book. But Thomas’s Calculus would have the text, then would have problems, and our teacher would assign, say, the even numbered problems, or something like that. I would also do the odd numbered problems. In the back of Thomas’s book he had supplementary problems, the teacher didn’t assign the supplementary problems; I worked the supplementary problems. I was, you know, I was scared I wouldn’t learn calculus, so I worked hard on it, and it turned out that of course it took me longer to solve all these problems than the kids who were only working on what was assigned, at first. But after a year, I could do all of those problems in the same time as my classmates were doing the assigned problems, and after that I could just coast in mathematics, because I’d learned how to solve problems. So it was good that I was scared, in a way that I, you know, that made me start strong, and then I could coast afterwards, rather than always climbing and being on a lower part of the learning curve.

The process of preparing programs for a digital computer is especially attractive, not only because it can be economically and scientifically rewarding, but also because it can be an aesthetic experience much like composing poetry or music.

AI has by now succeeded in doing essentially everything that requires ‘thinking’ but has failed to do most of what people and animals do ‘without thinking.

In the beginning, everything was void, and J. H. W. H. Conway began to create numbers. Conway said, "Let there be two rules which bring forth all numbers large and small. This shall be the first rule: Every number corresponds to two sets of previously created numbers, such that no member of the left set is greater than or equal to any member of the right set. And the second rule shall be this: One number is less than or equal to another number if and only if no member of the first number's left set is greater than or equal to the second number, and no member of the second number's right set is less than or equal to the first number." And Conway examined these two rules he had made, and behold! They were very good. … And Conway said, "Let the numbers be added to each other in this wise: The left set of the sum of two numbers shall be the sums of all left parts of each number with the other; and in like manner the right set shall be from the right parts, each according to its kind." Conway proved that every number plus zero is unchanged, and he saw that addition was good. And the evening and the morning were the third day. And Conway said, "Let the negative of a number have as its sets the negatives of the number's opposite sets; and let subtraction be addition of the negative." And it was so. Conway proved that subtraction was the inverse of addition, and this was very good. And the evening and the morning were the fourth day. And Conway said to the numbers, "Be fruitful and multiply. Let part of one number be multiplied by another and added to the product of the first number by part of the other, and let the product of the parts be subtracted. This shall be done in all possible ways, yielding a number in the left set of the product when the parts are of the same kind, but in the right set when they are of opposite kinds." Conway proved that every number times one is unchanged. And the evening and the morning were the fifth day. And behold! When the numbers had been created for infinitely many days, the universe itself appeared. And the evening and the morning were N day. And Conway looked over all the rules he had made for numbers, and saw that they were very, very good.

The real problem is that programmers have spent far too much time worrying about efficiency in the wrong places and at the wrong times; premature optimization is the root of all evil (or at least most of it) in programming.

Thinking about small things every day from today will lead you to rise to the ranks of Donald Knuth and Alan Turing in a few years.

I have only proven the algorithm correct, not tested it.

We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil.