General
No art, however minor, demands less than total dedication if you want to excel in it. — Leon Battista Alberti
It is the mark of an educated mind to be able to entertain a thought without accepting it. — Aristotle
I have no special talents. I am only passionately curious. — Albert Einstein
Was sich überhaupt sagen lässt, lässt sich klar sagen; und wovon man nicht reden kann, darüber muss man schweigen. — Wittgenstein in Tractatus Logico-Philosophicus
First do it, then do it right, then do it better. This is one fundamental I always keep in mind when developing anything. — Addy Osmani
Simplicity is the ultimate sophistication. — Leonardo da Vinci
Doubt is the origin of wisdom. — René Descartes
Divide each difficulty into as many parts as is feasible and necessary to resolve it. — René Descartes
Luck favors the prepared mind. — Louis Pasteur
The only way to be truly satisfied is to do what you believe is great work, and the only way to do great work is to love what you do. If you haven’t found it yet, keep looking, and don’t settle. As with all matters of the heart, you’ll know when you find it. And like any great relationship, it just gets better and better as the years roll on. So keep looking, don’t settle. — Steve Jobs
What we have to learn to do we learn by doing. — Aristotle, Nicomachean Ethics II
Some bookes are to bee tasted, others to bee swallowed, and some few to bee chewed and digested. — Francis Bacon, Essayes (1597)
“Non sunt multiplicanda entia praeter necessitatem.” “Do not multiply entities beyond necessity.” — Ockham’s Razor, William of Ockham (1285–1349?)
Civilization advances by extending the number of important operations which we can perform without thinking about them. — Alfred North Whitehead, An Introduction to Mathematics, 1911
People have said you don’t understand something until you’ve taught it in a class. The truth is you don’t understand something until you’ve taught it to a computer, until you’ve been able to program it. — George Forsythe
You can’t make imperfections on a perfect thing - you have to have another perfect thing. — Feynman
A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away. — Antoine de Saint-Exupéry
Keep the company of those who seek the truth — run from those who have found it. — Vaclav Havel
Fall in love with some activity, and do it! Nobody ever figures out what life is all about, and it doesn’t matter. Explore the world. Nearly everything is really interesting if you go into it deeply enough. Work as hard and as much as you want to on the things you like to do the best. Don’t think about what you want to be, but what you want to do. Keep up some kind of a minimum with other things so that society doesn’t stop you from doing anything at all. — Richard P. Feynman
Life is too short to worry about stupid things. Have fun. Fall in love. Regret nothing and don’t let people bring you down. — Richard P. Feynman
The taste to work on the right problem at the right time and in the right way is the secret of doing significant things. — Richard W. Hamming, Methods of mathematics applied to calculus, probability, and statistics
If you love something you can put beauty into it. — Donald Knuth
Not to be absolutely certain is, I think, one of the essential things in rationality. — Bertrand Russell, Am I An Atheist Or An Agnostic?
Computer
Programs should be written for people to read, and only incidentally for machines to execute. — Structure and Interpretation of Computer Programs
We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. Yet we should not pass up our opportunities in that critical 3%. A good programmer will not be lulled into complacency by such reasoning, he will be wise to look carefully at the critical code; but only after that code has been identified. — Donald Knuth
Inside every large program, there is a small program trying to get out. — Tony Hoare
Any fool can write code that a computer can understand. Good programmers write code that humans can understand. — Martin Fowler
There are two ways of constructing a software design: One way is to make it so simple that there are obviously no deficiencies and the other way is to make it so complicated that there are no obvious deficiencies. — Tony Hoare
What were the lessons I learned from so many years of intensive work on the practical problem of setting type by computer? One of the most important lessons, perhaps, is the fact that SOFTWARE IS HARD. From now on I shall have significantly greater respect for every successful software tool that I encounter. During the past decade I was surprised to learn that the writing of programs for TeX and Metafont proved to be much more difficult than all the other things I had done (like proving theorems or writing books). The creation of good software demands a significantly higher standard of accuracy than those other things do, and it requires a longer attention span than other intellectual tasks. — Donald Knuth, Keynote address to 11th World Computer Congress (IFIP Congress 89).
Reliability can be purchased only at the price of simplicity. — Tony Hoare, An axiomatic basis for computer programming
The price of reliability is the pursuit of the utmost simplicity. — Tony Hoare, The Emperor’s Old Clothes
The art of programming is the art of organising complexity, of mastering multitude and avoiding its bastard chaos as effectively as possible. — Edsger W. Dijkstra, Notes on structured programming
Program testing can be used to show the presence of bugs, but never to show their absence! — Edsger W. Dijkstra, Notes on structured programming
Once a person has understood the way in which variables are used in programming, he has understood the quintessence of programming. — Edsger W. Dijkstra, Notes on structured programming
Programming (or problem solving in general?) as the judicious postponement of decisions and commitments! — Edsger W. Dijkstra, Notes on structured programming
Simple things should be simple, complex things should be possible. — Alan Kay
More computing sins are committed in the name of efficiency (without necessarily achieving it) than for any other single reason—including blind stupidity. — Wulf, W. A Case Against the GOTO. 1972.
As programmers, we should be alert to opportunities to identify the underlying abstractions in our programs and to build upon them and generalize them to create more powerful abstractions. This is not to say that one should always write programs in the most abstract way possible; expert programmers know how to choose the level of abstraction appropriate to their task. But it is important to be able to think in terms of these abstractions, so that we can be ready to apply them in new contexts. The significance of higher-order procedures is that they enable us to represent these abstractions explicitly as elements in our programming language, so that they can be handled just like other computational elements. — Structure and Interpretation of Computer Programs
It is practically impossible to teach good programming to students that have had a prior exposure to BASIC: as potential programmers they are mentally mutilated beyond hope of regeneration. — Edsger W.Dijkstra, EWD498
The hardest part of the software task is arriving at a complete and consistent specification, and much of the essence of building a program is in fact the debugging of the specification. — Fred Brooks, No Silver Bullet
Avoid the need for special handling. — Leo Brodie, Thinking Forth
Programming Language
It was a fundamental principle that every value in the language should be expressible by some external denotation. — C. H. Lindsey, A history of ALGOL 68
An unreliable programming language generating unreliable programs constitutes a far greater risk to our environment and to our society than unsafe cars, toxic pesticides, or accidents at nuclear power stations. Be vigilant to reduce that risk, not to increase it. — Tony Hoare, The emperor’s old clothes
It is relatively easy to add a new feature to meet a well-understood
need in an existing simple language; it is almost impossible to
remove an over-elaborate feature from a language which has already
gone into use!
— Tony Hoare, Everything You’ve Wanted to Know about Programming Languages but Have Been Afraid to Ask
The real merit in a programming language is its success in combining a
useful (but not redundant) set of features into single programming
tool, which can be widely used and efficiently implemented. It is the
right balance between features, and the avoidance of interaction
effects, that is most important.
— Tony Hoare, Everything You’ve Wanted to Know about Programming Languages but Have Been Afraid to Ask
Listen carefully to what language users say they want, until you have an understanding of what they really want. — Tony Hoare, Hints on Programming Language Design
… it is absurd to make elaborate security checks on debugging runs, when no trust is put in the results, and then remove them in production runs, when an erroneous result could be expensive or disastrous. What would we think of a sailing enthusiast who wears his life-jacket when training on dry land but takes it off as soon as he goes to sea? — Tony Hoare, Hints on Programming Language Design
Writing
If you try to write for the novice, you will communicate with the experts — otherwise you communicate with nobody. — Donald Knuth
If you are thinking without writing, you only think you are thinking. — Leslie Lamport
Writing is nature’s way of letting you know how sloppy your thinking is. — Guindon
The best writing is rewriting. — E. B. White
Mathematics
In mathematics you don’t understand things, you just get used to them. — John von Neumann
Beauty is the first test: there is no permanent place in this world for ugly mathematics. — G. H. Hardy, A Mathematician’s Apology
It is not mere ‘piling of subtlety of generalization upon subtety of generalization’ which is the outstanding achievement of modern mathematics … too much tends inevitably to insipidity … mathematical ideas also become dim unless they have plenty of individuality. — G. H. Hardy, A Mathematician’s Apology
It is certain that your knowledge, or my knowledge, or your students’ knowledge in mathematics is not based on formal proofs alone. — George Polya, How to Solve It
The more general problem may be easier to solve. […] The main achievement in solving the special problem was to invent the general problem. — George Polya, How to Solve It
We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building. — George Polya, How to Solve It
Mathematics presented with rigor is a systematic deductive science but mathematics in the making is an experimental inductive science. — George Polya, How to Solve It
Science
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it. . . . An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out, and that the growing generation is familiarized with the ideas from the beginning: another instance of the fact that the future lies with the youth. — Max Planck, Scientific autobiography
All models are wrong, but some are useful. — George Box
In science if you know what you are doing you should not be doing it. In engineering if you do not know what you are doing you should not be doing it. Of course, you seldom, if ever, see either pure state. — Richard Hamming, The Art of Doing Science and Engineering: Learning to Learn
There is no royal road to logic, and really valuable ideas can only be had at the price of close attention. — C. S. Peirce, How to make our ideas clear
As far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. — Einstein
It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience. — Albert Einstein, On the Method of Theoretical Physics
… any attempt logically to derive the basic concepts and laws of mechanics from the ultimate data of experience is doomed to failure. — Albert Einstein, On the Method of Theoretical Physics
The axiomatic basis of theoretical physics cannot be an inference from experience, but must be free invention. — Albert Einstein, On the Method of Theoretical Physics
Our experience up to date justifies us in feeling sure that in Nature is actualized the ideal of mathematical simplicity. It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them which give us the key to the understanding of the phenomena of Nature. — Albert Einstein, On the Method of Theoretical Physics
Doubt is not a pleasant condition, but certainty is absurd. — Voltaire
A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist. — The Feynman Lectures on Physics, Volume II, Chapter 2
The data cannot speak for themselves; and they never have, in any real problem of inference. — E. T. Jaynes, Probability Theory: The Logic of Science
It is just the accumulation of unchanging prior information about the world that gives the mature person the mental stability that rejects arbitrary fantasies. — E. T. Jaynes, Probability Theory: The Logic of Science
No proposition is in itself either probable or improbable, just as no place can be intrinsically distant; and the probability of the same statement varies with the evidence presented, which is, as it were, its origin of reference. — J. M. Keynes, A Treatise on Probability
… before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through Faraday’s Experimental Researches on Electricity. — James Clerk Maxwell, A Treatise on Electricity and Magnetism
It is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state. — James Clerk Maxwell, A Treatise on Electricity and Magnetism
Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of quantitative theory, to make possible the comparison with experiment. — Einstein and Infield, The Evolution of Physics
Science is not and will never be a closed book. Every important advance brings new questions. Every development reveals, in the long run, new and deeper difficulties. — Einstein and Infield, The Evolution of Physics
Science is not just a collection of laws, a catalogue of unrelated facts. It is a creation of the human mind, with its freely invented ideas and concepts. Physical theories try to form a picture of reality and to establish its connection with the wide world of sense impressions. Thus the only justification for our mental structures is whether and in what way our theories form such a link. — Einstein and Infield, The Evolution of Physics
In the theory which I propose to develope, the mathematical methods are founded upon the smallest possible amount of hypothesis, and thus equations of the same form are found applicable to phenomena which are certainly of quite different natures, as, for instance, electric induction through dielectrics; conduction through conductors, and magnetic induction. — James Clerk Maxwell, A Treatise on Electricity and Magnetism
Education
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats
Try to learn something about everything and everything about something. — Thomas Huxley
The Euclidean way of exposition, however, cannot be recommended without reservation if the purpose is to convey an argument to a reader or to a listener who never heard of it before. — George Polya, How to Solve It
Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity — to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs — you deny them mathematics itself. — Paul Lockhart, A Mathematician’s Lament