Out of Context: On Programming (Definitions)

"[...] computer programming is an art, because it applies accumulated knowledge to the world, because it requires skill and ingenuity, and especially because it produces objects of beauty." (Donald E Knuth, "The Art of Computer Programming", 1968)

"The art of programming is the art of organizing complexity, of mastering multitude and avoiding its bastard chaos as effectively as possible." (Edsger W Dijkstra, "Notes On Structured Programming", 1970)

"Computer programming is a human activity. " (Gerald Weinberg, 1971)

"Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians." (Edsger W Dijkstra, "How do we tell truths that might hurt?", 1975)

"Programming is the art of writing essays in crystal clear prose and making them executable." (Per B Hansen, "The architecture of concurrent programs", 1977) 

"Programming is like pinball. The reward for doing it well is the opportunity to do it again." (Rick Cook, "The Wizardry Compiled", 1989)

"Programming is the ability to talk to the computer in a language it can understand and using grammar and syntax that it can follow to get it to perform useful tasks for you." (Adrian Kingsley-Hughes & Kathie Kingsley-Hughes, "Beginning Programming", 2007)

"Programming is a personal activity and there is no general process that is usually followed." (Ian Sommerville, "Software Engineering" 9th Ed., 2011)

"Programming is a science dressed up as art, because most of us don’t understand the physics of software and it’s rarely, if ever, taught." (Pieter Hintjens, "ZeroMQ: Messaging for Many Applications", 2012)

"Programming is the process of taking an algorithm and encoding it into a notation that the computer can execute." (Bradley N Miller et al, "Python Programming in Context", 2019)

On Inequalities I

"The worst form of inequality is to try to make unequal things equal." (Aristotle)

"Among simple even numbers, some are superabundant, others are deficient: these two classes are as two extremes opposed to one another; as for those that occupy the middle position between the two, they are said to be perfect. And those which are said to be opposite to each other, the superabundant and the deficient, are divided in their condition, which is inequality, into the too much and the too little." (Nicomachus of Gerasa,"Introductio Arithmetica", cca. 100 AD)

"Inequality is the cause of all local movements. There is no rest without equality." (Leonardo da Vinci, Codex Atlanticus, 1478)

"It is from this absolute indifference and tranquility of the mind, that mathematical speculations derive some of their most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality. (Edmund Burke, "On the Sublime and Beautiful", 1757)

"Nature is unfair? So much the better, inequality is the only bearable thing, the monotony of equality can only lead us to boredom." (Francis Picabia, "Comoedia", 1922)

"The fundamental results of mathematics are often inequalities rather than equalities." Edwin Beckenbach & Richard Bellman, "An Introduction to Inequalities", 1961)

"There are three reasons for the study of inequalities: practical, theoretical and aesthetic. On the aesthetic aspects, as has been pointed out, beauty is in the eyes of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive." (Richard E Bellman, 1978)

"Linear programming is concerned with the maximization or minimization of a linear objective function in many variables subject to linear equality and inequality constraints."  (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)

"From the historical point of view, since inequalities are associated with order, they arose as soon as people started using numbers, making measurements, and later, finding approximations and bounds. Thus inequalities have a long and distinguished role in the evolution of mathematics." (Claudi Alsina & Roger B Nelsen, "When Less is More: Visualizing Basic Inequalities", 2009)

"Inequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too often. especially in secondary and collegiate mathematics. the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubti mportant, they do not possess the richness and variety that one finds with inequalities." (Claudi Alsina & Roger B Nelsen, "When Less is More: Visualizing Basic Inequalities", 2009)

George B Dantzig - Collected Quotes

 "All such problems can be formulated as mathematical programming problems. Naturally, we can propose many sophisticated algorithms and a theory but the final test of a theory is its capacity to solve the problems which originated it." (George B Dantzig, "Linear Programming and Extensions", 1963)

"If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming." (George B Dantzig, "Linear Programming and Extensions", 1963)

"Linear programming is viewed as a revolutionary development giving man the ability to state general objectives and to find, by means of the simplex method, optimal policy decisions for a broad class of practical decision problems of great complexity. In the real world, planning tends to be ad hoc because of the many special-interest groups with their multiple objectives." (George B Dantzig, "Mathematical Programming: The state of the art", 1983)

"Linear programming and its generalization, mathematical programming, can be viewed as part of a great revolutionary development that has given mankind the ability to state general goals and lay out a path of detailed decisions to be taken in order to 'best' achieve these goals when faced with practical situations of great complexity. The tools for accomplishing this are the models that formulate real-world problems in detailed mathematical terms, the algorithms that solve the models, and the software that execute the algorithms on computers based on the mathematical theory."  (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)

"Linear programming is concerned with the maximization or minimization of a linear objective function in many variables subject to linear equality and inequality constraints."  (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)

"Mathematical programming (or optimization theory) is that branch of mathematics dealing with techniques for maximizing or minimizing an objective function subject to linear, nonlinear, and integer constraints on the variables."  (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)

"Models of the real world are not always easy to formulate because of the richness, variety, and ambiguity that exists in the real world or because of our ambiguous understanding of it." (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)

"The linear programming problem is to determine the values of the variables of the system that (a) are nonnegative or satisfy certain bounds, (b) satisfy a system  of linear constraints, and (c) minimize or maximize a linear form in the variables called an objective." (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)

Donald E Knuth - Collected Quotes

"It’s the idea that counts true; but we need a name for the idea, so we can apply it more easily next time." (Donald E Knuth, "Surreal Numbers", 1968)

"[…] random numbers should not be generated with a method chosen at random. Some theory should be used." (Donald E Knuth, "The Art of Computer Programming" Vol. II, 1968)

"The process of preparing programs for a digital computer is especially attractive, not only because it can economically and scientifically rewarding, but also because it can be an aesthetic experience much like composing poetry or music." (Donald E Knuth, "The Art of Computer Programming: Fundamental algorithms", 1968)

"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." (Donald E Knuth, "Computer Programming as an Art", 1968)

"These machines have no common sense; they have not yet learned to "think," and they do exactly as they are told, no more and no less. This fact is the hardest concept to grasp when one first tries to use a computer." (Donald E Knuth, "The Art of Computer Programming", 1968)

"We have seen that computer programming is an art, because it applies accumulated knowledge to the world, because it requires skill and ingenuity, and especially because it produces objects of beauty. A programmer who subconsciously views himself as an artist will enjoy what he does and will do it better. Therefore we can be glad that people who lecture at computer conferences speak of the state of the Art." (Donald E Knuth, "the Art of Computer Programming", 1968)

"Meta-design is much more difficult than design; it's easier to draw something than to explain how to draw it." (Donald E Knuth, "The METAFONTbook", 1986)

"Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren’t ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive." (Donald E Knuth et al, "Concrete Mathematics: A Foundation for Computer Science", 1989)

"The ultimate goal of mathematics is to eliminate all need for intelligent thought." (Donald E Knuth, "Concrete Mathematics: A Foundation for Computer Science", 1990)

"Science is what we understand well enough to explain to a computer. Art is everything else we do." (Donald E Knuth, [foreword to the book "A=B" by Marko Petkovsek et al] 1996)

"The whole thing that makes a mathematician's life worthwhile is that he gets the grudging admiration of three or four colleagues." (Donald E Knuth, [interview] 1996)

"Let us change our traditional attitude to the construction of programs: Instead of imagining that our main task is to instruct a computer what to do, let us concentrate rather on explaining to human beings what we want a computer to do." (Donald E Knuth, "Literate Programming", 1984)

"The difference between art and science is that science is what people understand well enough to explain to a computer. All else is art." (Donald E Knuth)