Explore a curated collection of quotes on the evolution, purpose, and impact of computation. From foundational insights to modern reflections on its role in science and society, these quotes reveal how computation shapes our understanding of mathematics, scientific inquiry, and the world around us.
The Purpose of Computation
“The purpose of computation is insight, not numbers.” — Richard Hamming
“Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others.” — Sir Isaac Newton
“Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation.” — Sir Isaac Newton
“In Geometry, that ought to be reckoned best which is geometrically most simple.” — Sir Isaac Newton
“The desire to economize time and mental effort in arithmetical computations, and to eliminate human liability to error is probably as old as the science of arithmetic itself.” — Howard Hathaway Aiken
The Evolution and Power of Computation
“There are now three types of scientists: experimental, theoretical, and computational.” — Silvan S. Schweber
“The most extensive computation known has been conducted over the last billion years on a planet-wide scale: it is the evolution of life. The power of this computation is illustrated by the complexity and beauty of its crowning achievement, the human brain.” — David Rogers
“At the present time there exist problems beyond our ability to solve, not because of theoretical difficulties, but because of insufficient means of mechanical computation.” — Howard Hathaway Aiken
“Perhaps some day in the dim future it will be possible to advance the computations faster than the weather advances and at a cost less than the saving to mankind due to the information gained. But that is a dream.” — Lewis Fry Richardson
Mathematics as a Language and Tool
“Mathematics is no more the art of reckoning and computation than architecture is the art of making bricks or hewing wood, no more than painting is the art of mixing colors on a palette, no more than the science of geology is the art of breaking rocks, or the science of anatomy the art of butchering.” — Cassius Jackson Keyser
“The student should not lose any opportunity of exercising himself in numerical calculation and particularly in the use of logarithmic tables. His power of applying mathematics to questions of practical utility is in direct proportion to the facility which he possesses in computation.” — Augustus De Morgan
“It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.” — Pierre-Simon Laplace
“The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of the great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.” — H.G. Wells
The Integrity and Precision of Mathematical Proofs
“We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.” — Hermann Weyl
“Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.” — Johann Friedrich Herbart
“As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning.” — Johann Friedrich Herbart
“It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation.” — Johann Friedrich Herbart
Computation, Experiment, and Reality
“In general, we look for a new law by the following process. First, we guess it. Then we—don’t laugh, that’s really true. Then we compute the consequences of the guess to see if this is right—if this law that we guessed is right—we see what it would imply. And then we compare those computation results to nature—or, we say compare to experiment or experience—compare it directly with observation to see if it works. If it disagrees with experiment, it’s wrong.” — Richard P. Feynman
“If you ask … the man in the street … the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline… [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.” — Cassius Jackson Keyser
“No one believes the results of the computational modeler except the modeler, for only he understands the premises. No one doubts the experimenter’s results except the experimenter, for only he knows his mistakes.” — Anonymous
“For it is the duty of an astronomer to compose the history of the celestial motions or hypotheses about them. Since he cannot in any certain way attain to the true causes, he will adopt whatever suppositions enable the motions to be computed correctly from the principles of geometry for the future as well as for the past.” — Andreas Osiander
Applications of Computation in Society
“The computational formalism of mathematics is a thought process that is externalised to such a degree that for a time it becomes alien and is turned into a technological process. A mathematical concept is formed when this thought process, temporarily removed from its human vessel, is transplanted back into a human mold. To think … means to calculate with critical awareness.” — Yuri Manin
“Historically, Statistics is no more than State Arithmetic, a system of computation by which differences between individuals are eliminated by the taking of an average. It has been used—indeed, still is used—to enable rulers to know just how far they may safely go in picking the pockets of their subjects.” — Michael J. Moroney
“When the aggregate amount of solid matter transported by rivers in a given number of centuries from a large continent, shall be reduced to arithmetical computation, the result will appear most astonishing to those…not in the habit of reflecting how many of the mightiest of operations in nature are effected insensibly, without noise or disorder.” — Sir Charles Lyell
“There is no end of hypotheses about consciousness, particularly by philosophers. But most of these are not what we might call principled scientific theories, based on observables and related to the functions of the brain and body. Several theories of consciousness based on functionalism and on the machine model of the mind… have recently been proposed. These generally come in two flavors: one in which consciousness is assumed to be efficacious, and another in which it is considered an epiphenomenon. In the first, consciousness is likened to the executive in a computer systems program, and in the second, to a fascinating but more or less useless by-product of computation.” — Gerald Maurice Edelman
Insight, Innovation, and Computational Thought
“Chess is not a game. Chess is a well-defined form of computation. You may not be able to work out the answers, but in theory there must be a solution, a right procedure in any position. Now real games are not like that at all. Real life is not like that. Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do.” — John von Neumann
“I have tried to avoid long numerical computations, thereby following Riemann’s postulate that proofs should be given through ideas and not voluminous computations.” — David Hilbert
“I have constructed these [tables] anew, following absolutely no other reasoning than that which I have judged to be of maximum harmony.” — Erasmus Reinhold
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