Quotes about mathematics
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“Has anyone ever told you you’re sexy as hell when you’re mathematizing?”

Source: Dark Desires After Dusk

“It is now quite lawful for a Catholic woman to avoid pregnancy by a resort to mathematics, though she is still forbidden to resort to physics and chemistry.”

H.L. Mencken (1880–1956) American journalist and writer

Law

“Anyone who cannot cope with mathematics is not fully human. At best, he is a tolerable subhuman who has learned to wear his shoes, bathe, and not make messes in the house.”

Robert A. Heinlein (1907–1988) American science fiction author

Shoe, Learning, Housing

“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

Letter to high school student Barbara Lee Wilson (7 January 1943), Einstein Archives 42-606
1940s

“Sex is mathematics. Individuality no longer an issue. What does intelligence signify? Define reason. Desire - meaningless. Intellect is not a cure. Justice is dead.”

Bret Easton Ellis (1964) American novelist

Justice, Sex, Intelligence, Dead

“Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth.”

Brian Greene (1963) American physicist

Source: The Fabric of the Cosmos: Space, Time, and the Texture of Reality

Truth

“The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

Problem

“An a priori decision to eliminate spiritual intelligence from consideration is no more justifiable than a decision to admit it by fiat or on faith. After all, once one includes the understanding of the personal realm within a study of intelligence, such human proclivities as the spiritual must legitimately be considered. There certainly are no easy grounds for a decision, but several other intelligences deal with phenomena other than sheer physical matter. If the abstract realm of mathematics constitutes a reasonable area of intelligence (and few would challenge that judgment), why not the abstract realm of the spiritual?”

Howard Gardner (1943) American developmental psychologist

Source: Intelligence reframed: Multiple intelligences for the 21st century, 1999, p. 51

Faith, Intelligence, Understanding, Decision

“I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.”

Andrew Wiles (1953) British mathematician

Nova Interview

Love, Childhood

“This essential coalition between royal military power and often dubious supernatural authority anticipated a similar alliance between the scientists and mathematical games theorists with the higher agents of government today, and was subject to similar corruptions, miscalculations, and hallucinations.”

Lewis Mumford book The Myth of the Machine

pg 176
The Myth of the Machine (1967-1970), Technics and Human Development (1967)

Game

“Mathematics because of its nature and structure is peculiarly fitted for high school instruction [Gymnasiallehrfach]. Especially the higher mathematics, even if presented only in its elements, combines within itself all those qualities which are demanded of a secondary subject. It engages, it fructifies, it quickens, compels attention, is as circumspect as inventive, induces courage and self-confidence as well as modesty and submission to truth. It yields the essence and kernel of all things, is brief in form and overflows with its wealth of content. It discloses the depth and breadth of the law and spiritual element behind the surface of phenomena; it impels from point to point and carries within itself the incentive toward progress; it stimulates the artistic perception, good taste in judgment and execution, as well as the scientific comprehension of things. Mathematics, therefore, above all other subjects, makes the student lust after knowledge, fills him, as it were, with a longing to fathom the cause of things and to employ his own powers independently; it collects his mental forces and concentrates them on a single point and thus awakens the spirit of individual inquiry, self-confidence and the joy of doing; it fascinates because of the view-points which it offers and creates certainty and assurance, owing to the universal validity of its methods. Thus, both what he receives and what he himself contributes toward the proper conception and solution of a problem, combine to mature the student and to make him skillful, to lead him away from the surface of things and to exercise him in the perception of their essence. A student thus prepared thirsts after knowledge and is ready for the university and its sciences. Thus it appears, that higher mathematics is the best guide to philosophy and to the philosophic conception of the world (considered as a self-contained whole) and of one’s own being.”

Christian Heinrich von Dillmann (1829–1899) German educationist

Source: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 40.

Truth, World, School, Law

“In mathematics, it's not a game where the fastest wins. But rather, it's more like who can see farther, who can see deeper. That's the one who achieves more.”

Edward Frenkel (1968) mathematician working in representation theory, algebraic geometry, and mathematical physics

Are Mathematicians Past Their Prime at 35? http://www.massey.ac.nz/~rmclachl/overthehill.html

Game

“This new quantum mechanics promised to explain all of chemistry. And though I felt an exuberance at this, I felt a certain threat, too. “Chemistry,” wrote Crookes, “will be established upon an entirely new basis…. We shall be set free from the need for experiment, knowing a priori what the result of each and every experiment must be.” I was not sure I liked the sound of this. Did this mean that chemists of the future (if they existed) would never actually need to handle a chemical; might never see the colors of vanadium salts, never smell a hydrogen selenide, never admire the form of a crystal; might live in a colorless, scentless, mathematical world? This, for me, seemed and awful prospect, for I, at least, needed to smell and touch and feel, to place myself, my senses, in the middle of the perceptual world.”

Oliver Sacks book Uncle Tungsten

Source: Uncle Tungsten (2001), pp. 312–313

World, Color, Feeling, Sense

“I've played Bach since I was a little girl. I can't let a day go by without playing him. He's so witty and secretive and funny and mathematical and brilliant.”

Joanna MacGregor (1959) British musician

The Independent, 23/06/2003
Childhood

Secret, Girl

“If you refuse to study anatomy, the arts of drawing and perspective, the mathematics of aesthetics, and the science of color, let me tell you that this is more a sign of laziness than of genius.”

Salvador Dalí (1904–1989) Spanish artist

Source: Quotes of Salvador Dali, 1961 - 1970, Diary of a Genius (1964), p. 81

Art, Color, Study, Science

“The investigation of the form and brightness of the rings or rays surrounding the image of a star as seen in a good telescope, when a diaphragm bounded by a rectilinear contour is placed upon the object-glass, though sometimes tedious is never difficult. The expressions which it is necessary to integrate are always sines and cosines of multiples of the independent variable, and the only trouble consists in taking properly the limits of integration. Several cases of this problem have been completely worked out, and the result, in every instance, has been entirely in accordance with observation. These experiments… have seldom been made except by those whose immediate object was to illustrate the undulatory theory of light. There is however a case of a somewhat different kind; which in practice recurs perpetually, and which in theory requires for its complete investigation the value of a more difficult integral; I mean the usual case of an object-glass with a circular aperture. The desire of submitting to mathematical investigation every optical phænomenon of frequent occurrence has induced me to procure the computation of the numerical values of the integral that presents itself in this inquiry: and I now beg leave to lay before the Society the calculated table, with a few remarks upon its application.”

George Biddell Airy (1801–1892) English mathematician and astronomer

Star, Problem, Light

“To appreciate the nature of fractals, recall Galileo's splendid manifesto that "Philosophy is written in the language of mathematics and its characters are triangles, circles and other geometric figures, without which one wanders about in a dark labyrinth." Observe that circles, ellipses, and parabolas are very smooth shapes and that a triangle has a small number of points of irregularity. Galileo was absolutely right to assert that in science those shapes are necessary. But they have turned out not to be sufficient, "merely" because most of the world is of infinitely great roughness and complexity. However, the infinite sea of complexity includes two islands: one of Euclidean simplicity, and also a second of relative simplicity in which roughness is present, but is the same at all scales.”

Benoît Mandelbrot (1924–2010) Polish-born, French and American mathematician

A Theory of Roughness (2004)

World, Nature, Science, Sea

“The calculus is to mathematics no more than what experiment is to physics, and all the truths produced solely by the calculus can be treated as truths of experiment. The sciences must proceed to first causes, above all mathematics where one cannot assume, as in physics, principles that are unknown to us. For there is in mathematics, so to speak, only what we have placed there… If, however, mathematics always has some essential obscurity that one cannot dissipate, it will lie, uniquely, I think, in the direction of the infinite; it is in that direction that mathematics touches on physics, on the innermost nature of bodies about which we know little.”

Bernard Le Bovier de Fontenelle (1657–1757) French writer, satirist and philosopher of enlightenment

Elements de la géométrie de l'infini (1727) as quoted by Amir R. Alexander, Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (2002) citing Michael S. Mahoney, "Infinitesimals and Transcendent Relations: The Mathematics of Motion in the Late Seventeenth Century" in Reappraisals of the Scientific Revolution, ed. David C. Lindberg, Robert S. Westman (1990)

Truth, Lie, Nature, Thinking

“To the pure geometer the radius of curvature is an incidental characteristic — like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

The Expanding Universe. (1933) Ch. IV The Universe and the Atom

Cats

“Only an unashamed dogmatist would dare to assert that the issue has finally been resolved now, in favor of the view that, outside logic or mathematics, the method of modern science is the only method to employ in seeking knowledge. The dogmatist who made this assertion would have to be more than ashamed. He would have to blind himself to the fact that his own assertion was not established by the experimental method, nor made as an indisputable conclusion of mathematical reasoning or of purely logical analysis.”

Robert Maynard Hutchins (1899–1977) philosopher and university president

Great Books: The Foundation of a Liberal Education (1954)

Knowledge, Science

“The signs on Bell’s door read “J. Bell” and “M. Bell.” I knocked and was invited in by Bell. He looked about the same as he had the last time I saw him, a couple of years ago. He has long, neatly combed red hair and a pointed beard, which give him a somewhat Shavian figura. On one wall of the office is a photograph of Bell with something that looks like a halo behind his head, and his expression in the photograph is mischievous. Theoretical physicists’ offices run the gamut from chaotic clutter to obsessive neatness; the Bells’ is somewhere in between. Bell invited me to sit down after warning me that the “visitor’s chair” tilted backward at unexpected angles. When I had mastered it, and had a chance to look around, the first thing that struck me was the absence of Mary. “Mary,” said Bell, with a note of some disbelief in his voice, “has retired.” This, it turned out, had occurred not long before my visit. “She will not look at any mathematics now. I hope she comes back,” he went on almost plaintively; “I need her. We are doing several problems together.” In recent years, the Bells have been studying new quantum mechanical effects that will become relevant for the generation of particle accelerators that will perhaps succeed the LEP. Bell began his career as a professional physicist by designing accelerators, and Mary has spent her entire career in accelerator design. A couple of years ago Bell, like the rest of the members of CERN theory division, was asked to list his physics speciality. Among the more “conventional” entries in the division such as “super strings,” “weak interactions,” “cosmology,” and the like, Bell’s read “quantum engineering.””

Jeremy Bernstein (1929) American physicist

Quantum Profiles (1991), John Stewart Bell: Quantum Engineer

Hope, Problem, Study, Chance

“To be perfectly ignorant in all the Terms of them is only tolerable in those, who think their Tongues of as little Use to them, as generally their Understandings are. Those whom Necessity has obliged to get their Bread by Manual Industry, where some Degree of Art is required to go along with it, and who have had some Insight into these Studies, have very often found Advantages from them sufficient to reward the Pains they were at in acquiring them. And whatever may have been imputed (how justly I'm not now to determine) to some other Studies, under the Notion of Insignificancy and Loss of Time; yet these, I believe, never caused Repentance in any, except it was for their Remissness in the Prosecution of them. And though Plato's Censure, that those who did not understand the 117 Prop. of the 10th Element, ought not to be ranked among Rational Creatures, wax unreasonable and unjust: Yet to give a Man the Character of Universal Learning that is destitute of a competent Knowledge in the Mathematics, is no less so.”

Jacques Ozanam (1640–1718) French mathematician

Preface
A Mathematical Dictionary: Or; A Compendious Explication of All Mathematical Terms, 1702

Pain, Art, Understanding, Knowledge

“Everything is so arranged that the blind logic of mathematics executes the will of the most enlightened and free Mind.”

Pierre Louis Maupertuis (1698–1759) French mathematician, philosopher and man of letters

Les Loix du Mouvement et du Repos, déduites d'un Principe Métaphysique (1746)

“In this world, everything has a pulse or a vibration. This sound is unique to each living or non-living thing and in itself creates a music that no-one can hear. I believe that this has a very powerful resonance with, and a deep effect on, our lives. What would happen if we took this further and applied it to bigger things, more powerful things; like an entire solar system or galaxy say, what would that sound like?
Musica Universalis is the ancient theory that every celestial body, the sun, the moon and the stars, has an inner music. This is a harmonic and mathematical concept derived from the movements of the planets in the solar system. The music created is inaudible to the human ear.
Music of the Spheres is my interpretation of this theory. Every planet and every star; the whole universe has music within it that no-one can hear. This is what it would sound like if it was set free. This is Music of the Spheres.”

Mike Oldfield (1953) English musician, multi-instrumentalist

from the introduction to Music of the Spheres

World, Music, Star, Universe

“We shall see that the mathematical treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.”

James Clerk Maxwell book A Treatise on Electricity and Magnetism

A Treatise on Electricity and Magnetism (1873), §36.

“The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. …The conic sections, invented in an attempt to solve the problem of doubling the alter of an oracle, ended by becoming the orbits followed by the planets… The imaginary magnitudes invented by Cardan and Bombelli describe… the characteristic features of alternating currents. The absolute differential calculus, which originated as a fantasy of Reimann, became the mathematical model for the theory of Relativity. And the matrices which were a complete abstraction in the days of Cayley and Sylvester appear admirably adapted to the… quantum of the atom.”

Tobias Dantzig (1884–1956) American mathematician

Number: The Language of Science (1930)

Problem, Appearance

“The pretended rights of these theorists are all extremes: and in proportion as they are metaphysically true, they are morally and politically false. The rights of men are in a sort of middle, incapable of definition, but not impossible to be discerned. The rights of men in government are their advantages; and these are often in balances between differences of good; in compromises between good and evil, and sometimes between evil and evil. Political reason is a computing principle: adding, subtracting, multiplying, and dividing, morally and not metaphysically or mathematically, true moral denominations.”

Edmund Burke book Reflections on the Revolution in France

Reflections on the Revolution in France (1790)

Men, Evil, Falseness

“In a mathematical sense, space is manifoldness, or combination of numbers. Physical space is known as the 3-dimension system. There is the 4-dimension system, there is the 10-dimension system.”

Charles Proteus Steinmetz (1865–1923) Mathematician and electrical engineer

New York Times interview (1911)

Sense

“Fancy what a game at chess would be if all the chessmen had passions and intellects, more or less small and cunning; if you were not only uncertain about your adversary's men, but a little uncertain also about your own; if your knight could shuffle himself on to a new square by the sly; if your bishop, in disgust at your castling, could wheedle your pawns out of their places; and if your pawns, hating you because they are pawns, could make away from their appointed posts that you might get checkmate on a sudden. You might be the longest-headed of deducted reasoners, and yet you might be beaten by your own pawns. You would be especially likely to be beaten, if you depended arrogantly on your mathematical imagination, and regarded your passionate pieces with contempt.
Yet this imaginary chess is easy compared with the game a man has to play against his fellow-men with other fellow-men for his instruments. He thinks himself sagacious, perhaps, because he trusts no bond except that of self-interest; but the only self-interest he can safely rely on is what seems to be such to the mind he would use or govern. Can he ever be sure of knowing this?”

George Eliot book Felix Holt, the Radical

Start of Chapter 29 (at page 237)
Felix Holt, the Radical (1866)

Men, Hate, Imagination, Game

“I have in this treatise followed the mathematical method, if not with all strictness, at least imitatively, not in order, by a display of profundity, to procure a better reception for it, but because I believe such a system to be quite capable of it, and that perfection may in time be obtained by a cleverer hand, if stimulated by this sketch, mathematical investigators of nature should find it not unimportant to treat the metaphysical portion, which anyway cannot be got rid of, as a special fundamental department of general physics, and to bring it into unison with the mathematical doctrine of motion.”

Immanuel Kant book Metaphysical Foundations of Natural Science

Preface, Tr. Bax (1883)
Metaphysical Foundations of Natural Science (1786)

Nature, Time, Perfection

“This elegant generalization is mathematically very appealing; but physics means facing facts. You should take up case by case.”

Kariamanickam Srinivasa Krishnan (1898–1961) Indian physicist

One should not value elegant math above physical facts. As quoted by [Sundaram, R., 1998, December 10, K. S. Krishnan—the complete physicist, Current Science, 75, 11, 1263-1265]

“The essence of mathematics lies entirely in its freedom.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

Variant translation: The essence of mathematics is in its freedom.
From Kant to Hilbert (1996)

Freedom

“The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work”

James Whitbread Lee Glaisher (1848–1928) English mathematician and astronomer

Source: "Presidential Address British Association for the Advancement of Science," 1890, p. 467 : On the importance of broad training

School, Reality, Effort, Study

“Mathematical activity has taken the forms of a science, a philosophy and an art.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

Art, Science

“First Shakespeare sonnets seem meaningless; first Bach fugues, a bore; first differential equations, sheer torture. But training changes the nature of our spiritual experiences. In due course, contact with an obscurely beautiful poem, an elaborate piece of counterpoint or of mathematical reasoning, causes us to feel direct intuitions of beauty and significance. It is the same in the moral world.”

Aldous Huxley book Ends and Means

Ends and Means (1937)

World, Beauty, Feeling, Nature

“[T]he lectures… may be expected to remain tolerably commensurate to the state of the sciences for a much longer period; since, in investigations so intimately connected with mathematical principles, the essential improvements will always bear a very small proportion to the number of innovations. …the references, which it contains, are… sufficient to lead those, who may consult the passages quoted, to the works of every author of eminence that has treated of the respective subjects.”

Thomas Young (scientist) (1773–1829) English polymath

Preface
A Course of Lectures on Natural Philosophy and the Mechanical Arts (1807)

Quotes, Science

“The pragmatist regards any theory as a mere mathematical machine for generating numbers which he then compares with experiment. A pragmatist is concerned with results, not reality. The pragmatist refuses on principle to speculate about deep reality, such a concept being meaningless from his point of view. Pragmatism is an intelectually safe but ultimately sterile philosophy.”

Nick Herbert (1936) American physicist

Source: Quantum Reality - Beyond The New Physics, Chapter 9, Four Quantum Realities, p. 159

Reality

“Gravitational force is simple, and a thing by itself, as also are electric and magnetic forces as long as the electric and magnetic poles stand at rest. But as soon as motion comes into the picture, the whole situation is changed. Forces of new kinds come into play, for moving electric charges exert magnetic forces in addition to the electric forces they exert when at rest, while moving magnets exert electric forces in addition to the magnetic forces they exert while at rest. When the exact laws governing these intricate laws had been discovered by a great number of experimenters, Clerk Maxwell succeeded in expressing them in a mathematical form which was both simple and elegant.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

Law, Change

“Modern man lacks a unified conception of the world. He lives in a dual world: in his environment, which is naturally given to him, and, at the same time, in the world which since the beginning of the modern era has been created for him by sciences founded upon the principle that the laws of nature are, in essence, mathematical. The non-unity which has thus come to penetrate our entire life is the true source of the spiritual crisis we are going through today.”

Jan Patočka (1907–1977) Czech essayist and philosopher

Jan Patočka, cited in: Paul F.H. Lauxtermann, "Kant, Goethe, and the Mechanization of the World-Picture." in: Schopenhauer’s Broken World-View. Springer Netherlands, 2000. p.9

Life, World, Law, Nature

“Physics is essentially an intuitive and concrete science. Mathematics is only a means for expressing the laws that govern phenomena.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

From Lettre à Maurice Solvine, by A. Einstein (Gauthier-Villars: Paris 1956)
Attributed in posthumous publications, Albert Einstein: A guide for the perplexed (1979)

Law, Science

“Economics is the most human of sciences. It is the science of wants and frustrations. It is psychology subject to the abstract, amplifying forces of mathematics.”

Ian McDonald book The Dervish House

Source: The Dervish House (2010), Ch. 2, §8 (p. 72)

Science

“In mathematics, as in physics, so much depends on chance, on a propitious moment.”

Stanislaw Ulam (1909–1984) Polish-American mathematician

Source: Adventures of a Mathematician - Third Edition (1991), Chapter 5, Harvard Years, p. 95

Chance, Dependency

“Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic 31 geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence.”

James Joseph Sylvester (1814–1897) English mathematician

James Joseph Sylvester. "A Plea for the Mathematician, Nature," Vol. 1, p. 238; Collected Mathematical Papers, Vol. 2 (1908), pp. 655, 656.

Law, Idea, Effort, Light

“These computing machines had already been designed, and some built, by {[w|Vannevar Bush}}, Norbert Wiener, and others, and were almost ready-made for the job. These scientists, as well as others such as von Neumann, Shannon and Bigelow, were in a position to see that machines of an electronic kind were ideally suited to carry out the whole of the operations of range-finding and location without any human intervention whatever.
These electronic computing machines were already developed to a very high degree of efficiency for the solution of mathematical equations, and some technical difficulties had led to the suggestion that a process of scanning, similar to that used in television, might be incorporated into the computer. Another innovation was the use of binary notation rather than decimal notation as in the early Harvard Mark I computer.”

Frank Honywill George (1921–1997) British psychologist

Source: The Brain As A Computer (1962), p.18

“Chess is not Mathematics, where ten is always more than one; in chess the King with a pawn can beat opponent's King with all pieces if they are placed badly.”

Ashot Nadanian (1972) chess player

Interview at S'pore Chess News, 23 August 2010 http://www.singaporechessnews.com/interview_ashot_nadanian.html

“When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.”

John Von Neumann (1903–1957) Hungarian-American mathematician and polymath

As quoted in John von Neumann, 1903-1957 (1958) by John C. Oxtoby and B. J. Pettis, p. 128

“The goal of deriving all the phenomena of nature from a few basic physical laws and the axioms of mathematics had been set by Galileo…
In studying curvilinear motions on the earth Galileo had found the parabola to be the basic curve. In the heavens… Kepler… had found the ellipse to be the basic curve. Why this difference? …since parabola and ellipse are both conic sections there was the provocative suggestion that perhaps some physical law unified these related paths of motion. …
It has often happened in the history of mathematics and science that major problems remained outstanding… great minds… succeeded only in revealing the true difficulties… and in generating an atmosphere of dispair… Then a genius appeared… with ideas that seemed remarkably simple once propounded, clarified the entire situation, dispelled the confusion, restored order, and produced a new synthesis that embraced far more even than the phenomena under consideration. The genius who… picked up the torch of science dropped by Galileo, was Isaac Newton.”

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 225

Law, History, Idea, Nature

“I think it is a rule that men in business should not be taught other things. Any one will be almost sure to make money who has no other idea in his head. A college education, or intense study of abstract truth, will not enable a man to drive a bargain … The best politicians are not those who are deeply grounded in mathematical or in ethical science. Rules stand in the way of expediency. Many a man has been hindered from pushing his fortune in the world by an early cultivation of his moral sense.”

William Hazlitt (1778–1830) English writer

"On the Disadvantages of Intellectual Superiority" Table Talk: Essays On Men And Manners http://www.blupete.com/Literature/Essays/TableHazIV.htm (1821-1822)

Men, Money, Truth, World

“There is a certain way of searching for the truth in mathematics that Plato is said first to have discovered; Theon named it analysis, and defined it as the assumption of that which is sought as if it were admitted and working through its consequences to what is admitted to be true. This is opposed to synthesis, which is the assuming what is admitted and working through its consequences to arrive at and to understand that which is sought.”

François Viète (1540–1603) French mathematician

Source: In artem analyticem Isagoge (1591), Ch. 1 as quoted by Douglas M. Jesseph, Squaring the Circle: The War Between Hobbes and Wallis (1999) p. 225

Truth, Way, Search, Understanding

“Gordon Tullock, on the other hand, might be characterized as the somewhat cynical pragmatist, who set out to understand the world, not to change it. This side of Tullock is visible in his early paper on simple majority rule, and is perhaps most apparent in his work on rent seeking. These differences should not be pushed too far, however. Buchanan (1980) also contributed to the rent-seeking literature, and often has described public choice as “politics without romance.” One of the most dispiriting contributions to the public choice literature has to be Kenneth Arrow’s (1951) famous impossibility theorem. In a too little appreciated article, Tullock (1967b) demonstrated with the help of a somewhat torturous geometrical analysis, that the cycling that underlies the impossibility theorem is likely to be constrained to a rather small subset of Pareto-optimal outcomes, and thus Arrow’s theorem was “irrelevant,” a rather happy result, and one which anticipated work appearing more than a decade later on the uncovered set. In Chap. 10 of Toward a Mathematics of Politics, Tullock (1967a) engages in a bit of wishful thinking about constitutional design by describing how one could achieve an ideal form of proportional representation in a legislative body. He also was an early enthusiast of the potential for using a demand-revelation process to reveal individual preferences for public goods”

Dennis Mueller (1940) American economist

Tideman and Tullock 1976
James Buchanan, Gordon Tullock, and The Calculus (2012)

Happiness, World, Literature, Optimism

“There is no prophet which preaches the superpersonal God more plainly than mathematics.”

Paul Carus (1852–1919) American philosopher

"Reflections on Magic Squares" in The Monist, Vol. 16 (1906), p. 147
Variant: There is no science which teaches the harmonies of nature more clearly than mathematics.

God

“Yes. God makes the world using mathematics, and he has given us minds that can see it. We can discover the laws He used! It is a most beautiful thing to witness and understand! It's prayer. It's more than prayer, it's a sacrament, a kind of communion. An apprehension—an epiphany—it's seeing God, while still in this body and in this world! How blessed we are, to be able to experience God like that! Who would not devote their time to understanding more, to seeing deeper in God's manner of thinking about these things?”

Kim Stanley Robinson book Galileo's Dream

As quoted in John Clute, "Scores" http://www.strangehorizons.com/2010/20100118/clute-c.shtml, in Strange Horizons (18 January 2010) Galileo's Dream (2009)

God, World, Law, Beauty

“It is true that many of the problems with which professional philosophers deal do require quite a high level of abstract thought. However, the same is true of almost any intellectual pursuit: philosophy is no different in this respect from physics, literary criticism, computer programming, geology, mathematics, or history.”

Nigel Warburton (1962) British author and lecturer

Philosophy : the basics (Fifth Edition, 2013), Introduction

History, Problem

“The contemporary mathematical and symbolic logic is certainly very different from its classical predecessor, but they share the radical opposition to dialectical logic. In terms of this opposition, the old and the new formal logic express the same mode of thought. it is purged from that “negative” which loomed so large at the origins of logic and of philosophic thought — the experience of the denying, deceptive, falsifying power of the established reality. And with the elimination of this experience, the conceptual effort to sustain the tension between “is” and “ought”, and to subvert the established universe of discourse in the name of its own truth is likewise eliminated from all thought which is to be objective, exact, and scientific. For the scientific subversion of the immediate experience which establishes the truth of science as against that of immediate experience does not develop the concepts which carry in themselves the protest and the refusal. The new scientific truth which they oppose to the accepted one does not contain in itself the judgment that condemns the established reality. … In contrast, dialectical thought is and remains unscientific to the extent to which it is such judgment.”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), pp. 139-140

Truth, Reality, Effort, Universe

“The Society for General Systems Theory and its publication General Systems was a mixed bag. Few authors were actually doing research - they philosophized, and many prematurely resolved dilemmas by mathematical equations in a language poorly understood by the empirical investigator.”

Roy R. Grinker, Sr. (1900–1993) American psychiatrist and neurologist

Grinker (1976) in General systems. Vol.19, p. 57

“They [the true instructors of the people] will accustom children to the vegetable régime. The peoples living on vegetable foods, are, of all men, the handsomest, the most vigorous, the least exposed to diseases and to passions, and they whose lives last longest. Such, in Europe, are a large proportion of the Swiss. The greater part of the peasantry who, in every country, form the most vigorous portion of the people, eat very little flesh-meat. The Russians have multiplied periods of fasting and days of abstinence, from which even the soldiers are not exempt; and yet they resist all kinds of fatigues. The negroes, who undergo so many hard blows in our colonies, live upon manioc, potatoes, and maize alone. The Brahmins of India, who frequently reach the age of one hundred years, eat only vegetable foods. It was from the Pythagorean sect that issued Epaminondas, so celebrated by for his virtues, Archytas, by his genius for mathematics and mechanics; Milo of Crotona, by his strength of body. Pythagoras himself was the finest man of his time, and, without dispute, the most enlightened, since he was the father of philosophy amongst the Greeks. Inasmuch as the non-flesh diet introduces with many virtues and excludes none, it will be well to bring up the young upon it, since it has so happy an influence upon the beauty of the body and upon the tranquillity of the mind. This regimen prolongs childhood, and, by consequence, human life.”

Jacques-Henri Bernardin de Saint-Pierre (1737–1814) writer and botanist from France

Vœux d'un solitaire, pour servir de suite aux "Études de la nature", as quoted in The Ethics of Diet by Howard Williams (University of Illinois Press, 2003, p. 175 https://books.google.it/books?id=o9ugCcZ13BMC&pg=PA175)

Life, Men, Happiness, Children

“Wherefore it is impossible to succeed in comparing wealth of different eras or different nations. This, in political economy, like squaring the circle in mathematics, is impracticable, for want of a common mean or measure to go by.”

Jean-Baptiste Say (1767–1832) French economist and businessman

Source: A Treatise On Political Economy (Fourth Edition) (1832), Book I, On Production, Chapter XXI, Section VI, p. 244

Wealth

“The moon was still high. The sky’s transformations—the metamorphoses of its multitudinous vaults in ever more masterfully described configurations—were unending. Like a silver astrolabe, the sky had opened up that night its bewitching internal mechanism, exhibiting in endless cycles the gilded mathematics of its cogs and wheels.”

Bruno Schulz (1892–1942) Polish novelist and painter

“The Cinnamon Shops” http://www.schulzian.net/translation/shops/shops.htm His father, The heavens

Night

“For to pass by those Ancients, the wonderful Pythagoras, the sagacious Democritus, the divine Plato, the most subtle and very learned Aristotle, Men whom every Age has hitherto acknowledged as deservedly honored, as the greatest Philosophers, the Ring-leaders of Arts; in whose Judgments how much these Studies [mathematics] were esteemed, is abundantly proclaimed in History and confirmed by their famous Monuments, which are everywhere interspersed and bespangled with Mathematical Reasonings and Examples, as with so many Stars; and consequently anyone not in some Degree conversant in these Studies will in vain expect to understand, or unlock their hidden Meanings, without the Help of a Mathematical Key: For who can play well on Aristotle’s Instrument but with a Mathematical Quill; or not be altogether deaf to the Lessons of natural Philosophy, while ignorant of Geometry? Who void of (Geometry shall I say, or) Arithmetic can comprehend Plato’s 218 Socrates lisping with Children concerning Square Numbers; or can conceive Plato himself treating not only of the Universe, but the Polity of Commonwealths regulated by the Laws of Geometry, and formed according to a Mathematical Plan?”

Isaac Barrow (1630–1677) English Christian theologian, and mathematician

Source: Mathematical Lectures (1734), pp. 26-27

Men, Children, Age, Law

“The more advanced the sciences have become, the more they have tended to enter the domain of mathematics, which is a sort of center towards which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation.”

Adolphe Quetelet (1796–1874) Belgian astronomer, mathematician, statistician and sociologist

Edward Mailly, Essai sur la vie et les ouv rages de Quetelet in the Annuaire de Vacadimie royale des sciences des lettres et des beaux-arts de Belgique (1875) Vol. xli pp. 109-297 found also in "Conclusions" of Instructions populaires sur le calcul des probabilités p. 230

Science, Perfection

“The idea that a few people have about the gene being the target of selection is completely impractical; a gene is never visible to natural selection, and in the genotype, it is always in the context with other genes, and the interaction with those other genes make a particular gene either more favorable or less favorable. In fact, Dobzhanksy, for instance, worked quite a bit on so-called lethal chromosomes which are highly successful in one combination, and lethal in another. Therefore people like Dawkins in England who still think the gene is the target of selection are evidently wrong. In the 30s and 40s, it was widely accepted that genes were the target of selection, because that was the only way they could be made accessible to mathematics, but now we know that it is really the whole genotype of the individual, not the gene. Except for that slight revision, the basic Darwinian theory hasn't changed in the last 50 years”

Ernst Mayr (1904–2005) German-American Evolutionary Biologist

Part of the answer to the question "Where do you think Darwinism is going to go in the next 50 years?"
What evolution is: Talk with Ernst Mayr (2001)

People, Way, Idea, Nature

“Discovery in mathematics is not a matter of logic. It is rather the result of mysterious powers which no one understands, and in which unconscious recognition of beauty must play an important part. Out of an infinity of designs, a mathematician chooses one pattern for beauty's sake and pulls it down to earth.”

Marston Morse (1892–1977) American mathematician

Attributed in Princeton & Mathematics: A Notable Record, Chaplin, Virginia, Princeton Alumni Weekly, May 9, 1958 http://www.princeton.edu/~mudd/finding_aids/mathoral/pmcxpaw.htm,

Beauty, Understanding, Parting

“Yes," I continued, "I discovered this model recently and her style never fails to be mathematically perfect. She seems to come by it naturally. As if she were born resonant. I notice Japanese models tend to do this. Like I said, they seem to have resonance somewhere deep in their culture. But Yuri Nakagawa, she's the best I've ever seen. The best model, with the most powerful resonance. I need her to probe deeper into this profound mathematical instinct, which I call resonance.”

Alexei Maxim Russell (1976) Canadian writer

from Trueman Bradley - The Next Great Detective.

Nature, Perfection

“Mathematical programming assisted by electronic computers becomes the fundamental instrument of long-term economic planning, as well as of solving dynamic economic problems of a more limited scope. Here, the electronic computer does not replace the market. It fulfils a function which the market never was able to perform.”

Oskar R. Lange (1904–1965) Polish economist

"The computer and the market" (1967)

Problem

“MacUser: Which person do you most admire?
Jef Raskin: For what attribute? Once again you ask a question that linearises a complex matter. I can name many. Let's start with people named George: George Cantor for moving infinity out of philosophy into mathematics, George Washington for showing how a leader should relinquish power, and George Bernard Shaw for his humanity… Or we can do it by subject and admire Aristotle, Isaac Newton and Albert Einstein for their pulling from nature comprehensible laws; or Euclid, Gauss and Gödel for their contributions to mathematics; or people who have influenced me very directly, in which case I'd mention my very admirable parents and the teacher who taught me to be intellectually independent, L R Genise; or how about Claude Shannon without whose work on information theory I would have been lost.”

Jef Raskin (1943–2005) American computer scientist

MacUser interview (2004)

People, Law, Question, Nature

“Theorems often tell us complex truths about the simple things, but only rarely tell us simple truths about the complex ones. To believe otherwise is wishful thinking or "mathematics envy."”

Marvin Minsky (1927–2016) American cognitive scientist

Music, Mind, and Meaning (1981)

Truth, Thinking, Envy

“A man bringing himself, melody and mathematics into perfect and enviable proportions. / only more so, much more so.”

Peter Greenaway (1942) British film director

"The Eisenstein Song"
M is for Man, Music, and Mozart

Perfection

“I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce.”

Freeman Dyson (1923) theoretical physicist and mathematician

Missed Opportunities (1972)

Marriage, Past

“I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.”

George Boole (1815–1864) English mathematician, philosopher and logician

George Boole, " Solution of a Question in the Theory of Probabilities http://books.google.nl/books?id=9xtDAQAAIAAJ&pg=PA32" (30 November 1853) published in The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science‬‎ (January 1854), p. 32 1850s

Law, Question, Universe, Science

“If economic reality is actually so complex that it can only be described by complicated mathematical models that add epicycles to epicycles and externalities to externalities, then the reality should be simplified.”

Herman E. Daly (1938) American economist

Source: Steady-State Economics, 1977, p. 4

Reality

“Around 1650 I came across the mathematical writings of Torricelli, where among other things, he expounds the geometry of indivisibles of Cavalieri. …His method, as taught by Torricelli… was indeed all the more welcome to me because I do not know that anything of that kind was observed in the thinking of almost any mathematician I had previously met.”

John Wallis (1616–1703) English mathematician

Arithmetica Infinitorum (1656)

Thinking

“Mathematics, like music and poetry, is a creation of the mind; … the primary task of the mathematician, like that of any other artist, is to extend man's mental horizon by representation and interpretation.”

Graham Sutton (1903–1977) Welsh scientist

Mathematics in Action (1954) page 1

Music

“Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.”

Benoît Mandelbrot book The Fractal Geometry of Nature

The Fractal Geometry of Nature (1982)

World, Help

“Creation of absolutely the first rank — in philosophy, in music, in much of literature, in mathematics — continues to occur outside the American milieu. It is at once taken up and intelligently exploited, but the "motion of the spirit" has taken place elsewhere, amid the enervation of Europe, in the oppressive climate of Russia. There is, in a good deal of American intellectual, artistic production (recent paining may be a challenging exception) a characteristic near-greatness, a strength just below the best. Could it be that the United States is destined to be the "museum culture?"”

George Steiner (1929–2020) American writer

"Tomorrow".
In Bluebeard's Castle (1971)

Pain, Music, Intelligence, Literature

“I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypothesis was very well unlikely to be good economics: and I went more and more on the rules - (1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This last I do often.”

Alfred Marshall (1842–1924) British economist

Letter to A.L. Bowley, 27 February 1906, cited in: David L. Sills, Robert King Merton, Social Science Quotations: Who Said What, When, and Where http://books.google.com/books?id=WIKQbew5YKcC&pg=PA151 Transaction Publishers, 2000. p. 151.

Life, Feeling

“We do not discover mathematical truths; we remember them from our passages through this world outside our own.”

Ivar Ekeland (1944) French mathematician

Source: The Best of All Possible Worlds (2006), Chapter 1, Keeping The Beat, p. 6.

Truth, World

“The land of easy mathematics where he who works adds up and he who retires subtracts.”

Núria Añó (1973) Catalan writer novelist

2066. Beginning the age of correction

“During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Introductory p.2
A Budget of Paradoxes (1872)

Knowledge

“Upon Clifford's death the labour of revision and completion was entrusted to Mr. R. C. Rowe, then Professor of Pure Mathematics at University College, London. …On the sad death of Professor Rowe, in October 1884, I was requested… to take up the task of editing… For the latter half of Chapter III. and for the whole of Chapter IV. …I am alone responsible. Yet whatever there is in them of value I owe to Clifford; whatever is feeble or obscure is my own. …With Chapter V. my task has been by no means light. …Without any notice of mass or force it seemed impossible to close a discussion on motion; something I felt must be added. I have accordingly introduced a few pages on the laws of motion. I have since found that Clifford intended to write a concluding chapter on mass. How to express the laws of motion in a form of which Clifford would have approved was indeed an insoluble riddle to me, because I was unaware of his having written anything on the subject. I have accordingly expressed, although with great hesitation, my own views on the subject; these may be concisely described as a strong desire to see the terms matter and force, together with the ideas associated with them, entirely removed from scientific terminology—to reduce, in fact, all dynamic to kinematic. I should hardly have ventured to put forward these views had I not recently discovered that they have (allowing for certain minor differences) the weighty authority of Professor Mach, of Prag. But since writing these pages I have also been referred to a discourse delivered by Clifford at the Royal Institution in 1873, some account of which appeared in Nature, June 10, 1880. Therein it is stated that 'no mathematician can give any meaning to the language about matter, force, inertia used in current text-books of mechanics.”

William Kingdon Clifford (1845–1879) English mathematician and philosopher

This fragmentary account of the discourse undoubtedly proves that Clifford held on the categories of matter and force as clear and original ideas as on all subjects of which he has treated; only, alas! they have not been preserved.
Preface by Karl Pearson
The Common Sense of the Exact Sciences (1885)

Death, Books, Sadness, Law

“Many of the greatest masters of the mathematical sciences were first attracted to mathematical inquiry by problems relating to numbers, and no one can glance at the periodicals of the present day which contain questions for solution without noticing how singular a charm such problems still continue to exert. The interest in numbers seems implanted in the human mind, and it is a pity that it should not have freer scope in this country. The methods of the theory of numbers 271 are peculiar to itself, and are not readily acquired by a student whose mind has for years been familiarized with the very different treatment which is appropriate to the theory of continuous magnitude; it is therefore extremely desirable that some portion of the theory should be included in the ordinary course of mathematical instruction at our University. From the moment that Gauss, in his wonderful treatise of 1801, laid down the true lines of the theory, it entered upon a new day, and no one is likely to be able to do useful work in any part of the subject who is unacquainted with the principles and conceptions with which he endowed it.”

James Whitbread Lee Glaisher (1848–1928) English mathematician and astronomer

Source: "Presidential Address British Association for the Advancement of Science," 1890, p. 467 : On the theory of numbers

Question, Problem, Universe, Science

“The clash between reason and Portuguese experience. Hooykaas' starting point is the intellectual challenge which, from the early 15th century onward, was posed by the discoveries of the Portuguese mariners… There follows an array of fascinating accounts of, and quotations from, works by contemporary authors who were compelled to face as facts numerous phenomena the ancients had been quite sure could not possibly be observed because they were bound not to exist. Examples are Aristotle's denial that the tropics could be inhabited; Ptolemy's mathematically derived conviction that all dry land is confined to part of the Northern Hemisphere, and so on. …In Hooykaas' view we are witnessing here a birth of 'natural history' in the domain of the hard and given fact… The narrow world of sense-data to which the ancient natural philosophers had confined their all-too-rational speculations was now being blown to pieces. And this was not being done by fellow natural philosophers, but rather at the urging of scarcely literate sailors!”

Floris Cohen (1946) Dutch historian

Floris Cohen, The Scientific Revolution: A Historiographical Inquiry (1994)

World, History, Birth, Nature

“Do not mathematics and all sciences seem full of contradictions and impossibilities to the ignorant, which are all resolved and cleared to those that understand them?”

Richard Baxter (1615–1691) English Puritan church leader, poet, and hymn-writer

Reported in Josiah Hotchkiss Gilbert, Dictionary of Burning Words of Brilliant Writers (1895), p. 36.

Understanding, Science

“While studying antiaircraft fire control, Wiener may have conceived the idea of considering the operator as part of the steering mechanism and of applying to him such notions as feedback and stability, which had been devised for mechanical systems and electrical circuits. No doubt this kind of analogy had been operative in Wiener’s mathematical work from the beginning and sometimes had even been productive. As time passed, such flashes of insight were more consciously put to use in a sort of biological research for which Wiener consulted all kinds of people, except mathematicians, whether or not they had anything to do with it. Cybernetics, or Control and Communication in the Animal and the Machine (1948) is a rather eloquent report of these abortive attempts, in the sense that it shows there is not much to be reported. The value and influence of Cybernetics, and other publications of this kind, should not, however, be belittled. It has contributed to popularizing a way of thinking in communication theory terms, such as feedback, information, control, input, output, stability, homeostasis, prediction, and filtering. On the other hand, it also has contributed to spreading mistaken ideas of what mathematics really means”

Hans Freudenthal (1905–1990) Dutch mathematician

Norbert Wiener (2008)

People, Way, Communication, Idea

“The study of Euler's works will remain the best school for the different fields of mathematics and nothing else can replace it.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

As quoted by Louise Grinstein, Sally I. Lipsey, Encyclopedia of Mathematics Education (2001) p. 235.

School, Study

“I learned later that economic reasoning was not just mathematics and could be applied to a wide variety of social problems. Now, I think that no forms of social interaction—including religion, love, crime, and fertility choice—are immune from the power of economic reasoning. Hence, even widely held beliefs—for example, that beauty is an illegitimate credential of a worker or that democracy is important for economic growth—are not sacred truths and are subject to analysis.”

Robert Barro (1944) American classical macroeconomist

Source: Nothing Is Sacred (2002), p. xiii

Love, Truth, Religion, Beauty

“Everyone is sure of this [that errors are normally distributed], Mr. Lippman told me one day, since the experimentalists believe that it is a mathematical theorem, and the mathematicians that it is an experimentally determined fact.”

Henri Poincaré (1854–1912) French mathematician, physicist, engineer, and philosopher of science

Tout le monde y croit cependant, me disait un jour M. Lippmann, car les expérimentateurs s'imaginent que c'est un théorème de mathématiques, et les mathématiciens que c'est un fait expérimental.
Calcul des probabilités (2nd ed., 1912), p. 171

Error

“We find that at present the human race is divided into one wise man, nine knaves, and ninety fools out of every hundred. That is, by an optimistic observer. The nine knaves assemble themselves under the banner of the most knavish among them, and become 'politicians'; the wise man stands out, because he knows himself to be hopelessly outnumbered, and devotes himself to poetry, mathematics, or philosophy; while the ninety fools plod off under the banners of the nine villains, according to fancy, into the labyrinths of chicanery, malice and warfare. It is pleasant to have command, observes Sancho Panza, even over a flock of sheep, and that is why the politicians raise their banners. It is, moreover, the same thing for the sheep whatever the banner. If it is democracy, then the nine knaves will become members of parliament; if fascism, they will become party leaders; if communism, commissars. Nothing will be different, except the name. The fools will be still fools, the knaves still leaders, the results still exploitation. As for the wise man, his lot will be much the same under any ideology. Under democracy he will be encouraged to starve to death in a garret, under fascism he will be put in a concentration camp, under communism he will be liquidated.”

T. H. White book The Book of Merlyn

The Book of Merlyn (1977)

Death, Fools, Democracy, Communication

“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 Dantzig (1914–2005) American mathematician

Source: Linear programming and extensions (1963), p. 2

“There is only one other survey, Datta and Singh’s 1938 History of Hindu Mathematics, recently reprinted but very hard to obtain in the West (I found a copy in a small specialized bookstore in Chennai). They describe in some detail the Indian work in arithmetic and algebra and, supplemented by the equally hard to find Geometry in Ancient and Medieval India by Sarasvati Amma (1979), one can get an overview of most topics.”

David Mumford (1937) American mathematician

[David Mumford, Book Review, Notices of the AMS, March 2010, 57, 3, http://www.ams.org/notices/201003/rtx100300385p.pdf]

History

“At the present time it is of course quite customary for physicists to trespass on chemical ground, for mathematicians to do excellent work in physics, and for physicists to develop new mathematical procedures… Trespassing is one of the most successful techniques in science.”

Wolfgang Köhler (1887–1967) German-American psychologist and phenomenologist

Source: Dynamics in Psychology, 1940, p. 116

Science, Time, Success

“During this century mathematics has been transformed…”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“Five hundred years ago, when faced with an eclipse, many of us would have believed it was the work of an angry god. But as we've unearthed the language of the Code, we've discovered that the apparent mysteries of our world can be understood without invoking the supernatural. And this for me is what's so remarkable. That despite the incredible complexity of the world we live in, it can all, ultimately, be explained by numbers. Just like the orbit of the planets, life too follows a pattern. And it can all be reduced to cause and effect. In the end, even the flip of a coin is determined by how fast it's spinning and how long it takes to hit the ground. The ultimate symbol of chance isn't random at all. It only appears that way. When we don't understand the Code, the only way we can make sense of our world is to make up stories. But the truth is far more extraordinary. Everything has mathematics at its heart. When everything is stripped away all that remains is the Code.”

Marcus du Sautoy (1965) British professor of mathematics

Conclusion in BBC's The Code, episode 3.

Life, God, Truth, World

“It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, “Economics is what economists do,” and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1970s, Economics As a Science, 1970, p. 97

Parting

“It strikes me that mathematical writing is similar to using a language. To be understood you have to follow some grammatical rules. However, in our case, nobody has taken the trouble of writing down the grammar; we get it as a baby does from parents, by imitation of others. Some mathematicians have a good ear; some not (and some prefer the slangy expressions such as 'iff'). That's life.”

Jean-Pierre Serre (1926) French mathematician

Jean-Pierre Serre in letter to David Goss, quoted in: David Goss. " Some Hints on Mathematical Style https://people.math.osu.edu/goss.3/hint.pdf," at people.math.osu.edu, accessed 08.2016

Life, Parent, Baby

“Throughout the nineteenth century, apart from the division in theoretical sciences and arts, classifiers attempted to divide the sciences into two groups. Already they had before them the examples of Francis Bacon (speculative and descriptive) and Hobbes (quantitative and qualitative). For Coleridge, the sciences were either pure (Grammar, Logic, Rhetoric, Mathematics, Metaphysics) or mixed. Arthur Schopenhauer’s similar groups were called pure and empirical, Wilhelm Wundt in 1887 called them formal and empirical, Globot mathematical and theoretical, and the St. Louis Congress of Arts and Sciences (1904) normative and physical.”

Brian Campbell Vickery (1918–2009) British information theorist

Karl Pearson made similar division of the sciences into abstract and concrete
Source: Classification and indexing in science (1958), Other Chapters, p. 154.

Art, Science

“Our mathematical concepts, structures, ideas have been invented as tools to organise the phenomena of the physical, social and mental world. Phenomenology of a mathematical concept, structure, or idea means describing it in its relation to the phenomena for which it was created, and to which it has extended in the learning process of mankind, and, as far as this description is concerned with the learning process of the young generation, it is didactical phenomenology, a way to show the teacher the places where the learner might step into the learning process of mankind.”

Hans Freudenthal (1905–1990) Dutch mathematician

Source: The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961), p. ix

World, Way, Idea, Learning

“In our time mathematics has penetrated into economics so solidly, widely and variously, and the chosen theme is connected with such a variety of facts and problems that it brings us to cite the words of which are very popular in our country: "One can not embrace the unembraceable". The appropriateness of this wise sentence is not diminished by the fact that the great thinker is only a pen-name.”

Leonid Kantorovich (1912–1986) Russian mathematician

Lead paragraph
"Mathematics in Economics: Achievements, Difficulties, Perspectives," 1975

Problem, Time, Country

“Augustus Fagan, Esquire, Ph. D., Llanabba Castle, N. Wales, requires immediately junior assistant to teach Classics and English to University Standard with subsidiary Mathematics, German and French. Experience essential; first-class games essential…
'Might have been made for you,' said Mr Levy.
'But I don't know a word of German, I've had no experience, I've got no testimonials, and I can't play cricket.'
'It doesn't do to be too modest,' said Mr Levy. 'It's wonderful what one can teach when one tries..”

Evelyn Waugh book Decline and Fall

Part One, Chapter One
Decline and Fall (1928)

Game, Universe, Parting

“Mathematics is merely a convenient tool by which the designer determines the physical proportions and details of a planned structure in order to transform his ideas… to the actuality of a finished structure.”

Eduardo Torroja (1899–1961) Spanish architect

p, 125
Philosophy of Structures (1958)

Idea

“I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.”

Charles Darwin (1809–1882) British naturalist, author of "On the origin of species, by means of natural selection"

volume I, chapter II: "Autobiography", page 46 http://darwin-online.org.uk/content/frameset?pageseq=64&itemID=F1452.1&viewtype=image The Life and Letters of Charles Darwin (1887)

Men, Understanding, Sense

Quotes about mathematics page 3

Quotes about mathematics
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