Quotes about mathematics
page 8

"King of Sweden" presenting "Professor Mortimer" with the 2056 Nobel prize, in "Simon Conway Morris forecasts the future" at NewScientist.com (15 November 2006) http://www.newscientist.com/channel/opinion/science-forecasts/dn10477-simon-conway-morris-forecasts-the-future.html.

Way, Imagination, Spring, Idea

“Business is the highest evolution of consciousness, responsibility, and morality. No other living organism is even remotely able to function on a business level. The essences of business are honesty, effort, responsibility, integration, abstraction, conceptualization, objectivity, long-range planning, discipline, thought, control. Business creates essentially every major human value, ranging from the development of consciousness, language, mathematics, the arts, up to the electronic and biogenic revolutions.”

Frank R. Wallace (1932–2006) Philosopher, author, entrepreneur

Wallace, Frank. The Neo-Tech Discovery. Appendix F http://www.neo-tech.com/discovery/appendixf.html

Art, Business, Effort

“A trembling and some laughter, / a squirt of pee, a spit, / whispers of the heart, / a smell, / the drift to sleep, / pursuit by Gods, / exposure of the bum, / mathematics …”

Peter Greenaway (1942) British film director

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

God, Laughter, Sleep, Heart

“As the natural sciences have developed to encompass increasingly complex systems, scientific rationality has become ever more statistical, or probabilistic. The deterministic classical mechanics of the enlightenment was revolutionized by the near-equilibrium statistical mechanics of late 19th century atomists, by quantum mechanics in the early 20th century, and by the far-from-equilibrium complexity theorists of the later 20th century. Mathematical neo-Darwinism, information theory, and quantitative social sciences compounded the trend. Forces, objects, and natural types were progressively dissolved into statistical distributions: heterogeneous clouds, entropy deviations, wave functions, gene frequencies, noise-signal ratios and redundancies, dissipative structures, and complex systems at the edge of chaos.”

Nick Land (1962) British philosopher

"Statistical Mentality" https://web.archive.org/web/20110718052233/http://www.thatsmags.com/shanghai/index.php/article/detail/522/statistical-mentality (2011)

Nature, Science

“[Mathematics were] scarce looked upon as Academical studies but rather Mechanical… And among more than two hundred students (at that time) in our college, I do not know of any two (perhaps not any) who had more of Mathematicks than I, (if so much) which was then but little; and but very few, in that whole university. For the study of Mathematicks was at that time more cultivated in London than in the universities.”

John Wallis (1616–1703) English mathematician

(1635) as quoted by W. W. Rouse Ball, A History of the Study of Mathematics at Cambridge https://books.google.com/books?id=Pl32YkKFIhsC (1889) pp. 41-42.

Study, Universe, Time

“Do not let us imagine that discoveries in the world of the higher mathematics, of physics or biology are going to remove or even reduce our difficulties on the moral plane…The realm of morals is a world neither of quantity nor of chemical action. It is a world of values. It is precisely these values of right and wrong, of good and evil, of honesty and courage, which matter supremely for religion and national life…I am not despising science. I am only suggesting that moral values, eternal in their quality, transient in their form and application, are the foundation of a country's greatness. If moral values flourish in our common life all will be well with the nation.”

Stanley Baldwin (1867–1947) Former Prime Minister of the United Kingdom

Speech to the annual assembly of the Congregational Union, London (12 May 1931), published in This Torch of Freedom (1935), pp. 86-87.
1931

Life, World, Religion, Imagination

“Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.”

Kenneth E. Iverson (1920–2004) Canadian computer scientist

§0
Notation as a Tool of Thought (1979)

Way

“In 1946, a Macy Foundation interdisciplinary conference was organized to use the model provided by "feedback systems," honorifically referred to in earlier conferences as "teleological mechanisms," and later as "cybernetics," with the expectation that this model would provide a group of sciences with useful mathematical tools and, simultaneously, would serve as a form of cross-disciplinary communication. Out of the deliberations of this group came a whole series of fruitful developments of a very high order. Kurt Lewin (who died in 1947) took away from the first meeting the term "feedback". He suggested ways in which group processes, which he and his students were studying in a highly disciplined, rigorous way, could be improved by a "feedback process," as when, for example, a group was periodically given a report on the success or failure of its particular operations.”

Margaret Mead (1901–1978) American anthropologist

Source: 1960s, Continuities in Cultural Evolution (1964), p. 272-273

Way, Communication, Failure, Study

“In this branch of study exactness is an essential feature; and mathematical difficulties must not be shrunk from when the nature of the subject leads to them.”

William John Macquorn Rankine (1820–1872) civil engineer

p, 125
"On the Harmony of Theory and Practice in Mechanics" (Jan. 3, 1856)

Nature, Study

“It is with Bernhard Riemann's work that we finally have the mathematical glasses to explore such worlds of the mind. And now my journey through the abstract world of 20th century mathematics has revealed that maths is the true language that the universe is written in. They key to understanding the world around us. Mathematicians aren't motivated by money and material gain, or even by practical applications of their work. For us it's the glory of solving one of the great unsolved problems that have outwitted previous generations of mathematicians. David Hilbert was right; it’s the unsolved problems of mathematics which make it a living subject. Which obsess each new generation of mathematicians. Despite all the things we've discovered over the last 7 millennia, there are still many things we don't understand. And its Hilbert’s call of "We must know, we will know" which drives mathematics.”

Marcus du Sautoy (1965) British professor of mathematics

Conclusion in BBC's The Story of Maths, episode 4

Money, World, Motivation, Understanding

“Why do I think that Turing's paper "On computable numbers" is so important? Well, in my opinion it's a paper on epistemology, because we only understand something if we can program it, as I will explain in more detail later. And it's a paper on physics, because what we can actually compute depends on the laws of physics in our particular universe and distinguishes it from other possible universes. And it's a paper on ontology, because it shows that some real numbers are uncomputable, which I shall argue calls into question their very existence, their mathematical and physical existence.”

Gregory Chaitin (1947) Argentinian mathematician and computer scientist

"Epistemology as information theory: From Leibniz to Omega." https://arxiv.org/abs/math/0506552 arXiv preprint math/0506552 (2005). p. 3

Law, Understanding, Question, Thinking

“The laws of mathematics are stronger than the laws of man.”

John Twelve Hawks book Spark

Spark (2014)

Law

“There are not wanting, even to-day, chemists who advocate "purely chemical" methods in chemistry, and cannot appreciate the value of physical evidence in conjunction with mathematical calculations. We can only hope that their number is decreasing exponentially with time.”

J. R. Partington (1886–1965) British chemist

Introduction
Higher Mathematics for Chemical Students (1911)

Hope, Time

“The invention of logarithms and the calculation of the earlier tables form a very striking episode in the history of exact science, and, with the exception of the Principia of Newton, there is no mathematical work published in the country which has produced such important consequences, or to which so much interest attaches as to Napier’s Descriptio.”

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

Source: Encyclopedia Britannica, 9th Edition; Article “Logarithms.”; Reported in Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book, (1914) : On the invention of logarithms

History, Science, Country

“Over and above the specific theorems created by men such as Desargues, Pascal and La Hire, several new ideas and outlooks were beginning to appear. The first is the idea of continuous change of a mathematical entity from one state to another… [i. e., of a] a geometrical figure. It was Kepler, in his Astronomiae Optica of 1604, who first seemed to grasp the fact that parabola, ellipse, hyperbola, circle, and the degenerate conic consisting of a pair of lines are continuously derivable from each other…. The notion of a continuous change in a figure was also employed by Pascal. He allowed two consecutive vertices of his hexagon to approach each other so that the figure became a pentagon. In the same manner he passed from pentagons to quadrilaterals.
The second idea to emerge from the work of the projective geometers is that of transformation and invariance. To project a figure from some point and then take a section of that projection is to transform the figure to a new one. The properties… of interest are those that remain invariant under transformation. Other geometers of the seventeenth century, for example, Gregory of St. Vincent… and Newton, introduced transformations other than projection and section.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), pp. 298-299

Men, Idea, Appearance, Change

“When Physicists speak of "beauty" in their theories, they really mean that their theory possesses at least two essential features: 1. A unifying symmetry 2. The ability to explain vast amounts of experimental data with the most economical mathematical expressions.”

Michio Kaku book Hyperspace

Source: Hyperspace (1995), Ch.5 Quantum Heresy

Beauty

“What we, thanks to Jung, call "synchronicity" (coincidence on steroids), Buddhists have long known as "the interpenetration of realities." Whether it's a natural law of sorts or simply evidence of mathematical inevitability (an infinite number of monkeys locked up with an infinite number of typewriters eventually producing Hamlet, not to mention Tarzan of the Apes), it seems to be as real as it is eerie.”

Tom Robbins (1932) American writer

The Syntax of Sorcery (2012)

Law, Nature, Reality

“My decision to leave applied mathematics for economics was in part tied to the widely-held popular belief in the 1960s that macroeconomics had made fundamental inroads into controlling business cycles and stopping dysfunctional unemployment and inflation.”

Robert C. Merton (1944) American economist

Robert C. Merton, " Robert C. Merton - Biographical http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1997/merton-bio.html," at Nobelprize.org, 1997

Business, Decision, Parting

“Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw hi the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.”

Immanuel Kant book Critique of Pure Reason

Preface to the Second Edition [Tr. F. Max Müller], (New York, 1900), p. 690; as cited in: Robert Edouard Moritz, Memorabilia mathematica or, The philomath's quotation-book https://openlibrary.org/books/OL14022383M/Memorabilia_mathematica, Published 1914. p. 10 Critique of Pure Reason (1781; 1787)

Happiness, People, Hope, Way

“Without the aid of these, then, it is not possible to deal accurately with the forms of being nor to discover the truth in things, knowledge of which is wisdom, and evidently not even to philosophize properly, for "just as painting contributes to the menial arts toward correctness of theory, so in truth lines, numbers, harmonic intervals, and the revolutions of circles bear aid to the learning of the doctrines of wisdom," says the Pythagorean Androcydes. Likewise Archytas of Tarentum, at the beginning of… On Harmony, says… in about these words: "It seems to me that they do well to study mathematics, and it is not at all strange that they have correct knowledge about each thing, what it is. For if they knew rightly the nature of the whole, they were also likely to see well what is the nature of the parts. About geometry, indeed, and arithmetic and astronomy, they have handed down to us a clear understanding, and not least also about music. For these seem to be sister sciences; for they deal with sister subjects, the first two forms of being."”

Nicomachus (60–120) Ancient Greek mathematician

Nicomachus of Gerasa: Introduction to Arithmetic (1926)

Wisdom, Truth, Art, Music

“Modernity needs to understand that being rich and becoming rich are not mathematically, personally, socially, and ethically the same thing.”

Nassim Nicholas Taleb book The Bed of Procrustes: Philosophical and Practical Aphorisms

Source: The Bed of Procrustes: Philosophical and Practical Aphorisms (2010), p. 22

Understanding, Personality

“There is no agreed upon definition of mathematics, but there is widespread agreement that the essence of mathematics is extension, generalization, and abstraction… [which] often bring increased confidence in the results of a specific application, as well as new viewpoints.”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

Confidence

“Even measured by Wiener's standards Cybernetics is a badly organised work — a collection of misprints, wrong mathematical statements, mistaken formulas, splendid but unrelated ideas, and logical absurdities. It is sad that this work earned Wiener the greater part of his public renown, but this is an afterthought. At that time mathematical readers were more fascinated by the richness of its ideas than by its shortcomings.”

Hans Freudenthal (1905–1990) Dutch mathematician

Norbert Wiener (2008)

Sadness, Idea, Time, Parting

“That was what drew him to mathematics. Not because it was rarefied, but because it probed to the subtle, deeper reality. People said that mathematicians were unworldly, and yammered on about how Einstein couldn’t make correct change. Nonsense. Einstein just didn’t give a damn. It was the subtle, the beautiful that concerned him.”

Gregory Benford Artifact

Part 2, Chapter 6 (p. 76)
Artifact (1985)

People, Beauty, Reality, Change

“The bewildered novice in chess moves cautiously, recalling individual rules, whereas the experienced player absorbs a complicated situation at a glance and is unable to account rationally for his intuition. In like manner mathematical intuition grows with experience, and it is possible to develop a natural feeling for concepts such as four dimensional space.”

William Feller (1906–1970) Croatian-American mathematician

Introduction, The Nature of Probability Theory, p. 2.
An Introduction To Probability Theory And Its Applications (Third Edition)

Feeling, Nature

“It is clear today that modern science developed when people stopped debating metaphysical questions about the world and instead concerned themselves with the discovery of laws that were primarily mathematical.”

Mordechai Ben-Ari (1948) Israeli computer scientist

Source: Just a Theory: Exploring the Nature of Science (2005), Chapter 11, “Logic and Mathematics: Scientists Like It Clear and Precise” (p. 184)

People, World, Law, Question

“Greek mathematics reveals an important aspect of the Greek genius of which the student of Greek culture is apt to lose sight.”

Thomas Little Heath (1861–1940) British civil servant and academic

Preface p. v
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

“The introduction of the digit 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps…”

Alexander Grothendieck (1928–2014) French mathematician

R. Brown and T. Porter,Analogy, concepts and methodology, in mathematics, UWB Math Preprint, May 26,2006 Link http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf

“Ashtadhyayi distinguishes between usage in the spoken language and usage that is proper to the language of the sacred texts. The Ashtadhyayi is generative as well as descriptive. With its complex use of metarules, transformations, and recursions, the grammar in Ashtadhyayi has been likened to the Turing machine, an idealized mathematical model that reduces the logical structure of any computing device to its essentials.”

Pāṇini ancient Sanskrit grammarian

Encyclopedia Britannica in: "Panini Indian grammarian".

“For more than twenty-five years we have monitored beach nourishment projects around the United States. In order to secure federal funding and justify the enormous costs of these projects, anyone undertaking one must make a prediction of how long the sand will last on the replenished beach. The predictions are based on mathematical models that are said to be sophisticated and state of the art, and yet are consistently, dramatically wrong—always in an optimistic direction. In the rare instances when communities questioned the models after the predictions of a long healthy replenished beach clearly failed, the answer typically was that an unusual and unexpected storm caused the error. Well, the occurrence of storms at any beach is neither unusual nor unexpected. Eventually we became interested in how models were used in other fields. When you start looking into it, you find that a lot of global and local decisions are made based on modeling the environment. There are some fascinating (and discouraging) stories of model misuse and misplaced trust in models in the book.”

Orrin H. Pilkey (1934) American ecologist

Interview with Orrin Pilkey & Linda Jarvis-Pilkey https://web.archive.org/web/20080105132439/http://www.columbia.edu/cu/cup/publicity/pilkeyinterview.html. Useless Arithmetic: Why Environmental Scientists Can’t Predict the Future (2007)

Books, Art, Error, Communication

“The Mathematics which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately overreach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adheres to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depend upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the 47 unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.”

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

"Ration before the University of Cambridge on being elected Lucasian Professor of Mathematics," (1660), reported in: Mathematical Lectures, (1734), p. 28

Faith, Art, Exercises, Question

“Much of the skill of the true mathematical physicist and of the mathematical astronomer consists in the power of adapting methods and results carried out on an exact mathematical basis to obtain approximations sufficient for the purposes of physical measurements. It might perhaps be thought that a scheme of Mathematics on a frankly approximative basis would be sufficient for all the practical purposes of application in Physics, Engineering Science, and Astronomy, and no doubt it would be possible to develop, to some extent at least, a species of Mathematics on these lines. Such a system would, however, involve an intolerable awkwardness and prolixity in the statements of results, especially in view of the fact that the degree of approximation necessary for various purposes is very different, and thus that unassigned grades of approximation would have to be provided for. Moreover, the mathematician working on these lines would be cut off from the chief sources of inspiration, the ideals of exactitude and logical rigour, as well as from one of his most indispensable guides to discovery, symmetry, and permanence of mathematical form. The history of the actual movements of mathematical thought through the centuries shows that these ideals are the very life-blood of the science, and warrants the conclusion that a constant striving toward their attainment is an absolutely essential condition of vigorous growth. These ideals have their roots in irresistible impulses and deep-seated needs of the human mind, manifested in its efforts to introduce intelligibility in certain great domains of the world of thought.”

E. W. Hobson (1856–1933) British mathematician

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), pp. 285-286; Cited in: Moritz (1914, 229): Mathematics and Science.

Life, World, History, Intelligence

“Although there are other heresies in The General Theory, along with puzzles, opacities, loose ends, confusions, errors, exaggerations, and anachronisms galore, they do not detract from the book's relevance to our present troubles. Economists may have forgotten The General Theory and moved on, but economics has not outgrown it, or the informal mode of argument that it exemplifies, which can illuminate nooks and crannies that are closed to mathematics. Keynes's masterpiece is many things, but "outdated" it is not.”

Richard A. Posner (1939) United States federal judge

How I Became a Keynesian (2009)

Books, Error

“It was, however, from Spain, and not from Arabia, that a knowledge of eastern mathematics first came into western Europe. The Moors had established their rules in Spain in 747, and by the tenth or eleven century had attained a high degree of civilisation.”

W. W. Rouse Ball (1850–1925) English mathematician

W. W. Rouse Ball, A Short Account of the History of Mathematics (1888), Courier Dover, 1960, p. 164

Knowledge

“The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. … Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.”

George Pólya book How to Solve It

Source: How to Solve It (1945), p. 219

“The management science approach to organizational decision making is the analog to the rational approach by individual managers. Management science came into being during World War II. At that time, mathematical and statistical techniques were applied to urgent, large-scale military problems that were beyond the ability of individual decision makers. Mathematicians, physicists, and operations researchers used systems analysis to develop artillery trajectories, antisubmarine strategies, and bombing strategies such as salvoing (discharging multiple shells simultaneously). Consider the problem of a battleship trying to sink an enemy ship several miles away. The calculation for aiming the battleship's guns should consider distance, wind speed, shell size, speed and direction of both ships, pitch and roll of the firing ship, and curvature of the earth. Methods for performing such calculations using trial and error and intuition are not accurate, take far too long, and may never achieve success.
This is where management science came in. Analysts were able to identify the relevant variables involved in aiming a ship's guns and could model them with the use of mathematical equations. Distance, speed, pitch, roll, shell size, and so on could be calculated and entered into the equations. The answer was immediate, and the guns could begin firing. Factors such as pitch and roll were soon measured mechanically and fed directly into the targeting mechanism. Today, the human element is completely removed from the targeting process. Radar picks up the target, and the entire sequence is computed automatically.”

Richard L. Daft (1964) American sociologist

Source: Organization Theory and Design, 2007-2010, p. 500

War, World, Error, Problem

“The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.”

Alfred North Whitehead (1861–1947) English mathematician and philosopher

1920s, Science and the Modern World (1925)

Science

“Economic theory deals with two concepts, Value and Economy. Abstract reasoning regarding these concepts rests ultimately on mathematical concepts of quantity, time and energy. The three are inseparable, for quantity and time are dimensions of energy. The quantity relationships of energy, usually termed "statics," turn on the problem of the relation of the parts to the whole, while the time relationships, usually termed "dynamics," are the relations of a process that connects past, present and future.”

John R. Commons (1862–1945) United States institutional economist and labor historian

Source: Legal foundations of capitalism. 1924, p. 1; Lead paragraph first chapter on Mechanism, Scarcity, Working Rules

Problem, Time, Past, Future

“In the social equation, the value of a single life is nil; in the cosmic equation, it is infinite… Not only communism, but any political movement which implicitly relies on purely utilitarian ethics, must become a victim to the same fatal error. It is a fallacy as naïve as a mathematical teaser, and yet its consequences lead straight to Goya's Disasters, to the reign of the guillotine, the torture chambers of the Inquisition, or the cellars of the Lubianka.”

Arthur Koestler book The Invisible Writing

The Invisible Writing (1954).

Life, Error, Communication

“A later writer, such as Leijonhufvud, I knew to have it wrong, when he later argued the merits of Keynes’s subtle intuitions and downplayed the various (identical!) mathematical versions of The General Theory. The so-called 1937 Hicks or later Hicks–Hansen IS–LM diagram will do as an example for the debate.”

Paul A. Samuelson (1915–2009) American economist

New millennium, An Interview with Paul A. Samuelson, 2003

“"What do you think?" "Sir?" "Frightening? Did you ever learn mathematics?" "Yes, sir." "So add up how many Frenchmen can actually use their muskets."”

Bernard Cornwell (1944) British writer

Captain Richard Sharpe and Ensign Denny, commenting on an approaching French column, a formation that only allows the front rank to fire, p. 220
Sharpe (Novel Series), Sharpe's Eagle (1981)

Thinking, Learning

“Justice to others and to ourselves is the same; that we cannot define our duties by mathematical lines ruled by the square, but must fill with them the great circle traced by the compasses”

Albert Pike book Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry

Source: Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry (1871), Ch. III : The Master, p. 72

Justice

“. was one of the most brilliant students of the Ateneo Municipal as far as humanities and natural and mathematical sciences are concerned”

Epifanio de los Santos (1871–1928) Filipino politician

The Philippine review (Revista filipina) [1921]

Nature, Science

“Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians.”

Edsger W. Dijkstra (1930–2002) Dutch computer scientist

1970s, How do we tell truths that might hurt? (1975)

“Phys. I know that it is often a help to represent pressure and volume as height and width on paper; and so geometry may have applications to the theory of gases. But is it not going rather far to say that geometry can deal directly with these things and is not necessarily concerned with lengths in space?
Math. No. Geometry is nowadays largely analytical, so that in form as well as in effect, it deals with variables of an unknown nature. …It is literally true that I do not want to know the significance of the variables x, y, z, t that I am discussing. …
Phys. Yours is a strange subject. You told us at the beginning that you are not concerned as to whether your propositions are true, and now you tell us you do not even care to know what you are talking about.
Math.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

That is an excellent description of Pure Mathematics, which has already been given by an eminent mathematician <nowiki>[</nowiki>Bertrand Russell<nowiki>]</nowiki>.
Space, Time and Gravitation (1920)

Nature, Help

“…The pursuit of mathematics is a divine madness of the human spirit…”

Alfred North Whitehead (1861–1947) English mathematician and philosopher

Source: 1920s, Science and the Modern World (1925), Ch. 2: "Mathematics as an Element in the History of Thought"

Madness

“Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick.”

Martin Gardner (1914–2010) recreational mathematician and philosopher

Mathematics, Magic, and Mystery https://books.google.com/books?id=-kOFBQAAQBAJ&pg=PR11#v=onepage&q=%22Mathematical%20magic%20combines%22%23v%3Dsnippet&f=false (1956), p. ix

Beauty

“A model that unifies all types of selection (chemical, sociological, genetical, and every other kind of selection) may open the way to develop a general ‘Mathematical Theory of Selection’ analogous to communication theory… Selection has been studied mainly in genetics, but of course there is much more to selection than just genetical selection… yet, despite the pervading importance of selection in science and life, there has been no abstraction and generalisation from genetical selection to obtain a general selection theory and general selection mathematics”

George R. Price (1922–1975) American population geneticist

Price, G.R. (1995). "The nature of selection." Journal of Theoretical Biology 175:389-396 (written circa 1971)

Life, Way, Communication, Study

“Wenzel and Richter, the latter… of most pronounced mathematical temperament, laid the foundations of stoichiometry, or "the art of measuring the chemical elements."”

J. R. Partington (1886–1965) British chemist

Introduction
Higher Mathematics for Chemical Students (1911)

Art

“All acts of reasoning seem to me to be different cases of one uniform process which may perhaps be best described as the substitution of similars… The chief difficulty consists in showing that all the forms of the old logic, as well as the fundamental rules of mathematical reasoning, may be explained upon the same principle; and it is to this difficult task I have devoted the most attention.”

William Stanley Jevons (1835–1882) English economist and logician

Preface
The Substitution of Similars, The True Principles of Reasoning (1869)

“Copernicus published his manuscript in 1543 just in time for the council of Trent. So you're a church father and what this new system of Copernicus is saying is this: The Earth moves, although the Bible says it doesn't. It's no longer at the center of God's universe, although the Bible says it is. It's a planet, so heaven and Earth are no longer separate. And Aristotle was wrong, although church authority depends on him being right. You're a church father and you pick up this subversive, heretical, revolutionary piece of lunacy and you start foaming at the mouth, right? Wrong. When the council finally got around to reading Copernicus they were delighted. His new system had made calendar reform more precise. And the business of it turning every basic belief about the universe on its head? A mere fairytale since from the church's viewpoint he was talking nonsense. Astronomy drew lines and circles in the sky but they weren't really there, they're a mathematical convenience for measuring or teaching astronomy. While the Copernicus system might well have been brilliant mathematics, no one thought for a minute that he was actually suggesting the earth was whizzing around the sun. That kind of talk would blow holes in everything.”

James Burke (science historian) (1936) British broadcaster, science historian, author, and television producer

The Day the Universe Changed (1985)

God, Business, Fairytale, Universe

“The history of mathematics throws little light on the psychology of mathematical invention.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

History, Light

“Mathematics is the queen of the sciences.”

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

As quoted in Gauss zum Gedächtniss (1856) by Wolfgang Sartorius von Waltershausen; Variants: Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
Mathematics is the queen of the sciences and number theory is the queen of mathematics. [Die Mathematik ist die Königin der Wissenschaften und die Zahlentheorie ist die Königin der Mathematik.]

Science

“I think visual literacy and media literacy is not without value, but I think plain old-fashioned text literacy and mathematical literacy are much more powerful and flexible ways to organize your mind.”

Neal Stephenson (1959) American science fiction writer

Neal Stephenson coins the term "text literacy" during interview for the article "Pushing the Edge With 'Diamond Age' Nano-Machines," Associated Press, May 10, 1995

Way, Fashion, Thinking

“We begin to wonder if it is due to the fact that we don't know enough. But it can't be that. Because in terms of accumulated knowledge we know more today than men have known in any period of human history. We have the facts at our disposal. We know more about mathematics, about science, about social science, and philosophy than we've ever known in any period of the world's history. So it can't be because we don't know enough. And then we wonder if it is due to the fact that our scientific genius lags behind. That is, if we have not made enough progress scientifically. Well then, it can't be that. For our scientific progress over the past years has been amazing.”

Martin Luther King, Jr. (1929–1968) American clergyman, activist, and leader in the American Civil Rights Movement

1950s, Rediscovering Lost Values (1954)
Context: There is something wrong with our world, something fundamentally and basically wrong. I don't think we have to look too far to see that. I'm sure that most of you would agree with me in making that assertion. And when we stop to analyze the cause of our world's ills, many things come to mind. We begin to wonder if it is due to the fact that we don't know enough. But it can't be that. Because in terms of accumulated knowledge we know more today than men have known in any period of human history. We have the facts at our disposal. We know more about mathematics, about science, about social science, and philosophy than we've ever known in any period of the world's history. So it can't be because we don't know enough. And then we wonder if it is due to the fact that our scientific genius lags behind. That is, if we have not made enough progress scientifically. Well then, it can't be that. For our scientific progress over the past years has been amazing. Man through his scientific genius has been able to dwarf distance and place time in chains, so that today it's possible to eat breakfast in New York City and supper in London, England. Back in about 1753 it took a letter three days to go from New York City to Washington, and today you can go from here to China in less time than that. It can't be because man is stagnant in his scientific progress. Man's scientific genius has been amazing. I think we have to look much deeper than that if we are to find the real cause of man's problems and the real cause of the world's ills today. If we are to really find it I think we will have to look in the hearts and souls of men.

Men, World, History, Knowledge

“Mathematics is too arduous and uninviting a field to appeal to those to whom it does not give great rewards. These rewards are of exactly the same character as those of the artist. To see a difficult uncompromising material take living shape and meaning is to be Pygmalion, whether the material is stone or hard, stonelike logic. To see meaning and understanding come where there has been no meaning and no understanding is to share the work of a demiurge. No amount of technical correctness and no amount of labour can replace this creative moment, whether in the life of a mathematician or of a painter or musician. Bound up with it is a judgement of values, quite parallel to the judgement of values that belongs to the painter or the musician. Neither the artist nor the mathematician may be able to tell you what constitutes the difference between a significant piece of work and an inflated trifle; but if he is not able to recognise this in his own heart, he is no artist and no mathematician.”

Norbert Wiener (1894–1964) American mathematician

Ex-Prodigy: My Childhood and Youth (1964)

Life, Understanding, Heart

“This suiting my humor so well; I did thenceforth prosecute it, (at School and in the University) not as a formal Study, but as a pleasing Diversion, at spare hours; as books of Arithmetick or others Mathematical fel occasionally in my way. For I had none to direct me, what books to read, or what to seek, or in what Method to proceed. For Mathematicks, (at that time, with us) were scarce looked upon as Academical Studies, but rather Mechanical; as the business of Traders, Merchants, Seamen, Carpenters, Surveyors of Lands, or the like; and perhaps some Almanack-makers in London.”

John Wallis (1616–1703) English mathematician

Dr. Wallis's Account of some Passages of his own Life (1696)

Books, School, Way, Business

“In the years after 1936, whilst Hayek was working on The Pure Theory of Capital, most economists were convinced by Keynes, whose theory had an elegance and simplicity that Hayek’s did not. Keynes’ theory lacked Hayek’s theoretical rigor in that it was not based on equilibrium (on individual rationality), and there were places in the argument where Keynes relied on loose, informal arguments, preferring to put his trust in intuition rather than formal theory. Keynesians did not solve the problems with capital theory that Hayek had identified: they just bypassed or ignored them. According to Hayek’s methodological criteria, Keynes’ theory was decidedly inferior. Against this, Keynes’ theory provided opportunities for mathematical and statistical analysis that Hayek’s did not. Indeed, though Hayek paid some attention to data, he did so only minimally: he certainly made no attempt to test his theory against statistical data. The choice of Keynesian theory was, at least in part, a methodological one.”

Roger Backhouse (economist) (1951) British economist

"Hayek on money and the business cycle", 2006

Problem, Parting

“The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.”

Bill Gates book The Road Ahead

Source: The Road Ahead (1995), p. 265 in hardcover edition, corrected in paperback

Way

“Had it merely called to our attention the existence and exact nature of certain fundamental gaps in economic theory, the Theory of Economic Behavior by von Neumann and Morgenstern would have been a book of outstanding importance. But it does more than that. It is essentially constructive: where existing theory is considered to be inadequate, the authors put in its place a highly novel analytical apparatus designed to cope with the problem.
It would be doing the authors an injustice to say that theirs is a contribution to economics only. The scope of the book is much broader. The techniques applied by the authors in tackling economic problems are of sufficient generality to be valid in political science, sociology, or even military strategy. The applicability to games proper (chess and poker) is obvious from the title. Moreover, the book is of considerable interest from a purely mathematical point of view.”

Leonid Hurwicz (1917–2008) Russian-American economist and mathematician

Leonid Hurwicz. "The Theory of Economic Behavior," The American Economic Review, Vol. 35, No. 5 (Dec., 1945), pp. 909: Lead paragraphs of the article

Books, Behavior, Game, Nature

“Evolution is a technological, mathematical, informational, and biological process rolled into one. It could almost be said to be a law of physics, a principle that reigns over all created multitudes, whether they have genes or not.”

Kevin Kelly (1952) American author and editor

Out of Control: The New Biology of Machines, Social Systems and the Economic World (1995)

Law

“The so-called obvious was repeatedly scrutinized from every angle and was frequently found to be not obvious but false. "Obvious" is the most dangerous word in mathematics.”

Eric Temple Bell (1883–1960) mathematician and science fiction author born in Scotland who lived in the United States for most of his li…

Source: Mathematics: Queen and Servant of Science (1938), p. 16

Falseness

““The rules that society chooses to live by have always struck me as especially fascinating,” she said. “There are things one can do but not talk about, and there are things one can talk about but not do. There are things—not apparently gender-related—that men can do, but not women, and there are things women can do, but not men. We live in an invisible maze, and we have all learned where to turn and when, so as to find our way through.”
“Some of the rules are good, Mary, and many are necessary,” Lord Darcy said mildly.
“You misunderstood me, my dear,” Mary of Cumberland told him. “As in magic, where there are absolutely essential words to say and gestures to make or the spell won’t work; so in society there are absolutely essential words to say and gestures to make or we won’t understand each other or trust each other, and it will all come tumbling down around us. The problem is that the rules of society, unlike magic, have never been formalized mathematically, and we don’t know which words are essential to the spell and which are just silly words.””

Michael Kurland book Ten Little Wizards

Source: Ten Little Wizards (1988), Chapter 14 (p. 132)

Women, Men, Way, Understanding

“General systems theory deals with the most fundamental concepts and aspects of systems. Many theories dealing with more specific types of systems (e. g., dynamical systems, automata, control systems, game-theoretic systems, among many others) have been under development for quite some time. General systems theory is concerned with the basic issues common to all these specialized treatments. Also, for truly complex phenomena, such as those found predominantly in the social and biological sciences, the specialized descriptions used in classical theories (which are based on special mathematical structures such as differential or difference equations, numerical or abstract algebras, etc.) do not adequately and properly represent the actual events. Either because of this inadequate match between the events and types of descriptions available or because of the pure lack of knowledge, for many truly complex problems one can give only the most general statements, which are qualitative and too often even only verbal. General systems theory is aimed at providing a description and explanation for such complex phenomena.”

Mihajlo D. Mesarovic (1928) Serbian academic

Mihajlo D. Mesarovic and Y. Takahare (1975) General Systems Theory, Mathematical foundations. Academic Press. Cited in: Franz Pichler, Roberto Moreno Diaz (1993. Computer Aided Systems Theory. p. 134

Game, Knowledge, Problem, Science

“It is to be feared that few who are not experts in the history of mathematics have any acquaintance with the details of the original discoveries in mathematics of the greatest mathematician of antiquity, perhaps the greatest mathematical genius that the world has ever seen.”

Thomas Little Heath (1861–1940) British civil servant and academic

Source: Achimedes (1920), Ch. I. Archimedes, p.1

World, Fear, History

“The assumption that individuals act objectively in accordance with purely mathematical dictates to maximize their gain or utility cannot be sustained by empirical observation.”

Richard Arnold Epstein (1927) American physicist

Epilogue, p. 410
The Theory of Gambling and Statistical Logic (Revised Edition) 1977

“…The subjects we study at school can be divided roughly into two groups—the sciences and the arts. The sciences include mathematics, geography, chemistry, physics, and so on. Among the arts are drawing, painting, modelling, needlework, drama, music, literature. The purpose of education is to fit us for life in a civilised community, and it seems to follow from the subjects we study that the two most important things in civilised life are Art and Science.”

Anthony Burgess (1917–1993) English writer

Non-Fiction, English Literature: A Survey for Students (1958, revised 1974)

Life, Education, School, Art

“When I came back from Munich, it was September, and I was Professor of Mathematics at the Eindhoven University of Technology. Later I learned that I had been the Department's third choice, after two numerical analysts had turned the invitation down; the decision to invite me had not been an easy one, on the one hand because I had not really studied mathematics, and on the other hand because of my sandals, my beard and my "arrogance"”

Edsger W. Dijkstra (1930–2002) Dutch computer scientist

whatever that may be Dijkstra (1993) "From my Life" http://www.cs.utexas.edu/users/EWD/transcriptions/EWD11xx/EWD1166.html (EWD 1166). 1990s

Decision, Study, Learning, Universe

“The assimilation of tautologies and contradictions with true and false propositions respectively results from the fact that tautologies and contradictions can be taken as truth-functions just like ordinary propositions, and for determining the truth of falsity of the truth-function, tautologies and contradictions among its arguments must be counted as true or false respectively. …Are the propositions of symbolic logic and mathematics tautologies in Mr Wittgenstein's sense?”

Frank P. Ramsey (1903–1930) British mathematician, philosopher

The Foundations of Mathematics (1925)

Truth, Sense, Falseness

“Operations research has many precursors and allied fields, including Taylorism (after Frederick W. Taylor), scientific management and management science, industrial engineering and systems analysis. As one early textbook explained, the roots of OR "are as old as science and the management function. Its name dates back only to 1940" (Churchman et al. 1957: 3). Certainly its practitioners have expended much energy and ink in search of an acceptable definition of OR. Morse tried unsuccessfully to halt the debate by declaring OR to be 'the activity carried on by members of the Operations Research Society' (Morse 1953: 159) But his colleagues were not so easily dissuaded from debate. Much of the concern with definition focused on the sometimes elusive distinctions between OR and neighbouring fields; the attempt to define, or redefine, OR was also born of the desire to allow the subject to evolve beyond the orthodoxy of wartime experience. Crucial considerations included the balance between model and application, and the complexity of the mathematics involved.”

Ivor Grattan-Guinness (1941–2014) Historian of mathematics and logic

Source: Companion encyclopedia of the history and philosophy of the mathematical sciences (2003), p. 841.

Search, Science

“So far we have studies how, for each commodity by itself, the law of demand in connection with the conditions of production of that commodity, determines the price of it and regulates the incomes of its producers. We considered as given and invariable the prices of other commodities and the incomes of other producers; but, in reality the economic system is a whole of which the parts are connected and react on each other. An increase in the incomes of the producers of commodity A will affect the demand for commodities Band C, etc., and the incomes of their producers, and, by its reaction will involve a change in the demand for A. It seems, therefore, as if, for a complete and rigorous solution of the problems relative to some parts of the economic system, it were indispensable to take the entire system into consideration. But this would surpass the powers of mathematical analysis and of our practical methods of calculation, even if the values of all the constants could be assigned to them numerically.”

Antoine Augustin Cournot Researches into the Mathematical Principles of the Theory of Wealth

Source: Researches into the Mathematical Principles of the Theory of Wealth, 1897, p. 137

Law, Problem, Reality, Study

“I was early regarded as having unusual intellectual capacity. I was an omnivorous reader, and I added to that a desire to systematize my understanding. As a result, history, for example, was not merely a set of dates and colorful stories; I could understand it as a sequence in which one event flowed out of another. This sense of order crystallized during my high-school and college years into a predominant interest in mathematics and mathematical logic.”

Kenneth Arrow (1921–2017) American economist

Arrow (1984) "November 1984 lecture at Trinity University". Lecture presented November 5, 1984.
1970s-1980s

School, Color, History, Understanding

“Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i. e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

Reality, Sense, Study, Science

“The unnaturalness of mathematical symbolism is attested to by history. The algebra of the Egyptians, the Babylonians, the Greeks, the Hindus, and the Arabs was what is commonly called rhetorical algebra. …on the whole they used ordinary rhetoric to describe their mathematical work. Symbolism is a relatively modern invention of the sixteenth and seventeenth centuries…”

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 59

History

“Machine-held strings of binary digits can simulate a great many kinds of things, of which numbers are just one kind. For example, they can simulate automobiles on a freeway, chess pieces, electrons in a box, musical notes, Russian words, patterns on a paper, human cells, colors, electrical circuits, and so on. To think of a computer as made up essentially of numbers is simply a carryover from the successful use of mathematical analysis in studying models. Most of this series of lectures has been devoted to applications of computers, and this is not the time to give details about their usefulness. I merely wish to point out certain types of things being done with computers today that could not have been done in 1945. Some of these are technological, some are intellectual.”

George Forsythe (1917–1972) Stanford University computer scientist

As cited in: Zenon Pylyshyn (1970) Perspectives on the computer revolution. p. 379
"Educational implications of the computer revolution," 1963

Music, Color, Thinking, Study

“It is readily seen that any theory written by Laplace will be superior to all produced of lower standing. It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils.”

Niels Henrik Abel (1802–1829) Norwegian mathematician

Marginal note in his mathematical notebook (ca. 1826) as quoted by Øystein Ore, Niels Henrik Abel: Mathematician Extraordinary (1957)

Study, Appearance

“Physics, chemistry, astrophysics are obviously the ideal field for the tidy mind …in the biological and geological sciences the tidy mind often goes astray and the passive, unmathematical approach may me more suitable.
…The sciences that deal with natural process, geology or geography, or with life, zoology or botany, have an immensely more complicated task than physics or chemistry.
… A particular danger, I believe, lies in an oversimplified use of mathematical or statistical methods of investigation, in which obviously erroneous results may be obtained by a selection of only a few of many relevant factors to be considered.”

Claud William Wright (1917–2010) British paleontologist

From "Order and Disorder in Nature", 1958 Proceedings of the Geologists' Association, 69, 2, 77-82.

Life, Nature, Science

“The Mahomedan or Islamic culture hardly gave anything to the world which may be said to be of fundamental importance and typically its own; Islamic culture was mainly borrowed from others. Their mathematics and astronomy and other subjects were derived from India and Greece. It is true they gave some of these things a new turn, but they have not created much. Their philosophy and their religion are very simple and what they call Sufism is largely the result of gnostics who lived in Persia and it is the logical outcome of that school of thought largely touched by Vedanta…. I have, however, mentioned [in The Foundations of Indian Culture] that Islamic culture contributed the Indo-Saracenic architecture to Indian culture. I do not think it has done anything more in India of cultural value. It gave some new forms to art and poetry. Its political institutions were always semi-barbaric.”

Sri Aurobindo (1872–1950) Indian nationalist, freedom fighter, philosopher, yogi, guru and poet

September 12, 1923
India's Rebirth

World, School, Religion, Art

“I never failed in mathematics. Before I was fifteen I had mastered differential and integral calculus.”

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

Response to being shown a "Ripley's Believe It or Not!" column with the headline "Greatest Living Mathematician Failed in Mathematics" in 1935. Quoted in Einstein: His Life and Universe by Walter Isaacson (2007), p. 16 http://books.google.com/books?id=cdxWNE7NY6QC&lpg=PP1&pg=PA16#v=onepage&q&f=false 1930s

“This is not what I thought physics was about when I started out: I learned that the idea is to explain nature in terms of clearly understood mathematical laws; but perhaps comparisons are the best we can hope for.”

Hans Christian von Baeyer (1938) American physicist

Source: Information, The New Language of Science (2003), Chapter 22, Quantum Computing, Putting qubits to work, p. 203

Law, Hope, Idea, Nature

“A finished or even a competent reasoner is not the work of nature alone… education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided that it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history may be chosen for this purpose. Now, of all these, it is desirable to choose the one… in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not.
.. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:—
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except the self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is attained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if… reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded.
…These are the principal grounds on which… the utility of mathematical studies may be shewn to rest, as a discipline for the reasoning powers. But the habits of mind which these studies have a tendency to form are valuable in the highest degree. The most important of all is the power of concentrating the ideas which a successful study of them increases where it did exist, and creates where it did not. A difficult position or a new method of passing from one proposition to another, arrests all the attention, and forces the united faculties to use their utmost exertions. The habit of mind thus formed soon extends itself to other pursuits, and is beneficially felt in all the business of life.”

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

Source: On the Study and Difficulties of Mathematics (1831), Ch. I.

Life, Children, Truth, Education

“A textual critic engaged upon his business is not at all like Newton investigating the motions of the planets: he is much more like a dog hunting for fleas. If a dog hunted for fleas on mathematical principles, basing his researches on statistics of area and population, he would never catch a flea except by accident.”

A.E. Housman (1859–1936) English classical scholar and poet

"The Application of Thought to Textual Criticism", a lecture delivered on August 4, 1921

Dogs, Business

“The initial thesis of my enterprise - on the basis of which this entanglement of periodizations is organized by extracting the sense of each - is this following: the science of being qua being has existed since the Greeks - such is the sense and status of mathematics. However, it is only today that we have the means to know this. It follows from this thesis that philosophy is not centered on on ontology - which exists as a separate and exact discipline- rather it circulates between this ontology (this, mathematics), the modern theories of he subject and its own history. The contemporary complex of the conditions of philosophy includes everything referred to in my first three statements: the history of 'Western'thought, post-Cantorian mathematics, psychoanalysis, contemporary art and politics. Philosophy does not coincide with any of these conditions; nor does it map out the totality to which they belong. What philosophy must do is purpose a conceptual framework in which the contemporary compossibilty of these conditions can be grasped. Philosophy can only do this - and this is what frees it from any foundational ambition, in which it would lose itself- by designating amongst its own conditions, as a singular discursive situation, ontology itself in the form of pure mathematics. This is precisely what delivers philosophy and ordains it to the care of truths.”

Alain Badiou (1937) French writer and philosopher

Introduction
Being and Event (1988)

Truth, Art, History, Sense

“Mathematics is the bold luxury of pure reason, one of the few that remain today.”

Robert Musil (1880–1942) Austrian writer

Source: “Mathematical man” (1913), p. 41

“Most mathematicians are by nature Platonists who cheerfully, unreflectingly and habitually employ such loaded phrases as 'We assume there exists…' or 'Therefore there exists…' an entity with such and such characteristics. Challenged by the realist they would probably reply that since the truths of mathematics are absolute, universal and eternal it is hard indeed to deny them an existence independent of human intelligence.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

Truth, Intelligence, Nature, Universe

“The Object of this Treatise is—(1) To point out to the student of Mathematics, who has not the advantage of a tutor, the course of study which it is most advisable that he should follow, the extent to which he should pursue one part of the science before he commences another, and to direct him as to the sort of applications which he should make. (2) To treat fully of the various points which involve difficulties and which are apt to be misunderstood by beginners, and to describe at length the nature without going into the routine of the operations.”

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

Source: On the Study and Difficulties of Mathematics (1831), Chapter I. Introductory Remarks on the Nature and Objects of Mathematics.

Nature, Study, Science, Parting

“[P]robability as a measurable degree of certainty; necessity and chance; moral versus mathematical expectation; a priori an a posteriori probability; expectation of winning when players are divided according to dexterity; regard of all available arguments, their valuation, and their calculable evaluation; law of large numbers…”

Jacob Bernoulli book Ars Conjectandi

Ars Conjectandi (1713)

Law, Chance

“[There is a] basic problem … of building a mathematical model of thought processes, and in particular of those aspects of thought which are concerned with information and decision processes. The perceptron is one type of model -- a set of memory devices connected in random fashion-- which has not yet achieved useful results but certainly seems to be a promising approach. The self-adaptive feedback control system which goes beyond the normal servo function of controlling its output, and in addition controls the parameters by which it controls its output is another which has already achieved pragmatic results in equipment control. It may be that the question of self-adaptation is a key to the whole question of how the human functions in a decisioning situation. For in many cases the ability of the human mind to adapt itself to a changing and complex environment is beyond our present aims in model construction.”

Robert E. Machol (1917–1998) American systems engineer

p ix-x
Information and Decision Processes (1960)

Fashion, Question, Problem, Decision

“The field equations, in their most general form, contain a term multiplied by a constant, which is denoted by the Greek letter λ… sometimes called the "cosmical constant." This is a name without any meaning… We have, in fact, not the slightest inkling of what its real significance is. It is put in the equations in order to give them the greatest possible degree of mathematical generality, but, so far as its mathematical function is concerned, it is entirely undetermined: it may be positive or negative, it might also be zero.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“Science fiction these days is only half a step ahead of science. Astrophysicists and scientists are working in the same way as science fiction writers. They’re working things out in their imagination based on the slim scientific facts that they know. Hawking imagines a black hole and then discovers the mathematics that support his theory, and new possibilities come to light. That’s the imaginative flair that scientists have to have. For me as a sci-fi writer, spinning those ideas in your mind brings you to the point where you dream in science fiction. Suddenly you think of something in the middle of the night, and it’s so vivid you don’t need to write it down because you know you’ll remember it in the morning. That’s what these books, Zero G, reflect: a vivid imagination.”

William Shatner (1931) Canadian actor, musician, recording artist, author, and film director

"William Shtner on Sci-Fi, Aging and the Environment" http://www.saturdayeveningpost.com/2017/08/22/in-the-magazine/shatner.html as interviewed by Jeanne Wolf, Saturday Evening Post, September/October 2017

Books, Dreams, Way, Imagination

“Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect.”

Hermann Weyl (1885–1955) German mathematician

Symmetry (1952)

Art, Nature

“He who is unfamiliar with mathematics [literally, he who is a layman in mathematics] remains more or less a stranger to our time.”

Christian Heinrich von Dillmann (1829–1899) German educationist

Source: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 39.

Time

“Well! according to the sketch your picture [which Whistler sent him in a letter] seems well-composed, the lines of sky, sea, the position of the figures all that seems very, very well done[, ] on opening the letter it struck me immediately, an impression of decorative ornamentation which makes a good picture appeal to the eye as well - upside down and any other way up. Arrangement, layout, composition. etc - mysterious words harmonious laws - in no way conventional - needs of the Artist glory of the Raphael's Michelangelo's etc etc - for me a repetition a hesitation, a matter of feeling - which should also be a law, a mathematical thing, like form, like light, colour[. ] I find similarities with the colour method which works by opposing colours to arrive at a harmony that is to say to make a canvas a complete whole, to put into a small space an image with all the forces all the principles of nature - [instead of showing a part of it]..”

Henri Fantin-Latour (1836–1904) painter from France

quote from a letter of Fantin-Latour, Paris 7-14 October 1862 to James Whistler; from The Correspondence of James McNeill Whistler - Repository: Glasgow University Library http://www.whistler.arts.gla.ac.uk/correspondence/people/display/?cid=1075&nameid=Manet_E&sr=0&surname=&firstname=&rs=1 - System Number: 01075; Call Number: MS Whistler F 6.

Law, Way, Feeling, Nature

“As a single atom man is an enigma: as a whole he is a mathematical problem. As an individual he is a free agent, as a species the offspring of necessity.”

William Winwood Reade (1838–1875) British historian

Source: The Martyrdom of Man (1872), Chapter II, "Religion", pp. 143-4.

Problem

“So intimate is the union between Mathematics and Physics that probably by far the larger part of the accessions to our mathematical knowledge have been obtained by the efforts of mathematicians to solve the problems set to them by experiment, and to create for each successive class phenomena a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature. Sometimes the mathematician has been before the physicist, and it has happened that when some great and new question has occurred to the experimentalist or the observer, he has found in the armory of the mathematician the weapons which he needed ready made to his hand. But much oftener, the questions proposed by the physicist have transcended the utmost powers of the mathematics of the time, and a fresh mathematical creation has been needed to supply the logical instrument requisite to interpret the new enigma.”

Henry John Stephen Smith (1826–1883) mathematician

As quoted in The Century: A Popular Quarterly (1874) ed. Richard Watson Gilder, Vol. 7, pp. 508-509, https://books.google.com/books?id=ceYGAQAAIAAJ&pg=PA508 "Relations of Mathematics to Physics". Earlier quote without citation in Nature, Volume 8 (1873), page 450. Also quoted partially in Michael Grossman and Robert Katz, Calculus http://babel.hathitrust.org/cgi/mb?a=listis;c=216746186|Non-Newtonian (1972) p. iv. ISBN 0912938013.

Question, Nature, Knowledge, Problem

Quotes about mathematics page 8

Quotes about mathematics
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