Quotes about mathematics

A collection of quotes on the topic of mathematics, use, science, other.

Best quotes about mathematics

“Pure mathematics is in its way the poetry of logical ideas.”

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

1930s, Obituary for Emmy Noether (1935)
Context: Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

“It is already all in Dedekind.”

Emmy Noether (1882–1935) German mathematician

Es steht alles schon bei Dedekind.
As quoted by Bartel Leendert van der Waerden, "On the Sources of My Book Modern Algebra" (1975) Historia Mathematica Vol. 2, pp. 31-40.

“The laws of nature are but the mathematical thoughts of God.”

Euclid (-323–-285 BC) Greek mathematician, inventor of axiomatic geometry

The earliest published source found on google books that attributes this to Euclid is A Mathematical Journey by Stanley Gudder (1994), p. xv http://books.google.com/books?id=UiOxd2-lfGsC&q=%22mathematical+thoughts%22+euclid#search_anchor. However, many earlier works attribute it to Johannes Kepler, the earliest located being in the piece "The Mathematics of Elementary Chemistry" by Principal J. McIntosh of Fowler Union High School in California, which appeared in School Science and Mathematics, Volume VII ( 1907 http://books.google.com/books?id=kAEUAAAAIAAJ&pg=PR3#v=onepage&q&f=false), p. 383 http://books.google.com/books?id=kAEUAAAAIAAJ&pg=PA383#v=onepage&q&f=false. Neither this nor any other source located gives a source in Kepler's writings, however, and in an earlier source, the 1888 Notes and Queries, Vol V., it is attributed on p. 165 http://books.google.com/books?id=0qYXAQAAMAAJ&pg=PA165#v=onepage&q&f=false to Plato. It could possibly be a paraphrase of either or both of the following to comments in Kepler's 1618 book Harmonices Mundi (The Harmony of the World)': "Geometry is one and eternal shining in the mind of God" and "Since geometry is co-eternal with the divine mind before the birth of things, God himself served as his own model in creating the world".
Misattributed

“Dull minds are never either intuitive or mathematical.”

Blaise Pascal Pensées

Source: Pensées

“I am interested in mathematics only as a creative art.”

G. H. Hardy book A Mathematician's Apology

Source: A Mathematician's Apology (1941)

“Chess problems are the hymn-tunes of mathematics.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

“Pure mathematics is religion.”

Novalis book Blüthenstaub

Reine Mathematik ist Religion.
Blüthenstaub (1798), Unsequenced

“The highest life is mathematics.”

Novalis book Blüthenstaub

Das höchste Leben ist Mathematik.
Blüthenstaub (1798), Unsequenced

“Mathematics is the key and door to the sciences.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

As quoted in Building Fluency Through Practice and Performance (2008) by Timothy Rasinski and Lorraine Griffith, p. 64, but in fact a quotation by Roger Bacon: Et harum scientiarum porta et clavis est Mathematica, "And of these sciences the door and key is mathematics", from Bacon's Opus Majus (1267) https://books.google.co.uk/books?id=UfqcGd8NOFsC&pg=PA97&lpg=PA97&dq=%22porta+et+clavis%22+opus+majus&source=bl&ots=nGgt2Lhxqe&sig=88kIPB5EAKAKtm0APk6J5OrS1D0&hl=en&sa=X&ved=0ahUKEwiU36D2gIbLAhVBWBQKHSW9CKgQ6AEINDAE#v=onepage&q=%22porta%20et%20clavis%22%20opus%20majus&f=false.
Attributed

“Mathematics is a language.”

Josiah Willard Gibbs (1839–1903) physicist

At a Yale faculty meeting, during a discussion of language requirements in the undergraduate curriculum. Quoted in Muriel Rukeyser, Willard Gibbs (Garden City, NY: Doubleday, Doran & Co., 1942), p. 280.
Attributed

Quotes about mathematics

“If you’re going to set goals, it’s better for them to be big. If you write them down decisively, it’s easier to succeed. Indeed, my way of thinking is quite mathematical.”

Yuzuru Hanyu (1994) Japanese figure skater (1994-)

Translation source: https://kaerb.tumblr.com/post/170346243034/if-youre-going-to-set-goals-its-better-for (user-translation) from 31 January 2018.
Annotation: This quote is excerpted from an interview filmed in Yokohama on 22 November 2009 after an official practice at Japanese Junior Nationals, aired 23 December 2009 in 2009全日本フィギュアスケートジュニア選手権大会 (2009 All Japan Figure Skating Junior Championships) by BS Fuji.
Page: 124.
Original: (ja) 目標を書くなら大きいほうがいい。具体的に書いたほうが達成しやすい。けっこう理数系です。

Thinking , Decision , Way

“Teachers need to be trained on how children learn, not only how to solve mathematical problems. They must know how to make learners well understand the New Math and enable them to solve mathematical problems.”

Sukavich Rangsitpol (1935) Thai politician

Teacher

Understanding , Children , Learning , Teachers

“The beauty of mathematics only shows itself to more patient followers.”

Maryam Mirzakhani (1977–2017) Iranian mathematician

Source: http://www.theguardian.com/science/2014/aug/13/interview-maryam-mirzakhani-fields-medal-winner-mathematician

Beauty

“I don’t think that everyone should become a mathematician, but I do believe that many students don’t give mathematics a real chance.”

Maryam Mirzakhani (1977–2017) Iranian mathematician

Interview with Research Fellow Maryam Mirzakhani | january 2008

Thinking , Chance

“I obtained scientific guidance and stimulation mainly through personal mathematical contacts in Erlangen and in Göttingen. Above all I am indebted to Mr. E. Fischer from whom I received the decisive impulse to study abstract algebra from an arithmetical viewpoint, and this remained the governing idea for all my later work.”

Emmy Noether (1882–1935) German mathematician

Idea , Decision , Study , Personality

“Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.”

Nikola Tesla (1856–1943) Serbian American inventor

"Radio Power Will Revolutionize the World" in Modern Mechanics and Inventions (July 1934)

Reality

“He is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world.”

Aryabhata (476–550) Indian mathematician-astronomer

Bhaskara I, quoted in: J J O'Connor and E F Robertson "Aryabhata the Elder".

Sea , Learning , Knowledge , World

“Mathematics is the gate and key of the sciences. … Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy.”

Roger Bacon book Opus Majus

cited in: Morris Kline (1969) Mathematics and the physical world. p. 1
Opus Majus, c. 1267

Men , World , Knowledge , Science

“Young man, in mathematics you don't understand things. You just get used to them.”

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

Reply, according to Dr. Felix T. Smith of Stanford Research Institute, to a physicist friend who had said "I'm afraid I don't understand the method of characteristics," as quoted in The Dancing Wu Li Masters: An Overview of the New Physics (1979) by Gary Zukav, Bantam Books, p. 208, footnote.

Understanding

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”

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

Remark made by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947, as mentioned by Franz L. Alt at the end of "Archaeology of computers: Reminiscences, 1945--1947", Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694.

Life , People

“Look, when you realize how fake it all is; the football, the basketball, the Lady Gaga, the Justin Bieber—you know, who gives you these carbon tax messages. They tell your kids they gotta love Justin Biebler [sic], and then Biebler [sic] says "hand in your guns", "pass the Cyber Security Act", and "the police state is good", and then your children are turned into a mindless vassals—who now, they look up to some twit, instead of looking up to Thomas Jefferson, or looking up to Nikola Tesla, or looking up to Magellan; I mean, kids, Magellan is a lot cooler than Justin Bieber! He circumnavigated with one ship the entire planet! He was killed by wild natives before they got back to Portugal! And when they got back there was only like eleven people alive of the two hundred and something crew and the entire ship was rotting down to the waterline! That's destiny! That's will! That's striving! That's being a trailblazer and explore! Going into space! Mathematics! Quantum mechanics! The secrets of the universe! It's all there! Life is fiery with its beauty! Its incredible detail! Tuning into it! They wanna shutter your mind, talking about Justin Bieber! It's pure evil! They're taking your intellect, your soul, and giving you Michael Jordan and Bieber. Unlock your human potential! Defeat the globalists who wanna shutter your mind!—Your doorways to perception!—I wanna see you truly live! I wanna see you truly be who you are!”

Alex Jones (1974) American radio host, author, conspiracy theorist and filmmaker

Alex Jones: The "Justin Biebler" Rant https://www.youtube.com/watch?v=VDMB0KyhPN8, 21 February 2011.
2011

Love , Life , Children , People

“As a fraction of the lifespan of the universe as measured from the beginning to the evaporation of the last black hole, life as we know it is only possible for one-thousandth of a billion billion billionth, billion billion billionth, billion billion billionth, of a percent (10^-84). And that's why, for me, the most astonishing wonder of the universe isn't a star or a planet or a galaxy. It isn't a thing at all. It's an instant in time. And that time is now. Humans have walked the earth for just the shortest fraction of that briefest of moments in deep time. But in our 200,000 years on this planet we've made remarkable progress. It was only 2,500 years ago that we believed that the sun was a god and measured its orbit with stone towers built on the top of a hill. Today the language of curiosity is not sun gods, but science. And we have observatories that are almost infinitely more sophisticated than those towers, that can gaze out deep into the universe. And perhaps even more remarkably through theoretical physics and mathematics we can calculate what the universe will look like in the distant future. And we can even make concrete predictions about its end. And I believe that it's only by continuing our exploration of the cosmos and the laws of nature that govern it that we can truly understand ourselves and our place in this universe of wonders.”

Brian Cox (physicist) (1968) English physicist and former musician

Conclusion in Wonders of the Universe - Destiny

Life , God , Law , Star

“If you are receptive and humble, mathematics will lead you by the hand.”

Paul Dirac (1902–1984) theoretical physicist

As quoted in The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom (2009) by Graham Farmelo, p. 435
Context: If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics led me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.

“Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.”

Alan Turing Systems of Logic Based on Ordinals

"Systems of Logic Based on Ordinals," section 11: The purpose of ordinal logics (1938), published in Proceedings of the London Mathematical Society, series 2, vol. 45 (1939)
In a footnote to the first sentence, Turing added: "We are leaving out of account that most important faculty which distinguishes topics of interest from others; in fact, we are regarding the function of the mathematician as simply to determine the truth or falsity of propositions."
Context: Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

Exercises

“For the things of this world cannot be made known without a knowledge of mathematics.”

Roger Bacon book Opus Majus

Cited in: Opus majus: A translation by Robert Belle Burke. Vol 1 (1962). p. 128
Opus Majus, c. 1267
Context: For the things of this world cannot be made known without a knowledge of mathematics. For this is an assured fact in regard to celestial things, since two important sciences of mathematics treat of them, namely theoretical astrology and practical astrology. The first … gives us definite information as to the number of the heavens and of the stars, whose size can be comprehended by means of instruments, and the shapes of all and their magnitudes and distances from the earth, and the thicknesses and number, and greatness and smallness, … It likewise treats of the size and shape of the habitable earth … All this information is secured by means of instruments suitable for these purposes, and by tables and by canons.. For everything works through innate forces shown by lines, angles and figures.

World , Knowledge

“What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe.”

Stephen Hawking book A Brief History of Time

Source: A Brief History of Time (1988), Ch. 12
Context: Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?

Question , Universe , Science

“If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. …Hence the question of whether axioms are a priori becomes pointless since they are arbitrary.”

Hans Reichenbach (1891–1953) American philosopher

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

Idea , Question , Falseness

“Mathematicians have constructed a very large number of different systems of geometry, Euclidean or non-Euclidean, of one, two, three, or any number of dimensions. All these systems are of complete and equal validity. They embody the results of mathematicians' observations of their reality, a reality far more intense and far more rigid than the dubious and elusive reality of physics. The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real. …There may be three dimensions in this room and five next door. As a professional mathematician, I have no idea; I can only ask some competent physicist to instruct me in the facts.
The function of a mathematician, then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics. …Among them there perhaps none quite so fascinating, with quite the astonishing contrasts of sharp outline and shade, as that which constitutes the theory of numbers.”

G. H. Hardy (1877–1947) British mathematician

"The Theory of Numbers," Nature (Sep 16, 1922) Vol. 110 https://books.google.com/books?id=1bMzAQAAMAAJ p. 381

Beauty , Mountain , Idea , Fashion

“There cannot be a greater mistake than that of looking superciliously upon the practical applications of science. The life and soul of science is its practical application; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.”

William Thomson (1824–1907) British physicist and engineer

Lecture on "Electrical Units of Measurement" (3 May 1883), published in Popular Lectures Vol. I, p. 73, as quoted in The Life of Lord Kelvin (1910) by Silvanus Phillips Thompson

Life , World , Soul , Knowledge

“The kind of mathematics foisted on children in schools is not meaningful, fun, or even very useful. This does not mean that an individual child cannot turn it into a valuable and enjoyable personal game. For some the game is scoring grades; for others it is outwitting the teacher and the system. For many, school math is enjoyable in its repetitiveness, precisely because it is so mindless and dissociated that it provides a shelter from having to think about what is going on in the classroom. But all this proves is the ingenuity of children. It is not a justifications for school math to say that despite its intrinsic dullness, inventive children can find excitement and meaning in it.”

Seymour Papert book Mindstorms: Children, Computers, and Powerful Ideas

Source: Mindstorms: Children, Computers, and Powerful Ideas (1980), Chapter 2, Mathophobia: The Fear of Learning

Children , School , Game , Thinking

“The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

World , Beauty , Way , Idea

“The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

Nature , Knowledge , Science

“The employment of mathematical symbols is perfectly natural when the relations between magnitudes are under discussion; and even if they are not rigorously necessary, it would hardly be reasonable to reject them, because they are not equally familiar to all readers and because they have sometimes been wrongly used, if they are able to facilitate the exposition of problems, to render it more concise, to open the way to more extended developments, and to avoid the digressions of vague argumentation.”

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, pp. 3-4; Cited in: Moritz (1914, 199)

Way , Nature , Problem

“Either mathematics is too big for the human mind, or the human mind is more than a machine.”

Kurt Gödel (1906–1978) logician, mathematician, and philosopher of mathematics

As quoted in Topoi : The Categorial Analysis of Logic (1979) by Robert Goldblatt, p. 13

“Now, the velocity of wave propagation can be seen, without the aid of any mathematical analysis, to depend on the elasticity of the medium and its density; for we can see that if a medium is highly elastic the disturbance would be propagated at a great speed.”

Albert A. Michelson (1852–1931) American physicist

Light Waves and Their Uses Page 146.

Dependency , Speed

“That logic, as a science, is susceptible of very wide applications is admitted; but it is equally certain that its ultimate forms and processes are mathematical.”

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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: William Stanley Jevons (1887) The Principles of Science: : A Treatise on Logic and Scientific Method. p. 155

Science

“Reality contains not only evidence, but also the means (such as our minds, and our artefacts) of understanding it. There are mathematical symbols in physical reality. The fact that it is we who put them there does not make them any less physical.”

David Deutsch book The Fabric of Reality

Source: The Fabric of Reality (1997), Ch.3

Understanding , Reality

“The way the mathematics game is played, most variations lie outside the rules, while music can insist on perfect canon or tolerate a casual accompaniment.”

Marvin Minsky (1927–2016) American cognitive scientist

Music, Mind, and Meaning (1981)

Lie , Music , Way , Game

“An ancient writer said that arithmetic and geometry are the wings of mathematics; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity. Not only are they the foundation, they are also, as it were, the capstones; for, whenever a result has been arrived at, in order to use that result, it is necessary to translate it into numbers or into lines; to translate it into numbers requires the aid of arithmetic, to translate it into lines necessitates the use of geometry.”

Joseph Louis Lagrange (1736–1813) Italian mathematician and mathematical physicist

Dans Les Leçons Élémentaires sur les Mathématiques (1795) Leçon cinquiéme, Tr. McCormack, cited in Moritz, Memorabilia mathematica or, The philomath's quotation-book (1914) Ch. 15 Arithmetic, p. 261. https://archive.org/stream/memorabiliamathe00moriiala#page/260/mode/2up

Science

“Our design, not respecting arts, but philosophy, and our subject, not manual, but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this — from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena…”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Preface
Philosophiae Naturalis Principia Mathematica (1687)

Art , Nature

“Einstein's relativity work is a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king… its exponents are brilliant men but they are metaphysicists rather than scientists.”

Nikola Tesla (1856–1943) Serbian American inventor

New York Times (11 July 1935), p. 23, c.8

Men , People , Error , Clothes

“Music is a mysterious mathematical process whose elements are part of Infinity. … There is nothing more musical than a sunset.”

Claude Debussy (1862–1918) French composer

As quoted in The Harvard Biographical Dictionary of Music (1996) by Don Michael Randel
Context: Music is a mysterious mathematical process whose elements are part of Infinity. … There is nothing more musical than a sunset. He who feels what he sees will find no more beautiful example of development in all that book which, alas, musicians read but too little — the book of Nature.

Music , Parting

“There is a noticeable general difference between the sciences and mathematics on the one hand, and the humanities and social sciences on the other.”

Noam Chomsky (1928) american linguist, philosopher and activist

Quotes 1990s, 1990-1994, Noam Chomsky: A Life of Dissent, 1992
Context: There is a noticeable general difference between the sciences and mathematics on the one hand, and the humanities and social sciences on the other. It's a first approximation, but one that is real. In the former, the factors of integrity tend to dominate more over the factors of ideology. It's not that scientists are more honest people. It's just that nature is a harsh taskmaster. You can lie or distort the story of the French Revolution as long as you like, and nothing will happen. Propose a false theory in chemistry, and it'll be refuted tomorrow.

Science

“One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.”

Paul Dirac (1902–1984) theoretical physicist

The Evolution of the Physicist's Picture of Nature (1963)
Context: It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

God , Universe

“It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis,”

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

Source: 1840s, The Mathematical Analysis of Logic, 1847, p. iii
Context: That to the existing forms of Analysis a quantitative interpretation is assigned, is the result of the circumstances by which those forms were determined, and is not to be construed into a universal condition of Analysis. It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis, regardless that in its object and in its instruments it must at present stand alone.

“I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Definitions - Scholium
Philosophiæ Naturalis Principia Mathematica (1687)

People , Relation ships , Time

“Pure mathematics is useless to ordinary people, but useful to those who wish to understand Absolute Truth, God or Infinity. Applied maths is useful in our daily life.”

Mwanandeke Kindembo (1996) Congolese author

God , Understanding , People , Truth

“It has become almost a cliché to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics.”

Richard Dawkins (1941) English ethologist, evolutionary biologist and author

The Richard Dimbleby Lecture: Science, Delusion and the Appetite for Wonder (1996)

Literature , Science

“I tell them that if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lusts of the flesh.”

Thomas Mann (1875–1955) German novelist, and 1929 Nobel Prize laureate

Study

“There was a footpath leading across fields to New Southgate, and I used to go there alone to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more of mathematics.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Suicide

“Numbers written on restaurant bills within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe. This single fact took the scientific world by storm.”

Douglas Adams Life, the Universe and Everything

Source: Life, the Universe and Everything

World , Law , Universe , Parting

“I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.”

Malcolm X book The Autobiography of Malcolm X

Source: The Autobiography of Malcolm X

Thinking

“But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.”

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

Earliest source located is the book Brighter than a Thousand Suns: A Personal History of the Atomic Scientists by Robert Jungk (1958), p. 249, which says that Einstein made the comment during "a walk with Ernst Straus, a young mathematician acting as his scientific assistant at Princeton."
Variant: "Equations are more important to me, because politics is for the present, but an equation is something for eternity." From A Briefer History of Time by Stephen Hawking (2005), p. 144 http://books.google.com/books?id=4Y0ZBW19n_YC&lpg=PP1&pg=PA144#v=onepage&q&f=false.
Earlier, Straus recalled the German version of the quote in Helle Zeit, Dunkle Zeit: In Memoriam Albert Einstein (1956) edited by Carl Seelig, p. 71. There the quote was given as Ja, so muß man seine Zeit zwischen der Politik und unseren Gleichungen teilen. Aber unsere Gleichungen sind mir doch viel wichtiger; denn die Politik ist für die Gegenwart da, aber solch eine Gleichung is etwas für die Ewigkeit.
Attributed in posthumous publications
Context: Yes, we now have to divide up our time like that, between politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.

“But in my opinion, all things in nature occur mathematically.”

René Descartes (1596–1650) French philosopher, mathematician, and scientist

Nature

“Cats can work out mathematically the exact place to sit that will cause most inconvenience.”

Pam Brown (1948) Australian poet

Cats

“Canada is the essence of not being. Not English, not American, it is the mathematic of not being. And a subtle flavour - we're more like celery as a flavour.”

Mike Myers (1963) Canadian- British- American actor, comedian, singer, screenwriter, and film producer

“Mathematics rightly viewed possesses not only truth but supreme beauty.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

1900s, "The Study of Mathematics" (November 1907)
Context: Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.

Truth , Beauty

“Increasingly, the mathematics will demand the courage to face its implications.”

Michael Crichton book Jurassic Park

Source: Jurassic Park

Courage

“Philosophy is written in this grand book, which stands continually open before our eyes (I say the 'Universe'), but can not be understood without first learning to comprehend the language and know the characters as it is written. It is written in mathematical language, and its characters are triangles, circles and other geometric figures, without which it is impossible to humanly understand a word; without these one is wandering in a dark labyrinth.”

Galileo Galilei book The Assayer

From Italian: La filosofia è scritta in questo grandissimo libro, che continuamente ci sta aperto innanzi agli occhi (io dico l'Universo), ma non si può intendere, se prima non il sapere a intender la lingua, e conoscer i caratteri ne quali è scritto. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi ed altre figure geometriche, senza i quali mezzi è impossibile intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro labirinto.
Other translations:
Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.
The Assayer (1623), as translated by Thomas Salusbury (1661), p. 178, as quoted in The Metaphysical Foundations of Modern Science (2003) by Edwin Arthur Burtt, p. 75.
Philosophy is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth.
As translated in The Philosophy of the Sixteenth and Seventeenth Centuries (1966) by Richard Henry Popkin, p. 65
Il Saggiatore (1623)
Source: Galilei, Galileo. Il Saggiatore: Nel Quale Con Bilancia Efquifita E Giufta Si Ponderano Le Cofe Contenute Nellalibra Astronomica E Filosofica Di Lotario Sarsi Sigensano, Scritto in Forma Di Lettera All'Illustr. Et Rever. Mons. D. Virginio Cesarini. In Roma: G. Mascardi, 1623. Google Play. Google. Web. 22 Dec. 2015. <https://play.google.com/store/books/details?id=-U0ZAAAAYAAJ>.

Books , Understanding , Learning , Universe

“The treatises of Darboux (1842–1917) and Bianchi (1856–1928) on surface theory are among the great works in the mathematical literature. They are: G. Darboux, Théorie générale des surfaces, Tome 1 (1887), 2 (1888), 3 (1894), 4 (1896), and later editions and reprints. L. Bianchi. Lezioni di Geometria Differenziale, Pisa 1894; German translation by Lukat, Lehrbuch der Differentialgeometrie, 1899. The subject is basically local surface theory.”

Shiing-Shen Chern (1911–2004) mathematician (1911–2004), born in China and later acquiring U.S. citizenship; made fundamental contributio…

[1991, Surface Theory with Darboux and Bianchi, Miscellanea Mathematica, 59–69, Springer, https://doi.org/10.1007/978-3-642-76709-8_4]

Literature

“The mathematical thermology created by Fourier may tempt us to hope that, as he has estimated the temperature of the space in which we move, me may in time ascertain the mean temperature of the heavenly bodies: but I regard this order of facts as for ever excluded from our recognition. We can never learn their internal constitution, nor, in regard to some of them, how heat is absorbed by their atmosphere. We may therefore define Astronomy as the science by which we discover the laws of the geometrical and mechanical phenomena presented by the heavenly bodies.”

Auguste Comte (1798–1857) French philosopher

Book II: Astronomy, Ch. I: General View
The Positive Philosophy of Auguste Comte (1853)

Law , Hope , Learning , Science

“Einstein is the only figure in the physical sciences with a stature that can be compared with Newton. Newton is reported to have said "If I have seen further than other men, it is because I stood on the shoulders of giants." This remark is even more true of Einstein who stood on the shoulders of Newton. Both Newton and Einstein put forward a theory of mechanics and a theory of gravity but Einstein was able to base General Relativity on the mathematical theory of curved spaces that had been constructed by Riemann while Newton had to develop his own mathematical machinery. It is therefore appropriate to acclaim Newton as the greatest figure in mathematical physics and the Principia is his greatest achievement.”

Stephen Hawking (1942–2018) British theoretical physicist, cosmologist, and author

"Newton's Principia" in 300 Years of Gravitation. (1987) by S. W. Hawking and W. Israel, p. 4

Men , Science

“Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the world, but every possible world, must conform.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

1900s, "The Study of Mathematics" (November 1907)

World

“If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics…”

Roger Bacon book Opus Majus

Bk. 1, ch. 4. Translated by Robert B. Burke, in: Edward Grant (1974) Source Book in Medieval Science. Harvard University Press. p. 93
Opus Majus, c. 1267

Truth , Error , Knowledge , Science

“317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

Way , Thinking , Reality

“Notwithstanding the eminent difficulties of the mathematical theory of sonorous vibrations, we owe to it such progress as has yet been made in acoustics. The formation of the differential equations proper to the phenomena is, independent of their integration, a very important acquisition, on account of the approximations which mathematical analysis allows between questions, otherwise heterogeneous, which lead to similar equations. This fundamental property, whose value we have so often to recognize, applies remarkably in the present case; and especially since the creation of mathematical thermology, whose principal equations are strongly analogous to those of vibratory motion. This means of investigation is all the more valuable on account of the difficulties in the way of direct inquiry into the phenomena of sound. We may decide the necessity of the atmospheric medium for the transmission of sonorous vibrations; and we may conceive of the possibility of determining by experiment the duration of the propagation, in the air, and then through other media; but the general laws of the vibrations of sonorous bodies escape immediate observation. We should know almost nothing of the whole case if the mathematical theory did not come in to connect the different phenomena of sound, enabling us to substitute for direct observation an equivalent examination of more favorable cases subjected to the same law. For instance, when the analysis of the problem of vibrating chords has shown us that, other things being equal, the number of oscillations is hi inverse proportion to the length of the chord, we see that the most rapid vibrations of a very short chord may be counted, since the law enables us to direct our attention to very slow vibrations. The same substitution is at our command in many cases in which it is less direct.”

Auguste Comte (1798–1857) French philosopher

Bk. 3, chap. 4; as cited in: Moritz (1914, 240)
System of positive polity (1852)

Law , Way , Question , Problem

“One day he said: For the soul there is a satisfaction of a higher type; the material is not at all necessary. Whether I apply mathematics to a couple of clods of dirt, which we call planets, or to purely arithmetical problems, it s just the same; the latter have only a higher charm for me.”

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

Carl Friedrich Gauss: Titan of Science (1955) by Guy Waldo Dunnington. p. 348

Soul , Problem

“Boyle was among the first who recognized that the withdrawal of sympathy licenses conduct that would not be permissible within an animistic vision of nature. …The vision that he and his scientific colleagues were creating was fast becoming a mathematical abstraction lacking color, odor, texture, and personality. …The task of the natural philosopher, we are told, is to "probe," "penetrate," and "pierce" nature in all her "mysterious," secret," and "intimate recesses."”

Theodore Roszak (1933–2011) American social historian, social critic, writer

Source: The Gendered Atom: Reflections on the Sexual Psychology of Science (1999), Ch.7 The Rape of Nature

Secret , Color , Nature , Personality

“Remembering… that Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book I, Chapter VI, Sec. 9

Sun

“My work in the future must be devoted entirely to pure mathematics in its abstract meaning. I shall apply all my strength to bring more light into the tremendous obscurity which one unquestionably finds in analysis. It lacks so completely all plan and system that it is peculiar that so many have studied it. The worst of it is, it has never been treated stringently. There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general, and it is extremely peculiar that such a procedure has led to do few of the so-called paradoxes. It is really interesting to seek the cause.
In analysis, one is largely occupied by functions which can be expressed as powers. As soon as other powers enter—this, however, is not often the case—then it does not work any more and a number of connected, incorrect theorems arise from false conclusions. I have examined several of them, and been so fortunate as to make this clear. …I have had to be extremely cautious, for the presumed theorems without strict proof… had taken such a stronghold in me, that I was continually in danger of using them without detailed verification.”

Niels Henrik Abel (1802–1829) Norwegian mathematician

Letter to Christoffer Hansteen (1826) as quoted by Øystein Ore, Niels Henrik Abel: Mathematician Extraordinary (1957) & in part by Morris Kline, Mathematical Thought from Ancient to Modern Times (1972) citing Œuvres, 2, 263-65

Way , Study , Light , Future

“…there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, […] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as ‘real’, but […] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

Reality

“Evolution has ensured that our brains just aren't equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it's just as easy to think in 11 dimensions, as it is to think in three or four.”

Stephen Hawking (1942–2018) British theoretical physicist, cosmologist, and author

As quoted in "Return of the time lord" in The Guardian http://books.guardian.co.uk/departments/scienceandnature/story/0,6000,1579384,00.html (27 September 2005)

Thinking

“From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates while he separated the latter as common concepts—a proceeding which even on the part of his commentators was no longer understood, and likewise with modern mathematicians, unfortunately for science, has met with little imitation. As a matter of fact, the abstract methods of mathematical science know no axioms at all.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

As quoted in "Diverse Topics: The Origin of Thought Forms," The Monist (1892) Vol. 2 https://books.google.com/books?id=8akLAAAAIAAJ&pg=PA120 ed., Paul Carus, citing The Open Court Vol. II. No. 77. A Flaw in the Foundation of Geometry by Hermann Grassmann, translated from his Ausdehnungslehre

Science , Parting

“It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me.”

Stanislaw Ulam (1909–1984) Polish-American mathematician

Source: Adventures of a Mathematician - Third Edition (1991), Chapter 3, Travels Abroad, p. 52

“As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to "Non-Cooperative Games," also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph. D. thesis with the other results.”

John Nash (1928–2015) American mathematician and Nobel Prize laureate

Autobiographical essay (1994)

Game , Idea , Study

“I believe that no one who is familiar, either with mathematical advances in other fields, or with the range of special biological conditions to be considered, would ever conceive that everything could be summed up in a single mathematical formula, however complex.”

Ronald Fisher (1890–1962) English statistician, evolutionary biologist, geneticist, and eugenicist

The evolutionary modification of genetic phenomena. Proceedings of the 6th International Congress of Genetics 1, 165-72, 1932.
1930s

“Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Source: 1910s, Mysticism and Logic and Other Essays http://archive.org/stream/mysticism00russuoft/mysticism00russuoft_djvu.txt (1918), Ch. 5: Mathematics and the Metaphysicians

“The rules of logic are to mathematics what those of structure are to architecture.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

1900s, "The Study of Mathematics" (November 1907)

“It was the White Race who produced men like Columbus who crossed the unknown Atlantic; men like Magellan who first circumnavigated the globe; men like Michaelangelo, Leonardo da Vinci, Rembrandt, Velazquez, Bernini, Rubens, Raphael and thousands of other geniuses who created beautiful and exquisite productions in the fields of sculpture and painting; geniuses like Beethoven, Bach, Wagner and Verdi who created beautiful music; men like James Watt who invented the steam engine; men like Daimler who invented and built the reciprocating internal combustion engine; production geniuses like Henry Ford, inventors like Thomas Edison; such a prodigal genius as Nikola Tesla in the field of physics and electricity; literary geniuses like Shakespeare, Goethe and thousands of others, untold geniuses in the fields of mathematics, in the fields of chemistry and physics.”

Ben Klassen (1918–1993) American engineer, author and politician

Nature's Eternal Religion (1973), Ch. 2, Paragraph 4
Nature's Eternal Religion (1973)

Men , Beauty , Music , Painting

“Revealing great, unusual, and remarkable spectacles, opening these to the consideration of every man, and especially of philosophers and astronomers; as observed by Galileo Galilei, Gentleman of Florence, Professor of Mathematics in the University of Padua, with the aid of a spyglass lately invented by him, in the surface of the Moon, in innumerable fixed stars, in nebulae, and above all in four planets swiftly revolving about Jupiter at differing distances and periods, and known to no one before the author recently perceived them and decided they should be named the Medicean Stars”

Galileo Galilei book Sidereus Nuncius

Translation by Stillman Drake in Discoveries and Opinions of Galileo (1957)
Sidereus Nuncius (Venice, 1609)

Star , Universe

“If I have had any success in mathematical physics, it is, I think, because I have been able to dodge mathematical difficulties.”

Josiah Willard Gibbs (1839–1903) physicist

Quoted by C. S. Hastings in "Biographical Memoir of Josiah Willard Gibbs 1839-1903," National Academy of Sciences Biographical Memoirs, vol. VI (Washington, D.C.: National Academy of Sciences, 1909), p. 390. Complete memoir http://books.nap.edu/html/biomems/jgibbs.pdf
Attributed

Thinking , Success

“There is the definition [of mathematics], boldly proposed by Pierce that 'Mathematics is the science which draws necessary conclusions', and more explicitly formulated by Russel that 'Pure Mathematics is the class of all propositions of the form "p implies q"… it was… the purpose of Russell's treatise to provide a complete, exact and convincing justification of this definition… instead, he and Whitehead collaborated to give a magisterial account of the Principia Mathematica.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

Science , Drawing

“Since Leibniz there has perhaps been no man who has had a full command of all the intellectual activity of his day. Since that time, science has been increasingly the task of specialists, in fields which show a tendency to grow progressively narrower… Today there are few scholars who can call themselves mathematicians or physicists or biologists without restriction. A man may be a topologist or a coleopterist. He will be filled with the jargon of his field, and will know all its literature and all its ramifications, but, more frequently than not, he will regard the next subject as something belonging to his colleague three doors down the corridor, and will consider any interest in it on his own part as an unwarrantable breach of privacy… There are fields of scientific work, as we shall see in the body of this book, which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology; in which every single notion receives a separate name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.
It is these boundary regions which offer the richest opportunities to the qualified investigator. They are at the same time the most refractory to the accepted techniques of mass attack and the division of labor. If the difficulty of a physiological problem is mathematical in essence, then physiologists ignorant of mathematics will get precisely as far as one physiologists ignorant of mathematics, and no further. If a physiologist who knows no mathematics works together with a mathematician who knows no physiology, the one will be unable to state his problem in terms that the other can manipulate, and the second will be unable to put the answers in any form that the first can understand… A proper exploration of these blank spaces on the map of science could only be made by a team of scientists, each a specialist in his own field but each possessing a thoroughly sound and trained acquaintance with the fields of his neighbors; all in the habit of working together, of knowing one another's intellectual customs, and of recognizing the significance of a colleague's new suggestion before it has taken on a full formal expression. The mathematician need not have the skill to conduct a physiological experiment, but he must have the skill to understand one, to criticize one, and to suggest one. The physiologist need not be able to prove a certain mathematical theorem, but he must be able to grasp its physiological significance and to tell the mathematician for what he should look. We had dreamed for years of an institution of independent scientists, working together in one of these backwoods of science, not as subordinates of some great executive officer, but joined by the desire, indeed by the spiritual necessity, to understand the region as a whole, and to lend one another the strength of that understanding.”

Norbert Wiener book Cybernetics: Or Control and Communication in the Animal and the Machine

Source: Cybernetics: Or Control and Communication in the Animal and the Machine (1948), p. 2-4; As cited in: George Klir (2001) Facets of Systems Science, p. 47-48

Books , Dreams , Literature , Understanding

“With the publication of J. M. Keynes’s General Theory in 1936 and the mathematical formalizations of his theory by J. R. Hicks (1937) and others, the language of macro-economic theory became systems of simultaneous equations. These are general equilibrium systems of interdependence in the sense that the relationships describe an entire national economy, not just a particular industry or sector. The systems are usually not completely closed; they depend on exogenous parameters including instruments controlled by policy-makers. Seeking definite relationships of economic outcomes to policies and other exogenous variables, qualitative and quantitative, these models sacrifice detail and generality, limiting the number of variables and equations by aggregations over agents, commodities, assets, and time.”

James Tobin (1918–2002) American economist

Source: "Money and Finance in the Macro-Economic Process" (1982), p. 12

Sense , Time , Dependency

“I am persuaded that it [The Method of Mechanical Theorems] will be of no little service to mathematics; for I apprehend that some, either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.”

Archimedes book The Method of Mechanical Theorems

The Method of Mechanical Theorems

“Not all the geometrical structures are "equal". It would seem that the riemannian and complex structures, with their contacts with other fields of mathematics and with their richness in results, should occupy a central position in differential geometry. A unifying idea is the notion of a G-structure, which is the modern version of an equivalence problem first emphasized and exploited in its various special cases by Elie Cartan.”

Shiing-Shen Chern (1911–2004) mathematician (1911–2004), born in China and later acquiring U.S. citizenship; made fundamental contributio…

Idea , Problem

“Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.”

Stephen Hawking (1942–2018) British theoretical physicist, cosmologist, and author

As quoted in Stephen Hawking: A Biography (2005) by Kristine Larsen, p. 43

Parting

“Geometry can in no way be viewed… as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I… realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Forward, as quoted by Mario Livio, Is God a Mathematician? (2009)
Ausdehnungslehre (1844)

Law , Way , Nature

“Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment.”

Albert Einstein book The Evolution of Physics

The Evolution of Physics (1938) (co-written with Leopold Infeld)
1930s

Books , Idea

“The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.”

Ronald Fisher (1890–1962) English statistician, evolutionary biologist, geneticist, and eugenicist

Discussion to ‘Statistics in agricultural research’ by J.Wishart, Journal of the Royal Statistical Society, Supplement, 1, 26-61, 1934.
1930s

“There is no certainty in sciences where one of the mathematical sciences cannot be applied, or which are not in relation with these mathematics.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), XIX Philosophical Maxims. Morals. Polemics and Speculations.

Science

“Even in mathematics his whimsical fancy was sometimes suffered to peep out, and little girls who learnt the rudiments of calculation at his knee found the path they had imagined so thorny set about with roses by reason of the delightful fun with which he would turn a task into a joy. But when the fun was over the little girl would find that she had learnt the lesson (all unknowingly) just the same. Happy little girls who had such a master.”

Isa Bowman (1874–1958) British actress

Page 5.
The Story of Lewis Carroll (1899)

Imagination , Girl , Suffering , Joy

“Mathematics, trigonometry, chemistry, psychoanalysis, music, and what not have been related to cubism to give it an easier interpretation. All this has been pure literature, not to say nonsense, which brought bad results, blinding people with theories. Cubism has kept itself within the limits and limitations of painting, never pretending to go beyond it.”

Pablo Picasso (1881–1973) Spanish painter, sculptor, printmaker, ceramicist, and stage designer

As quoted by Marius de Zayas, in 'The Arts', New York, May 1923
1920s, The Arts', New York, May 1923

People , Music , Literature , Painting

“It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Letter to Gilbert Murray, April 3, 1902
1900s

People , Pleasure , World , Art

“I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza's God, it won't love us in return.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Letter to Lady Ottoline Morrell, March, 1912, as quoted in Gaither's Dictionary of Scientific Quotations (2012), p. 1318
1910s

Love , God , Universe

“The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term. The formal and abstract mathematical theory has an independent and sometimes lonely existence of its own. But when an undefined mathematical term such as random is given a definite operational meaning in physical terms, it takes on empirical and practical significance. Every mathematical theorem involving this mathematically undefined concept can then be given the following predictive form: If you do so and so, then such and such will happen.”

Walter A. Shewhart (1891–1967) American statistician

[Shewhart, Walter A., Deming, William E., Statistical Method from the Viewpoint of Quality Control, The Graduate School, The Department of Agriculture, 1939, 18]
Economic Control of Quality of Manufactured Product,1931

“Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.”

George Pólya (1887–1985) Hungarian mathematician

[Jon Fripp, Michael Fripp, Deborah Fripp, Speaking of Science: Notable Quotes on Science, Engineering, and the Environment, https://books.google.com/books?id=44ihCUS1XQMC&pg=PA45, 2000, Newnes, 978-1-878707-51-2, 45]

Science

“You & James Ferdinand simply can't learn to distinguish betwixt intellectual opinion & irrelevant instinctive emotion... For instance, he has the idea that I place an exaggerated intellectual valuation on the 18th century merely because my chance emotions have given me a strong but irrational subjective sense of belonging to it. I've told that bird dozens of times that I have no especial intellectual brief for Georgian days... He can't understand my ability to class as merely one period among others an age to which random early impressions have so closely bound my emotions & sense of identity... the point is that my own personal mess of subjective emotions has nothing whatever to do with my intellectual opinions. I have freely declared myself at all times (like everybody else in his respective way) a mere product of my background, & do not consider the values of that background as applicable to outsiders. The only way for the individual to achieve any contentment or harmonic relationship to a pattern is to adhere to the background naturally his; & that is what I am doing. Others I urge to adhere to their own respective backgrounds & traditions, however remote from mine these may be. When I venture now & then to suggest values of a more general kind, I approach the problem in an entirely different way—speaking not as Old Theobald of His Majesty's Rhode-Island Colony, but as the cosmic & impersonal Ec'h-Pi-El, denizen of the invisible world 'Ui-ulh in the second zone of curved space outside angled space... If there is any approach to an absolute value in the cosmos—or at least on this planet—then this is it. Sincerity—is-or-isn't-ness—technical perfection—harmony—coherence—consistency—symmetry—all these things are obviously aspects of one single property of space, energy, & general mathematical harmonics whose universality gives it the deepest possible significance. I have thought this all my life, & that is why to me one Newton or Einstein, one M. Atilius Regulus, M. Porcius Cato, or P. Cornelius Scipio, seems to me in certain ways worth a full dozen of your prattling little Keatses & Baudelaires.”

H.P. Lovecraft (1890–1937) American author

Letter to Frank Belknap Long (27 February 1931), in Selected Letters III, 1929-1931 edited by August Derleth and Donald Wandrei, p. 312
Non-Fiction, Letters, to Frank Belknap Long

Life , Age , World , Way

“Galileo wrote that 'the book of nature is written in the language of mathematics; without its help it is impossible to comprehend a single word of it.”

Steven Pinker book How the Mind Works

Source: How the Mind Works (1997), p. 359

Books , Nature , Help

“It came as a tremendous surprise, for in his student days Einstein had been a lazy dog… He never bothered about mathematics at all.”

Hermann Minkowski (1864–1909) German mathematician and physicist

as quoted in a conversation with Max Born about the development of the theory of relativity, by Carl Seelig, Albert Einstein: A Documentary Biography (1956)

Dogs

“Every attempt to refer chemical questions to mathematical doctrines must be considered, now and always, profoundly irrational, as being contrary to the nature of the phenomena.... but if the employment of mathematical analysis should ever become so preponderant in chemistry (an aberration which is happily almost impossible) it would occasion vast and rapid retrogradation….”

Auguste Comte (1798–1857) French philosopher

System of positive polity (1852)

Question , Nature

“We tend to believe the premises because we can see that their consequences are true, instead of believing the consequences because we know the premises to be true. But the inferring of premises from consequences is the essence of induction; thus the method in investigating the principles of mathematics is really an inductive method, and is substantially the same as the method of discovering general laws in any other science.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

"The Regressive Method of Discovering the Premises of Mathematics" (1907), in Essays in Analysis (1973), pp. 273–274
1900s

Law , Science

“Mathematics is more than a tool and language for science. It is also an end in itself, and as such, it has, over the centuries, affected our worldview in its own right.”

Stephen Hawking book God Created the Integers

Preface
God Created the Integers (2007)

Science

“Again, in regard to actual human existence, I have found myself giving honour to those who feel its tragedy, who think truly about Death, who are oppressed by ignoble things even when they are inevitable; yet these qualities appear to me to militate against happiness, not only to the possessors, but to all whom they affect. And, generally, the best life seems to me one which thinks truly and feels greatly about human things, and which, in addition, contemplates the world of beauty and of abstract truths. This last is, perhaps, my most anti-utilitarian opinion: I hold all knowledge that is concerned with things that actually exist – all that is commonly called Science – to be of very slight value compared to the knowledge which, like philosophy and mathematics, is concerned with ideal and eternal objects, and is freed from this miserable world which God has made.
[Utilitarians] have been strangely anxious to prove that the life of the pig is not happier than that of the philosopher – a most dubious proposition…”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Letter to Gilbert Murray, April 3, 1902
1900s

Life , Death , God , Truth

“A possible explanation of the physicist's use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person. As a result, when he finds a connection between two quantities which resembles a connection well-known from mathematics, he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection.”

Eugene Paul Wigner The Unreasonable Effectiveness of Mathematics in the Natural Sciences

"The Unreasonable Effectiveness of Mathematics in the Natural Sciences," Communications in Pure and Applied Mathematics, February 1960.

Law , Nature , Personality

“I want to emphasize the necessity for a sound mathematical basis for any fundamental physical theory. Any philosophical ideas that one may have play only a subordinate role. Unless such ideas have a mathematical basis they will be ineffective.”

Paul Dirac (1902–1984) theoretical physicist

The Mathematical Foundations of Quantum Theory (1978)

Idea

“In mathematical quarters, the regular division of the plane has been considered theoretically... Does this mean that it is an exclusively mathematical question? In my opinion, it does not. [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it.”

M. C. Escher (1898–1972) Dutch graphic artist

Quote of Escher, from his essay on Tessellation 1957; as cited by Tony Thomas, in 'The Strange Worlds of M C Escher' http://www.escapeintolife.com/essays/the-strange-worlds-of-m-c-escher/
1950's

Way , Lying , Question , Nature

“I was a solitary, shy, priggish youth. I had no experience of the social pleasures of boyhood and did not miss them. But I liked mathematics, and mathematics was suspect because it has no ethical content. I came also to disagree with the theological opinions of my family, and as I grew up I became increasingly interested in philosophy, of which they profoundly disapproved. Every time the subject came up they repeated with unfailing regularity, 'What is mind? No matter. What is matter? Never mind.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

After some fifty or sixty repetitions, this remark ceased to amuse me.
Source: 1950s, Portraits from Memory and Other Essays (1956), p. 9

Pleasure , Youth , Family , Time

“This [experimentation] is the custom—and properly so—in those sciences where mathematical demonstrations are applied to natural phenomena, as is seen in the case of perspective, astronomy, mechanics, music, and others where the principles, once established by well-chosen experiments, become the foundations of the entire superstructure.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

Salviati, Third Day. Change of Position
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)

Music , Nature , Science

“Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 3
1900s

Truth

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