Quotes about mathematics
page 9

“The fact that human intuition is ill suited to situations involving uncertainty was known as early as the 1930's, when researchers noted that people could neither make up a sequence of numbers that passed mathematical tests for randomness nor recognize reliably whether a given string was randomly generated.”

Leonard Mlodinow book The Drunkard's Walk

Prologue, p. ix
The Drunkard's Walk

People

“I am never forget the day I first meet the great Lobachevsky.
In one word he told me secret of success in mathematics: Plagiarize!
Plagiarize,
Let no one else's work evade your eyes,
Remember why the good Lord made your eyes,
So don't shade your eyes,
But plagiarize, plagiarize, plagiarize…
Only be sure always to call it please "research."”

Tom Lehrer (1928) American singer-songwriter and mathematician

"Lobachevsky"
Songs by Tom Lehrer (1953)

Secret, Success, Forgetting

“To analyse graphic representation precisely, it is helpful to distinguish it from musical, verbal and mathematical notations, all of which are perceived in a linear or temporal sequence. The graphic image also differs from figurative representation essentially polysemic, and from the animated image, governed by the laws of cinematographic time. Within the boundaries of graphics fall the fields of networks, diagrams and maps. The domain of graphic imagery ranges from the depiction of atomic structures to the representation of galaxies and extends into the spheres of topography and cartography.”

Jacques Bertin (1918–2010) French geographer and cartographer

Source: Semiology of graphics (1967/83), p. 2

Law, Music, Time, Help

“Traditional statistics is strong in devising ways of describing data and inferring distributional parameters from sample. Causal inference requires two additional ingredients: a science-friendly language for articulating causal knowledge, and a mathematical machinery for processing that knowledge, combining it with data and drawing new causal conclusions about a phenomenon.”

Judea Pearl (1936) Computer scientist

Pearl, Judea. "Causal inference in statistics: An overview." Statistics Surveys 3 (2009): 96-146.

Way, Knowledge, Strong, Science

“When I speak of language, I do not only mean poetic or verbal language: I am thinking of the language of mathematics, of physics, et cetera. It is a fascinating topic. Language is an interface between us and the world. Beyond language there is nothing but pure mystical contemplation of the universe.”

Caterina Davinio (1957) Italian writer

Source: Virtual Mercury House. Planetary & Interplanetary Events, p. 48

World, Thinking, Universe

“It was a biologist — Ludwig von Bertalanffy — who long ago perceived the essential unity of system concepts and techniques in the various fields of science and who in writings and lectures sought to attain recognition for “general systems theory” as a distinct scientific discipline. It is pertinent to note, however, that the work of Bertalannfy and his school, being motivated primarily by problems arising in the study of biological systems, is much more empirical and qualitative in spirit than the work of those system theorists who received their training in exact sciences.
In fact, there is a fairly wide gap between what might be regarded as “animate” system theorists and “inanimate” system theorists at the present time, and it is not at all certain that this gap will be narrowed, much less closed, in the near future.
There are some who feel this gap reflects the fundamental inadequacy of the conventional mathematics—the mathematics of precisely defined points, functions, sets, probability measures, etc.—for coping with the analysis of biological systems, and that to deal effectively with such systems, we need a radically different kind of mathematics, the mathematics of fuzzy or cloudy quantities which are not describable in terms of probability distributions. Indeed the need for such mathematics is becoming increasingly apparent even in the realms of inanimate systems”

Lotfi A. Zadeh (1921–2017) Electrical engineer and computer scientist

Zadeh (1962) "From circuit theory to system theory", Proceedings I.R.E., 1962, 50, 856-865. cited in: Brian R. Gaines (1979) " General systems research: quo vadis? http://pages.cpsc.ucalgary.ca/~gaines/reports/SYS/GS79/GS79.pdf", General Systems, Vol. 24 (1979), p. 12 1960s

School, Feeling, Motivation, Problem

“As far as the sensory experience of the spectator goes, the most outstanding American kinetic artist is unquestionably the Chinese-born Wen-Ying Tsai. His pieces, which are perfect on the technological level, serve the primary purpose of giving a complete visual experience to the spectator, whose sound solicitations provoke a choreographic, chromatic and rhythmic response in the ‘cybernetic sculptures’. […]
György Kepes has commented enthusiastically on the ‘magic rhythms emanating from this swaying, dancing steel trembling with life’, and he has also noted the sense of ‘an instant fellowship, a spontaneous celebration’ which is re-created in their presence. As he concludes: ‘Rhythm is friendship and in Tsai’s work there is friendship of light, sound and our own heart-beats.’
If this appraisal testifies to the success with which Tsai affects the sensory and emotional responses of the spectator, we must not neglect the fact that he is also addressing himself to reason and the scientific element in his audience. In effect, the observer can enter an almost mathematical relationship with these works, and sharpen his perceptual powers through the exact assessment of the various aesthetic parameters of vibration, sound, colour, wave movement, etc.”

Frank Popper (1918) French art historian

Frank Popper, Art--Action and Participation, New York University Press, 1975, p. 214

Life, Friendship, Sense, Light

“Little by little his conversation, always instructive and animated, gave a special direction to my tastes, which would have led me by preference towards letters. I resolved to complete my scientific studies and followed the courses in advanced mathematics given by M. [Jean Guillaume] Gamier. It was at the same time agreed by us that, in order to relieve him in his work, I should give some of the other courses with which he was charged. I thus found myself his pupil and his colleague.”

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

"Notice sur J.G. Garnier," Annuaire de l'acad. roy. de Brux. (1841) Vol. vii pp. 200-201 as quoted in Adolphe Quetelet as Statistician by Frank Hamilton Hankins

Study, Time, Animals

“Whenever I came to him (Fritz Sauter) with a pure physics idea, he would invariably say, with slight sarcasm: "But Mr. Kroemer, you ought to be able to formulate this mathematically! " If I came to him with a math formulation, I would get, in a similar tone: "But Mr. Kroemer, that is just math, what is the physics?" After a few encounters of this kind, you got the idea: You had to be able to go back and forth with ease. Yet, in the last analysis, concepts took priority over formalism, the latter was simply an (indispensable) means to an end.”

Herbert Kroemer (1928) Nobel laureate in physics

in his Autobiography http://nobelprize.org/nobel_prizes/physics/laureates/2000/kroemer-autobio.html, Herbert Kroemer, The Nobel Prize in Physics 2000

Idea

“My first contact with game theory was a popular article in Fortune Magazine which I read in my last high school year. I was immediately attracted to the subject matter and when I studied mathematics I found the fundamental book by von Neumann and Morgenstern in the library and studied it.”

Reinhard Selten (1930–2016) German economist

"Reinhard Selten - Biographical," 1994

Books, School, Game, Study

“Mathematical maturity is anyhow an uncertain concept, for the mind’s natural competence seems to change with age, its purview variable.”

Robert Langlands (1936) Canadian mathematician

Source: "Mathematical retrospections," 2013, p. 142

Age, Nature, Change

“The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.”

Freeman Dyson (1923) theoretical physicist and mathematician

"Freeman Dyson: Mathematician, Physicist, and Writer". Interview with Donald J. Albers, The College Mathematics Journal, vol 25, no. 1, (January 1994)

Problem

“I became aware that in Hank's recorded songs were the archetype rules of poetic songwriting. The architectural forms are like marble pillars and they had to be there. Even his words - all of the syllables are divided up so they make perfect mathematical sense. You can learn a lot about the structure of songwriting by listening to his records.”

Hank Williams (1923–1953) American country music singer

Bob Dylan, Chronicles: Volume One (2004)
About

Sense, Learning, Perfection

“In many ways it is true to say that syntax is mathematical logic, semantics is philosophy or philosophy of science, and pragmatics is psychology, but these fields are not really all distinct.”

Frank Honywill George (1921–1997) British psychologist

Source: The Brain As A Computer (1962), p.42 as cited in: Sica Pettigiani (1996) La comunicazione interumana. p.48

Way, Science

“Solving the value-loading problem is a research challenge worthy of some of the next generation’s best mathematical talent. We cannot postpone confronting this problem until the AI has developed enough reason to easily understand our intentions.”

Nick Bostrom book Superintelligence: Paths, Dangers, Strategies

Source: Superintelligence: Paths, Dangers, Strategies (2014), Ch. 12

Understanding, Problem

“The first intellectual operation in which I arrived at any proficiency, was dissecting a bad argument, and finding in what part the fallacy lay; and though whatever capacity of this sort I attained was due to the fact that it was an intellectual exercise in which I was most perseveringly drilled by my father, yet it is also true that the school logic, and the mental habits acquired in studying it, were among the principal instruments of this drilling. I am persuaded that nothing, in modern education, tends so much, when properly used, to form exact thinkers, who attach a precise meaning to words and propositions, and are not imposed on by vague, loose, or ambiguous terms. The boasted influence of mathematical studies is nothing to it; for in mathematical processes, none of the real difficulties of correct ratiocination occur.”

John Stuart Mill book Autobiography

Source: Autobiography (1873)

https://archive.org/details/autobiography01mill/page/19/mode/1up p. 19

Education, School, Exercises, Study

“First you must have faith in an eternal world independent of you; then you must have faith in your ability to perceive it, and finally you must try to explain it by means of concepts or mathematical constructions. But don't always accept traditional concepts without reexamining them. Even overthrow my relativity theory, if you find a better one.... You must believe that the world was created as a unified whole which is comprehensible to man. Of course, it's going to take an infinitely long time to investigate this unified creation. But to me that is the highest and most sacred duty—unifying physics. Simplicity is the criterion of the universe.”

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

Source: Attributed in posthumous publications, Einstein and the Poet (1983), p. 139

World, Faith, Universe, Time

“Mathematics is an ancient discipline. For as long as we can reliably reach into the past, we find its development intimately connected with the development of the whole of our civilization. For as long as we have a record of man's curiosity and his quest for understanding, we find mathematics cultivated and cherished, practiced and taught. Throughout the ages it has stood as an ultimate in rational thought and as a monument to man's desire to probe the workings of his own mind.”

Mark Kac (1914–1984) Polish-American mathematician

Postscript, p. 150.
Enigmas Of Chance (1985)

Age, Understanding, Past

“As a mathematical object, the constitution is maximally simple, consistent, necessarily incomplete, and interpretable as a model of natural law. Political authority is allocated solely to serve the constitution. There are no authorities which are not overseen, within nonlinear structures. Constitutional language is formally constructed to eliminate all ambiguity and to be processed algorithmically. Democratic elements, along with official discretion, and legal judgment, is incorporated reluctantly, minimized in principle, and gradually eliminated through incremental formal improvement. Argument defers to mathematical expertise. Politics is a disease that the constitution is designed to cure.”

Nick Land (1962) British philosopher

"A Republic, If You Can Keep It" https://web.archive.org/web/20140327090001/http://www.thatsmags.com/shanghai/articles/12321 (2013) (original emphasis)

Disease, Law, Nature

“Today, we are ranked so poorly in achievement scores. The average high school graduate in Japan has a better knowledge of science and mathematics than the average Filipino college graduate.”

Francis Escudero (1969) Filipino politician

2009, Speech: The Socio-Economic Peace Program of Senator Francis Escudero

School, Knowledge, Science

“There is a mistake into which several have fallen, and have deceived others, and perhaps themselves, by clothing some false reasoning in what they called a mathematical dress, imagining that by the application of mathematical symbols to their subject, they secured mathematical argument. This could not have happened if they had possessed a knowledge of the bounds within which the empire of mathematics is contained. That empire is sufficiently wide, and might have been better known, had the time which has been wasted in aggressions upon the domains of others, been spent in exploring the immense tracts which are yet untrodden.”

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

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

Imagination, Knowledge, Time, Falseness

“One might ask why the teachers do not notice the difficulty children have in learning BASIC. The answer is simple: Most teachers do not expect high performance from most students, especially in a domain of work that appears to be as "mathematical" and "formal" as programming. Thus the culture's general perception of mathematics as inaccessible bolsters the maintenance of BASIC, which in turn confirms these perceptions.”

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

Source: Mindstorms: Children, Computers, and Powerful Ideas (1980), Chapter 1, Computers and Computer Cultures

Children, Learning, Teachers, Appearance

“[Einstein's cosmological constant] is a name without any meaning. …We have, in fact, not the slightest inkling of what it's real significance is. It is put in the equations in order to give the greatest possible degree of mathematical generality.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932)

“You often hear that the language of science is mathematics. I don't completely agree with the article. I don't think it is a definite article. Mathematics is "a" language of science. But, it is only "a" language of science. The language of science is English. The language of science is Spanish.”

Daniel Alan Vallero (1953) American scientist

Acceptance speech, Alumni Achievement Award, Collinsville, Illinois. 2017.

Thinking, Science

“The next chapter is likely to provoke many mathematicians. This can't be helped. Mathematics is not what they think it is.”

David Deutsch book The Fabric of Reality

Source: The Fabric of Reality (1997), Ch. 10

Thinking, Help

“For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?”

Richard Courant (1888–1972) German American mathematician (1888-1972)

Richard Courant, What is Mathematics?, (1941) p. xix

Question

“A distinguished writer (Siméon Denis Poisson) has thus stated the fundamental definitions of the science:
:"The probability of an event is the reason we have to believe that it has taken place, or that it will take place."
:"The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible" (equally like to happen).
From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary.”

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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 243-4; As cited in: "George Boole (1815–64)" in: Oxford Dictionary of Scientific Quotations, Edited by W. F. Bynum and Roy Porter, January 2006

Knowledge, Thinking, Science

“With the aid of science we had built mighty civilizations thousands of years ago when most people in Europe (except in Greece and Rome) were living in forests. We had made outstanding scientific discoveries e. g. decimal system in mathematics, plastic surgery in medicine, etc. However, we subsequently took to the unscientific path of superstitions and empty rituals, which has led us to disaster. The way out of the present morass is to go back again to the path shown by our scientific ancestors, the path of Aryabhatta and Brahmagupta, Sushrut and Charak, Panini and Patanjali, Ramanujan and Raman.”

Markandey Katju (1946) Indian judge

As quoted in "Justice Markandey Katju's reply to two students who want to sue him" http://www.ndtv.com/india-news/justice-markandey-katjus-reply-to-two-students-who-want-to-sue-him-507071, NDTV (10 December 2012)

People, Way, Science

“In the same way as philosophy loses sight of its true object and appropriate matter, when either it passes into and merges in theology, or meddles with external politics, so also does it mar its proper form when it attempts to mimic the rigorous method of mathematics.”

Karl Wilhelm Friedrich Schlegel (1772–1829) German poet, critic and scholar

Philosophy of Life, Lecture 1

Way

“We don't know what energy is, any more than we know what information is, but as a now robust scientific concept we can describe it in precise mathematical terms, and as a commodity we can measure, market, regulate and tax it.”

Hans Christian von Baeyer (1938) American physicist

Source: Information, The New Language of Science (2003), Chapter 2, The Spell of Democritus, Why information will transform physics, p. 11

“Mathematics has also been developed as a philosophy, in the sense in which this term is defined by A. N. Whitehead as 'the endeavor to frame a coherent, logical and necessary system of general ideas in terms of which every element of our experience can be interpreted'. Substitute 'mathematics' for 'experience' and we have an admirable description of its speculative and philosophic development…. Philosophy of mathematics… has its paradoxes and antimonies, and also diverse schools of thought…”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

School, Idea, Sense

“Now with the big bang there is only one event that happened. So like the sun you can’t say that there are other big bangs going on that are what ours was like. The second problem is that at the big bang mathematics and physics break down. So there is no way of mathematically describing it. That is not a satisfactorily scientific approach, to ascribe something to speculations which you cannot justify using mathematics and physics.”

Jayant Narlikar (1938) Indian physicist

Jayant Narlikar's Cosmology

Way, Problem, Sun

“No statistician present at this moment will have been in doubt about the meaning of my words when I mentioned the common statistical model. It must be a stochastic device producing random results. Tossing coins or a dice or playing at cards are not flexible enough. The most general chance instrument is the urn filled with balls of different colours or with tickets bearing some ciphers or letters. This model is continuously used in our courses as a didactic tool, and in our statistical analyses as a means of translating realistic problems into mathematical ones. In statistical language " urn model " is a standard expression.”

Hans Freudenthal (1905–1990) Dutch mathematician

Source: The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961), p. 79; Partly cited in: Norman L. Johnson and Samuel Kotz (1977) Urn Models and Their Application: an. Approach to Modern Discrete Probability Theory http://dis.unal.edu.co/~gjhernandezp/sim/hide/Urn%20Models%20and%20Their%20Application%20-%20An%20approach%20to%20modern%20discrete%20probability%20theory_Norman%20L.Johnson(Wiley%201977%20413s).pdf, John Wiley & Sons.

Problem, Chance

“Complex adaptive systems have the property that if you run them—by just letting the mathematical variable of "time" go forward—they'll naturally progress from chaotic, disorganized, undifferentiated, independent states to organized, highly differentiated, and highly interdependent states. Organized structures emerge spontaneously… A weak system gives rise only to simpler forms of self-organization; a strong one gives rise to more complex forms, like life.”

J. Doyne Farmer (1952) American physicist and entrepreneur (b.1952)

The Third Culture: Beyond the Scientific Revolution (1995)

Life, Nature, Strong, Time

“The Elements has been considered as offering models of scrupulously rigorous demonstrations. It is certainly true that in point of rigour it compares favourably with its modern rivals; but when examined in the light of strict mathematical logic, it has been pronounced by C. S. Peirce to be "riddled with fallacies." The results are correct only because the writer's experience keeps him on his guard.”

Florian Cajori book A History of Mathematics

Source: A History of Mathematics (1893), p. 37. Reported in Moritz (1914)

Light

“Heisenberg now approached the problem from a new philosophical angle. He discarded all models, pictures and parables, and made a clear distinction between sure knowledge we gain from observation of nature and the conjectural knowledge we introduce when we use models, pictures and parables. Sure knowledge… can only be numerical, so that Heisenberg's results were inevitably mathematical in form, and could not disclose anything about the true nature of physical properties or entities.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

Nature, Knowledge, Problem

“The number of mathematical students, increased as it has been of late years, would be much augmented if those who hold the highest rank in science would condescend to give more effective assistance in clearing the elements of the difficulties which they present. If any one claiming that title should think my attempt obscure or enormus, he must share the blame with me, since it is through his neglect that I have been enabled to avail myself of an opportunity to perform a task which I would gladly have seen confided to more skilful hands.”

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

Author's Preface
On the Study and Difficulties of Mathematics (1831)

Confidence, Thinking, Science

“Pythagorean thought was dominated by mathematics, but it was also profoundly mystical.”

Vanna Bonta (1958–2014) Italian-American writer, poet, inventor, actress, voice artist (1958-2014)

Vanna Bonta Talks About Quantum fiction: Author Interview (2007)

“An uniformity of weights and measures, arranged upon mathematical principles, would be a benefit to the whole commercial world, if it were wise enough to adopt such an expedient.”

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

Source: A Treatise On Political Economy (Fourth Edition) (1832), Book III, On Consumption, Chapter VI, Section II, p. 433

World

“These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poised by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is roused by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplation. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers.”

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

Source: Mathematical Lectures (1734), p. 31: Prefatory Oration

Pleasure, Truth, Lie, Food

“There is no need in these mathematical days to defend the use of symbolism. It is regarded by many schools of modern thought as the only safe form of language. Wittgenstein treats symbols as something more than conventional signs, and regards them as corresponding in some way to the reality to which they refer. He would probably accept Gurdjieff’s dictum that:

Symbols not only transmit knowledge but show the way to it.

Even though other thinkers deny any objective reference to symbols, no one questions that symbolism has a power beyond that of ordinary language. It is different with the language of myth. This is despised by superficial thinkers, but the greatest philosophers have known its value.”

John G. Bennett (1897–1974) British mathematician and author

Gurdjieff’s All and Everything (1950)

School, Way, Question, Knowledge

“The theory of communication is partly concerned with the measurement of information content of signals, as their essential property in the establishment of communication links. But the information content of signals is not to be regarded as a commodity; it is more a property or potential of the signals, and as a concept it is closely related to the idea of selection, or discrimination. This mathematical theory first arose in telegraphy and telephony, being developed for the purpose of measuring the information content of telecommunication signals. It concerned only the signals themselves as transmitted along wires, or broadcast through the aether, and is quite abstracted from all questions of "meaning." Nor does it concern the importance, the value, or truth to any particular person. As a theory, it lies at the syntactic level of sign theory and is abstracted from the semantic and pragmatic levels. We shall argue … that, though the theory does not directly involve biological elements, it is nevertheless quite basic to the study of human communication -- basic but insufficient.”

Colin Cherry (1914–1979) British scientist

Source: On Human Communication (1957), What Is It That We Communicate?, p. 10

Truth, Communication, Idea, Question

“Purely mathematical symbols have no meaning by themselves; it is the privilege of pure mathematicians, to quote Bertrand Russell, not to know what they are talking about. …It is the physicist, and not the mathematician, who must know what he is talking about.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932)

Quotes

“Before a man can successfully plan a structure… he must study, from every possible angle, the ultimate purpose of his building. Attention must be directed to the basic structural concept before the mathematical process of calculation is undertaken.”

Eduardo Torroja (1899–1961) Spanish architect

p, 125
Philosophy of Structures (1958)

Study

“This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

Problem

“It is not of the essence of mathematics to be conversant with the ideas of number and quantity.”

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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: Alexander Bain (1870) Logic, p. 191

Idea

“The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician... Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.”

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

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 290; Cited in: Moritz (1914, 27): The Nature of Mathematics.

Nature, Appearance, Science

“Perhaps the least inadequate description of the general scope of modern Pure Mathematics—I will not call it a definition—would be to say that it deals with form, in a very general sense of the term; this would include algebraic form, functional relationship, the relations of order in any ordered set of entities such as numbers, and the analysis of the peculiarities of form of groups of operations.”

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

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 287; Cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/4/mode/2up, (1914), p. 5: Definitions and objects of mathematics.

Sense

“After earning the PhD degree and acquiring some relatively extensive experience in digital computers… It was time to leave the University. The result of an extensive search for the right job was a family move to Arlington Heights, Illinois, where it was a short commute to the Research Laboratories of the Pure Oil Company at Crystal Lake. I was given the title of Mathematical and Computer Consultant. The Labs were set in a beautiful campus, the professional personnel were eager to learn what I had to teach and to include me in many interesting projects where my knowledge and skills could be put to good use. I was encouraged to initiate my own program of research. I went to work with enthusiasm.
The corporate headquarters of Pure Oil were located in down town Chicago. Pure Oil had been trying to install an IBM 705 computer system for all their accounting needs including calculation of all data necessary for the management of exploration, drilling, refining and distribution of oil products and even royalties to shareholders in oil wells. Typical for those early days, the programming team was in deep difficulties and needed help; they lacked adequate resources and suitable training. The Executive Vice President of Pure Oil, when he heard that there was a computer expert already on the payroll at the Crystal Lake lab, ended our family blissful dream and I was reassigned to the down town office.”

A. Wayne Wymore (1927–2011) American mathematician

Systems Movement: Autobiographical Retrospectives (2004)

Family, Beauty, Dreams, Search

“Modern mind has become more and more calculating. The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world into an arithmetic problem, to fix every part of the world by mathematical formulas. Only money economy has filled the days of so many people with weighing, calculating, with numerical determinations, with a reduction of qualitative values to quantitative ones.”

Georg Simmel (1858–1918) German sociologist, philosopher, and critic

Source: The Metropolis and Modern Life (1903), p. 414

Life, Money, People, World

“Instead of wanting everyone to share and know of their discoveries the Pythagoreans suppressed the square root of two and the dodecahedron. The outside world was not to know. The Pythagoreans had discovered, in the mathematical underpinnings of nature, one of the two most powerful scientific tools, the other of course is experiment, but instead of using their insight to advance the collective voyage of human discovery they made of it little more than the hocus-pocus of a mystery cult. Science and mathematics were to be removed from the hands of the merchants and the artisans.”

Carl Sagan (1934–1996) American astrophysicist, cosmologist, author and science educator

38 min 10 sec
Cosmos: A Personal Voyage (1990 Update), The Backbone of Night [Episode 7]

World, Nature, Science

“I decided there ought to be another way of balancing out the various distortions without doing it mathematically.”

Arthur H. Robinson (1915–2004) American geographer

Robinson (1990) in The Times; As cited in: Myrna Oliver (2004): About the development of the Robinson projection.

Way

“I was a borderline computer science major before I came into interaction design; I’m really interested in physics and chemistry. This class was a way to throw design back into science and mathematics and help a community that is helping to give back to us.”

Akshay Agrawal (1998) Serial Social Entrepreneur

About working with MIT and JPL on an Ocean Eddy Simulation Visualization tool https://web.archive.org/web/20180518011711/https://designmattersatartcenter.org/proj/seeing-the-unseen/

Way, Communication, Science, Help

“Programming is much much harder than doing mathematics.”

Doron Zeilberger (1950) Israeli mathematician

The Narrow-Minded and Ignorant Referee's Report [and Zeilberger's Response] of Zeilberger's Paper "Automaric CounTilings" that was rejected by Helene Barcelo and the Members of the Advisory Board [that includes(!) Enumeration Expert Mireille Bousquet-Melou] of the Journal of Combinatorial Theory-Series A.

“Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.”

Freeman Dyson (1923) theoretical physicist and mathematician

The Scientist As Rebel (2006)

Truth, World, Behavior, Idea

“The history of mathematics is important also as a valuable contribution to the history of civilization. Human progress is closely identified with scientific thought. Mathematical and physical researches are a reliable record of intellectual progress.”

Florian Cajori book A History of Mathematics

Source: A History of Mathematics (1893), p. 4; Cited in: Moritz (1914, 90); Study and research in mathematics

History

“The West never came close to proletarian revolution. The Left likes to believe that it did. They like to argue that 'Franklin Roosevelt saved capitalism from itself'. This is another way of saying that John Maynard Keynes saved capitalism from itself. Both arguments are incorrect. Roosevelt and Keynes met only once. Roosevelt correctly assessed Keynes as a mathematician, not an economist. This was true. Keynes got his degree in mathematics, not economics. Roosevelt was the source of what we call Keynesianism, 1933-36, not Keynes, whose General Theory appeared in 1936. But scholars like to believe that academic arguments shape the world. They don't. They conform what has already begun to take root in the thinking and practices of the general public. When men decided that "thou shalt not steal" means "thou shalt not steal, except by majority vote," the Keynesian worldview was born. This view is dominant today. Marxism is dead. So is " means this: it is immoral to steal, with or without majority vote. This has nothing to do with the mode of production.”

Gary North (economist) (1942) American Christian Reconstructionist and economic historian

"Cultural Marxism Is an Oxymoron" http://www.garynorth.com/public/12623.cfm (1 July 2014), Gary North.

Men, World, Way, Thinking

“If paparazzi specialized in mathematical celebrities they'd camp outside the dining hall at the IAS and come away with a new batch of pictures every day.”

Cédric Villani book Birth of a Theorem

[Cédric Villani, Birth of a Theorem: A Mathematical Adventure, https://books.google.com/books?id=aN8tBQAAQBAJ&pg=PT70, 5 March 2015, Random House, 978-1-4481-5657-3, 70]

“Isaac Newton’s Philosophae Naturalis Principia Mathematica abstracted time from events, establishing its tractability to scientific calculation. Conceived as pure, absolute duration, without qualities, it conforms perfectly to its mathematical idealization (as the real number line). Since time is already pure, its reality indistinguishable from its formalization, a pure mathematics of change – the calculus – can be applied to physical reality without obstruction. The calculus can exactly describe things as they occur in themselves, without straying, even infinitesimally, from the rigorous dictates of formal intelligence. In this way natural philosophy becomes modern science.”

Nick Land (1962) British philosopher

"Time in Transition" https://web.archive.org/web/20121113235339/http://www.thatsmags.com/shanghai/article/777/time-in-transition (2011) (original emphasis)

Way, Intelligence, Nature, Reality

“Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery. One might think that time can now be conceived as a kind of space and try in vain to add visually a fourth dimension to the three dimensions of space. It is essential to guard against such a misunderstanding of mathematical concepts. If we add time to space as a fourth dimension it does not lose any of its peculiar character as time. …Musical tones can be ordered according to volume and pitch and are thus brought into a two dimensional manifold. Similarly colors can be determined by the three basic colors red, green and blue… Such an ordering does not change either tones or colors; it is merely a mathematical expression of something that we have known and visualized for a long time. Our schematization of time as a fourth dimension therefore does not imply any changes in the conception of time. …the space of visualization is only one of many possible forms that add content to the conceptual frame. We would therefore not call the representation of the tone manifold by a plane the visual representation of the two dimensional tone manifold.”

Hans Reichenbach (1891–1953) American philosopher

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

Music, Color, Thinking, Change

“Our future rates of gain will fall far short of those achieved in the past. Berkshire's capital base is now simply too large to allow us to earn truly outsized returns. If you believe otherwise, you should consider a career in sales but avoid one in mathematics (bearing in mind that there are really only three kinds of people in the world: those who can count and those who can't).”

Warren Buffett (1930) American business magnate, investor, and philanthropist

1998 Chairman's Letter http://www.berkshirehathaway.com/letters/1998pdf.pdf Letters to Shareholders (1957 - 2012)

People, World, Past, Future

“In general, it is possible to say that in artists as deliberate, as careful as [Durer and Holbein], drawing is particularly tight and the color is as cold as the verity of mathematics. In other artists, on the contrary, in those who are the poets of the heart, like Raphael, Correggio, Andrea del Sarto, line has more suppleness and color, more winning tenderness. In others whom we call realists that is to say, whose sensibility is more exterior, in Rubens, Velasquez, Rembrandt, for example, line has a living charm with its force and its repose, and the color sometimes bursts into a fanfare of sunlight, sometimes fades into mist.
So, the modes of expression of men of genius differ as much as their souls, and it is impossible to say that in some among them drawing and color are better or worse than in others.”

Auguste Rodin (1840–1917) French sculptor

Source: Art, 1912, Ch. V. Drawing and Color, p. 104-105

Men, Color, Soul, Heart

“Most mathematics books are filled with finished theorems and polished proofs, and to a surprising extent they ignore the methods used to create mathematics. It is as if you merely walked through a picture gallery and never told how to mix paints, how to compose pictures, or all the other "tricks of the trade."”

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

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

Books, Painting

“I must tell you that mathematicians are not scientists, they are artists…. Apart from the most elementary mathematics, like arithmetic or high school algebra, the symbols, formulas and words of mathematics have no meaning at all. The entire structure of pure mathematics is a monstrous swindle, simply a game, a reckless prank. You may well ask: "Are there no renegades to reveal the truth?" Yes, of course. But the facts are so incredible that no one takes them seriously. So the secret is in no danger.”

Theodore Kaczynski (1942) American domestic terrorist, mathematician and anarchist

The Net: The Unabomber, LSD and the Internet https://www.youtube.com/watch?v=xLqrVCi3l6E Interviews

Truth, Secret, School, Game

“A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?”

Martin Gardner (1914–2010) recreational mathematician and philosopher

The Dover Math and Science Newsletter http://www.doverpublications.com/mathsci/0516/d/ May 16, 2011

Beauty, Music

“Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.”

Ezra Pound book The Spirit of Romance

The Spirit of Romance (1910), p. 5

Science

“Life is not merely persistent, as Jock puts it; life is explosive. The basic theorem of population mathematics to which there has never been found an exception is that population increases always, not merely up to the extent of the food supply, but beyond it, to the minimum diet that will sustain life—the ragged edge of starvation.”

Robert A. Heinlein book Farmer in the Sky

Source: Farmer in the Sky (1950), Chapter 18, “Pioneer Party” (p. 196)

Life, Food

“The manner in which time and space are bound up with each other in the four-dimensional continuum is variable. It is difficult to express this variability of the cross-connections between space and time in simple language, and different interpretations of it are possible, corresponding to different mathematical transformations of the fundamental line-element, e. g. a different choice of the variable which we interpret as "time." Perhaps the best way we can express it is by saying that the solution of the field-equations of the theory of relativity shows that there is in the universe a tendency to change its scale, which at the present time results in an expansion, but may perhaps at other times become, or have been, a shrinking. This is true of the grand scale model of the universe.”

Willem de Sitter (1872–1934) Dutch cosmologist

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

Way, Universe, Change, Time

“There are people who have an instinctive yet perfect moral judgment, who can perform the most complex ethical calculations like an Indian peasant can sometimes perform astounding mathematical feats in a matter of seconds. Lily was such a person. I craved her approval.”

John Fowles book Daniel Martin

Daniel Martin (1977)

People, Personality, Perfection

“Journalism attracts people with exceptional linguistic talent, but I have found that very few have the mathematical sophistication to appreciate the difference between skill and luck.”

William J. Bernstein (1948) economist

Source: The Four Pillars of Investing (2002), Chapter 11, Oliver Stone Meets Wall Street, p. 220.

People

“The researches of the last thirty or forty years into the history of mathematics (I need only mention such names as those of [Carl Anton] Bretschneider, Hankel, Moritz Cantor, [Friedrich] Hultsch, Paul Tannery, Zeuthen, Loria, and Heiberg) have put the whole subject upon a different plane. I have endeavoured in this edition to take account of all the main results of these researches up to the present date. Thus, so far as the geometrical Books are concerned, my notes are intended to form a sort of dictionary of the history of elementary geometry, arranged according to subjects; while the notes on the arithmetical Books VII.-IX. and on Book X follow the same plan.”

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

p, 125
The Thirteen Books of Euclid's Elements (1908)

Books, History

“In 1963, when I completed my PhD, it was mostly on the steady-state theory using mathematical formulations to describe creation of matter. People always argued that you cannot have matter coming out of nothing, what would happen to the law of conservation of matter. It is a normal criticism of the steady-state theory. One could answer it either in one sentence by saying what is the big-bang theory where the entire universe came out of nothing, so you are violating the law of conservation of matter and energy in a big way. But that would be to point out the weakness of the other theories and not answering your own theory.”

Jayant Narlikar (1938) Indian physicist

An Exclusive Interview with Prof. Jayant Vishnu Narlikar

People, Law, Way, Universe

“Early in 1954 I was appointed Lecturer in Economics at the University of Queensland in Brisbane. Then, in 1956, I was awarded a Rockefeller Fellowship, enabling me and Anne to spend two years at Stanford University, where I got a Ph. D. in economics, whereas Anne got an M. A. in psychology. I had the good fortune of having Ken Arrow as advisor and as dissertation supervisor. I benefitted very much from discussing many finer points of economic theory with him. But I also benefitted substantially by following his advice to spend a sizable part of my Stanford time studying mathematics and statistics. These studies proved very useful in my later work in game theory.”

John Harsanyi (1920–2000) hungarian economist

"John C. Harsanyi - Biographical," 1994

Game, Study, Universe, Time

“There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.”

Nikolai Ivanovich Lobachevsky (1792–1856) Russian mathematician of Ukrainian origin

As quoted in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane, Springer (1998 [1975]), p. 225; also in Stanley Gudder, A Mathematical Journey, McGraw-Hill (1976), p. 36.

World

“The physicist … engages in complex and difficult calculations, involving the manipulating of ideal, mathematical quantities that, at first glance, are wholly lacking in the music of the living world and the beauty of the resplendent cosmos. It would seem as if there exists no relationship between these quantities and reality. Yet these ideal numbers that cannot be grasped by one's senses, these numbers that only are meaningful from within the system itself, only meaningful as part of abstract mathematical functions, symbolize the image of existence.”

Joseph B. Soloveitchik (1903–1993) American theologian

Source: Halakhic Man (1983), p. 83

World, Beauty, Music, Reality

“We built pyramids before Donald Trump even knew what architecture was. We taught philosophy and astrology [sic] and mathematics before Socrates and them Greek homos ever got around to it…Do some cracker come and tell you, ‘Well my mother and father blood go back to the Mayflower,’ you better hold your pocket. That ain’t nothing to be proud of, that means their forefathers was crooks.”

Al Sharpton (1954) American Baptist minister, civil rights activist, and television/radio talk show host

Speech at Kean College (1994), transcribed in The Forward (December 1995), as quoted in Foolish Words : The Most Stupid Words Ever Spoken (2003) by Laura Ward, p. 192.

“It is a far cry from the abacus to the modern keyboard accounting machine. It will be an equal step to the arithmetical machine of the future. But even this new machine will not take the scientist where he needs to go. Relief must be secured from laborious detailed manipulation of higher mathematics as well, if the users of it are to free their brains for something more than repetitive detailed transformations in accordance with established rules.”

Vannevar Bush book As We May Think

As We May Think (1945)

Future, Cry

“To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: 'Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy-Littlewood.”

John Edensor Littlewood (1885–1977) English Mathematician

Harald Bohr, [Harald Bohr, Collected Mathematical Works, 1, 1952, Dansk Matematisk Forening, Copenhagen, 3172542, xiii-xxxiv, Looking Backward], p. xxvii
About

“I made a very bad mistake; I miscounted these scraps of information on the record as 92, and in continual homage to this man who had been so influential to me, I began creating or constructing my own films on this so-called "magic" number of 92 … but when I eventually made a film about John Cage and met him, I explained this to him, and he found it very amusing because there are only 90 stories on the two sides of the record, and I'd based three years of my filmic career on this mathematical error!”

Peter Greenaway (1942) British film director

On John Cage's Indeterminacy, from an interview in Art and Design, no. 49
Interviews

Error

“A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.”

John Edensor Littlewood (1885–1977) English Mathematician

"Introduction to A Mathematician's Miscellany", p. 24.
Littlewood's Miscellany (1986)

“School children and students who love God should never say: "For my part I like mathematics"; "I like French"; "I like Greek." They should learn to like all these subjects, because all of them develop that faculty of attention which, directed toward God, is the very substance of prayer.”

Simone Weil (1909–1943) French philosopher, Christian mystic, and social activist

Waiting on God (1950), Reflections on the Right Use of School Studies with a View to the Love of God

Love, God, Children, School

“Anyone who compares the bibliography with the reprinted papers will notice that mathematics and physics have not been given equal treatment. There is a strong bias in favor of mathematics. The bias arises from the fact that mathematical papers, provided that are correct and not trivial, have permanent value, whereas most papers in physics journals are ephemeral. For this reason, it is customary to publish complete collected works of mathematicians but only selected works of physicists.”

Freeman Dyson (1923) theoretical physicist and mathematician

Selected Papers of Freeman Dyson with Commentary. https://books.google.com/books?id=nnyNUidX1OMC&pg=PA1 American Mathematical Soc. (1996) p. 1

Strong

“I am an anarchist, a political and social Huguenot; I deny everything and affirm naught but myself: because the sole truth of which I have material and moral proof and tangible, comprehensible and intelligible evidence, the only real, startling, non-arbitrary truth not susceptible to interpretation, is myself. I am. There I have a positive fact. Everything else is abstraction and, in mathematics, would be designated as "x", and unknown quantity; and I need not trouble myself with it.”

Anselme Bellegarrigue book Anarchist Manifesto

Anarchist Manifesto (1850)

Truth, Intelligence

“The function of logic in mathematics is critical rather than constructive.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“Music, also, the architect ought to understand so that he may have knowledge of the canonical and mathematical theory, and besides be able to tune ballistae, catapultae, and scorpiones to the proper key. For to the right and left in the beams are the holes in the frames through which the strings of twisted sinew are stretched by means of windlasses and bars, and these strings must not be clamped and made fast until they give the same correct note to the ear of the skilled workman.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book I, Chapter I, Sec. 8

Music, Understanding, Knowledge

Lysander Spooner (1808–1887) Anarchist, Entrepreneur, Abolitionist

Sections I–II, p. 11–12
Natural Law; or The Science of Justice (1882), Chapter II. The Science of Justice (Continued)

Men, Pleasure, World, Justice

“The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence,—an impression which the great Euler confessed he often could not get rid of. This feeling finds a sort of justification when we reflect that the majority of the ideas we deal with were conceived by others, often centuries ago. In a great measure it is really the intelligence of other people that confronts us in science.—Mach, Ernst.”

Ernst Mach (1838–1916) Austrian physicist and university educator

Source: 20th century, Popular Scientific Lectures, (Chicago, 1910), p. 196: Mathematics seems possessed of intelligence

People, Feeling, Intelligence, Idea

“Mathematics occupies a peculiar position in cultural life today. 'Everybody knows' that it is one of the most basic, and also ancient, types of knowledge; yet it is not part of normal cultural discourse, and few people know much about its historical development, or even that it has a history.”

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

Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, Volume 1, page 3, 2003.

Life, People, History, Knowledge

“The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.”

Nicholas Murray Butler (1862–1947) American philosopher, diplomat, and educator

The Meaning of Education and other Essays and Addresses https://books.google.com/books?id=H9cKAAAAIAAJ (1898) p. 45 as quoted by Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book https://books.google.com/books?id=G0wtAAAAYAAJ (1914)

History, Sense, Science

“The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic and construct its method; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and, finally, to collect from the various elements of truth brought to view in the course of these inquiries some probable intimations concerning the nature and constitution of the human mind.”

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

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 1; Ch. 1. Nature And Design Of This Work, lead paragraph

Truth, Law, Nature, Science

“In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.”

Hermann Weyl Invariants

Weyl, Hermann. Invariants. Duke Math. J. 5 (1939), no. 3, 489--502. doi:10.1215/S0012-7094-39-00540-5. http://projecteuclid.org/euclid.dmj/1077491405.

Angels, Soul, Fight

“With me, everything turns into mathematics.
More closely translated as: but in my opinion, all things in nature occur mathematically.”
Mais apud me omnia fiunt Mathematicè in Natura

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

""Mais"" is French for ""but"" and the ""but in my opinion"" comes from the context of the original conversation. apud me omnia fiunt Mathematicè in Natura is in latin. Sometimes the Latin version is incorrectly quoted as Omnia apud me mathematica fiunt. Sources: Correspondence with Mersenne http://fr.wikisource.org/wiki/Page%3aDescartes_-_%C5%92uvres,_%C3%A9d._Adam_et_Tannery,_III.djvu/48 note for line 7 (1640), page 36, Die Wiener Zeit http://books.google.com/books?id=9Xh3fVZLCycC&pg=PA532&lpg=PA532&dq=%22Omnia+apud+me+mathematica+fiunt%22+original+zitat&source=bl&ots=CgQOrveRiM&sig=WFHwIK20r5vRZ66FwCaxo857LCU&hl=de&sa=X&ei=_Wf2UcHlJYbfsgaf1IHABg#v=onepage&q=%22Omnia%20apud%20me%20mathematica%20fiunt%22%20original%20zitat&f=false page 532 (2008); StackExchange Math Q/A Where did Descartes write... http://math.stackexchange.com/questions/454599/where-did-descartes-write-with-me-everything-turns-into-mathematics?noredirect=1#comment978229_454599

Nature

“Babylonian mathematics and astronomy have left an indelible impression on our exact sciences. We still call some of the planets by their Babylonian names in translation.”

Cyrus H. Gordon (1908–2001) American linguist

Introduction
Adventures in the Nearest East (1957)

Science

“The brilliant summaries by Bourbaki (1969) and Weyl (1951)… set a high standard of exposition, but… there is room for a history of mathematical ideas which will demand less mathematical expertise and offer a more detailed account of the motivation of research.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

History, Motivation, Idea