Quotes about mathematics

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

Best quotes about mathematics

Maryam Mirzakhani photo

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

—  Maryam Mirzakhani Iranian mathematician 1977 - 2017

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

John Nash photo

„You don't have to be a mathematician to have a feel for numbers.“

—  John Nash American mathematician and Nobel Prize laureate 1928 - 2015

Statement of 2006, partly cited in Stop Making Sense: Music from the Perspective of the Real (2015) by Scott Wilson, p. 117
2000s
Context: You don't have to be a mathematician to have a feel for numbers. A movie, by the way, was made — sort of a small-scale offbeat movie — called Pi recently. I think it starts off with a big string of digits running across the screen, and then there are people who get concerned with various things, and in the end this Bible code idea comes up. And that ties in with numbers, so the relation to numbers is not necessarily scientific, and even when I was mentally disturbed, I had a lot of interest in numbers.

Albert Einstein photo

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

—  Albert Einstein German-born physicist and founder of the theory of relativity 1879 - 1955

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.

Emmy Noether photo

„It is already all in Dedekind.“

—  Emmy Noether German mathematician 1882 - 1935

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.

Euclid photo

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

—  Euclid Greek mathematician, inventor of axiomatic geometry -323 - -285 BC

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

René Descartes photo

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

—  René Descartes French philosopher, mathematician, and scientist 1596 - 1650

Joseph Fourier photo

„Profound study of nature is the most fertile source of mathematical discoveries.“

—  Joseph Fourier, book The Analytical Theory of Heat

Source: The Analytical Theory of Heat (1878), Ch. 1, p. 7

René Descartes photo

„With me, everything turns into mathematics.“

—  René Descartes French philosopher, mathematician, and scientist 1596 - 1650

Mais apud me omnia fiunt Mathematicè in Natura More closely translated as: but in my opinion, all things in nature occur mathematically. Note: "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

Paulo Coelho photo
Blaise Pascal photo

„Dull minds are never either intuitive or mathematical.“

—  Blaise Pascal, Pensées

Source: Pensées

All quotes about mathematics

Total 1328 quotes mathematics, filter:

Nikola Tesla photo

„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 Serbian American inventor 1856 - 1943

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

Maryam Mirzakhani photo

„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 Iranian mathematician 1977 - 2017

Interview with Research Fellow Maryam Mirzakhani | january 2008

Roger Bacon photo
Aryabhata photo
John Von Neumann photo

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

—  John Von Neumann Hungarian-American mathematician and polymath 1903 - 1957

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.

Alex Jones photo

„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 American radio host, author, conspiracy theorist and filmmaker 1974

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

Emmy Noether photo
David Hilbert photo
Antoine Augustin Cournot photo
Kurt Gödel photo

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

—  Kurt Gödel logician, mathematician, and philosopher of mathematics 1906 - 1978

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

George Boole photo

„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 English mathematician, philosopher and logician 1815 - 1864

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

Claude Debussy photo

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

—  Claude Debussy French composer 1862 - 1918

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.

Noam Chomsky photo

„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 american linguist, philosopher and activist 1928

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.

Alan Turing photo

„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.

Roger Bacon photo

„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.

George Boole photo

„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 English mathematician, philosopher and logician 1815 - 1864

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.

Stephen Hawking photo

„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?

Richard Dawkins photo

„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 English ethologist, evolutionary biologist and author 1941

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

Douglas Adams photo
Albert Einstein photo

„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 German-born physicist and founder of the theory of relativity 1879 - 1955

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<!-- Zurich: Europa Verlag -->, 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.

Mike Myers photo
Shiing-Shen Chern photo
Hans Reichenbach photo
William Thomson photo
Roger Bacon photo

„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

Vitruvius photo
John Nash photo
Ronald Fisher photo

„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 English statistician, evolutionary biologist, geneticist, and eugenicist 1890 - 1962

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

Archimedes photo
Shiing-Shen Chern photo
Albert Einstein photo
Ronald Fisher photo

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

—  Ronald Fisher English statistician, evolutionary biologist, geneticist, and eugenicist 1890 - 1962

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

Isa Bowman photo
Walter A. Shewhart photo
Steven Pinker photo
Brian Cox (physicist) photo

„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) English physicist and former musician 1968

Conclusion in Wonders of the Universe - Destiny

Frank P. Ramsey photo

„I thought we should require physical determinations, and not abstract integrations. A pernicious taste begins to infiltrate, from which real science will suffer far more than it will progress, and it would be often better for the true physics if there were no mathematics in the world.“

—  Daniel Bernoulli

Ich vermeinte, man verlange physische Determinationen und nicht abstracte integrationes. Es fängt sich ein verderblicher goût an einzuschleichen, durch welchen die wahren Wissenschaften viel mehr leiden, als sie avancirt werden, und wäre es oft besser für die realem physicam, wenn keine Mathematik auf der Welt wäre.
Letter to Leonhard Euler, 26 January 1750, published in [Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle, P. H. Fuss, Saint Petersburg, 1843, 650]

Mahmoud Ahmadinejad photo

„We had principles in mathematics that were granted to be absolute in mathematics for over 800 years, but new science has gotten rid of those absolutism, gotten — forward other different logics of looking at mathematics, and sort of turned the way we look at it as a science altogether after 800 years.“

—  Mahmoud Ahmadinejad 6th President of the Islamic Republic of Iran 1956

Columbia University speech, 24 September 2007
[24 September 2007, http://www.azstarnet.com/sn/hourlyupdate/202820.php, "Iran's president at Columbia University - a transcript", azstarnet.com, 2007-09-25]
2007

David Hilbert photo

„Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.“

—  David Hilbert German prominent mathematician 1862 - 1943

Quoted in Mathematical Circles Revisited (1971) by Howard Whitley Eves

Albert A. Michelson photo
David Deutsch photo
John Locke photo
David Hilbert photo
John Nash photo
Carl Gustav Jacob Jacobi photo

„Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case.“

—  Carl Gustav Jacob Jacobi German mathematician 1804 - 1851

Vorlesungen über analytische Mechanik [Lectures on Analytical Mechanics] (1847/48; edited by Helmut Pulte in 1996).

François Viète photo

„In mathematics there is a certain way of seeking the truth, a way which Plato is said first to have discovered and which was called "analysis" by Theon and was defined by him as "taking the thing sought as granted and proceeding by means of what follows to a truth which is uncontested"; so, on the other hand, "synthesis" is "taking the thing that is granted and proceeding by means of what follows to the conclusion and comprehension of the thing sought." And although the ancients set forth a twofold analysis, the zetetic and the poristic, to which Theon's definition particularly refers, it is nevertheless fitting that there be established also a third kind, which may be called rhetic or exegetic, so that there is a zetetic art by which is found the equation or proportion between the magnitude that is being sought and those that are given, a poristic art by which from the equation or proportion the truth of the theorem set up is investigated, and an exegetic art by which from the equation set up or the proportion, there is produced the magnitude itself which is being sought. And thus, the whole threefold analytic art, claiming for itself this office, may be defined as the science of right finding in mathematics…. the zetetic art does not employ its logic on numbers—which was the tediousness of the ancient analysts—but uses its logic through a logistic which in a new way has to do with species [of number]…“

—  François Viète French mathematician 1540 - 1603

Source: In artem analyticem Isagoge (1591), Ch. 1 as quoted by Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (1934-1936) Appendix.

Joseph Louis Lagrange photo
Mortimer J. Adler photo
Henri Fayol photo
John Nash photo

„I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia.“

—  John Nash American mathematician and Nobel Prize laureate 1928 - 2015

Statement of 1996, as quoted in Dr. Riemann's Zeros (2003) by Karl Sabbagh, p. 88
1990s

John Napier photo

„Arrange all these results as described, and you will produce a Table, certainly the most excellent of all Mathematical tables, and prepared for the most important uses.“

—  John Napier Scottish mathematician 1550 - 1617

The Construction of the Wonderful Canon of Logarithms (1889)
Context: From the Radical table completed in this way, you will find with great exactness the logarithms of all sines between radius and the sine 45 degrees; from the arc of 45 degrees doubled, you will find the logarithm of half radius; having obtained all these, you will find the other logarithms. Arrange all these results as described, and you will produce a Table, certainly the most excellent of all Mathematical tables, and prepared for the most important uses.

Rollo May photo

„It is interesting that the term mystic is used in this derogatory sense to mean anything we cannot segmentize and count. The odd belief prevails in our culture that a thing or experience is not real if we cannot make it mathematical, and that somehow it must be real if we can reduce it to numbers.“

—  Rollo May US psychiatrist 1909 - 1994

Existence (1956) p. 39; also published in The Discovery of Being : Writings in Existential Psychology (1983), Part III : Contributions to Therapy, Ch. 6 : To Be and Not to Be, p. 94
Existence (1958)
Context: It is interesting that the term mystic is used in this derogatory sense to mean anything we cannot segmentize and count. The odd belief prevails in our culture that a thing or experience is not real if we cannot make it mathematical, and that somehow it must be real if we can reduce it to numbers. But this means making an abstraction out of it … Modern Western man thus finds himself in the strange situation, after reducing something to an abstraction, of having then to persuade himself it is real. … the only experience we let ourselves believe in as real, is that which precisely is not.

Galén photo

„For truly on countless occasions throughout my life I have had this experience; persons for a time talk pleasantly with me because of my work among the sick, in which they think me very well trained, but when they learn later on that I am also trained in mathematics, they avoid me for the most part and are no longer at all glad to be with me.“

—  Galén Roman physician, surgeon and philosopher 129 - 216

Galen. Margaret Tallmadge May (trans.) On the Usefulness of the Parts of the Body, Ithaca, New York: Cornell U. Press, 1968. p. 502.
Context: A god, as I have said, commanded me to tell the first use also, and he himself knows that I have shrunk from its obscurity. He knows too that not only here but also in many other places in these commentaries, if it depended on me, I would omit demonstrations requiring astronomy, geometry, music, or any other logical discipline, lest my books should be held in utter detestation by physicians. For truly on countless occasions throughout my life I have had this experience; persons for a time talk pleasantly with me because of my work among the sick, in which they think me very well trained, but when they learn later on that I am also trained in mathematics, they avoid me for the most part and are no longer at all glad to be with me. Accordingly, I am always wary of touching on such subjects, and in this case it is only in obedience to the command of a divinity, as I have said, that I have used the theorems of geometry

David Hilbert photo

„Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.“

—  David Hilbert, Mathematical Problems

Mathematical Problems (1900)
Context: Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

David Hilbert photo

„A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts.“

—  David Hilbert, Mathematical Problems

Mathematical Problems (1900)
Context: A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

Aristotle photo
David Bohm photo

„My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc.“

—  David Bohm, book Wholeness and the Implicate Order

Wholeness and the Implicate Order (1980)
Context: My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc. (Perhaps we could say that this is what is involved in harmony between the 'left brain' and the 'right brain'). This kind of overall way of thinking is not only a fertile source of new theoretical ideas: it is needed for the human mind to function in a generally harmonious way, which could in turn help to make possible an orderly and stable society. <!-- p. xi

David Hilbert photo

„A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.“

—  David Hilbert, Mathematical Problems

Eine mathematische Theorie ist nicht eher als vollkommen anzusehen, als bis du sie so klar gemacht hast, daß du sie dem ersten Manne erklären könntest, den du auf der Straße triffst.
Mathematical Problems (1900)
Context: An old French mathematician said: A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

Paul Dirac photo

„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 theoretical physicist 1902 - 1984

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.

Jacques Lacan photo

„In order to understand the Freudian concepts, one must set out on the basis that it is the subject who is called—the subject of Cartesian origin. This basis gives its true function to what, in analysis, is called recollection or remembering. Recollection is not Platonic reminiscence —it is not the return of a form, an imprint, a eidos of beauty and good,a supreme truth, coming to us from the beyond. It is something that comes to us from the structural necessities, something humble, born at the level of the lowest encounters and of all the talking crowd that precedes us, at the level of the structure of the signifier, of the languages spoken in a stuttering, stumbling way, but which cannot elude constraints whose echoes, model, style can be found, curiously enough, in contemporary mathematics.“

—  Jacques Lacan French psychoanalyst and psychiatrist 1901 - 1981

Of the Network of Signifiers
The Four Fundamental Concepts of Psycho Analysis (1978)
Context: It is on this step that depends the fact that one can call upon the subject to re-enter himself in the unconscious—for, after all, it is important to know who one is calling. It is not the soul, either mortal or immortal, which has been with us for so long, nor some shade, some double, some phantom, nor even some supposed psycho-spherical shell, the locus of the defences and other such simplified notions. It is the subject who is called— there is only he, therefore, who can be chosen. There may be, as in the parable, many called and few chosen, but there will certainly not be any others except those who are called. In order to understand the Freudian concepts, one must set out on the basis that it is the subject who is called—the subject of Cartesian origin. This basis gives its true function to what, in analysis, is called recollection or remembering. Recollection is not Platonic reminiscence —it is not the return of a form, an imprint, a eidos of beauty and good, a supreme truth, coming to us from the beyond. It is something that comes to us from the structural necessities, something humble, born at the level of the lowest encounters and of all the talking crowd that precedes us, at the level of the structure of the signifier, of the languages spoken in a stuttering, stumbling way, but which cannot elude constraints whose echoes, model, style can be found, curiously enough, in contemporary mathematics.

Alhazen photo

„He lived in a period of competitive patronage of the sciences, especially mathematics and astronomy, in the Middle East and Central Asia. He is said to have been a high administrative official in a small principality made up of Basra, in what is now Iraq, and the adjacent region of Ahwâz.“

—  Alhazen Arab physicist, mathematician and astronomer 965 - 1039

Abdelhamid I. Sabra, in “Ibn al-Haytham Brief life of an Arab mathematician: died circa 1040 (September-October 2003)”

Ronald Fisher photo

„He has made contributions to many areas of science; among them are agronomy, anthropology, astronomy, bacteriology, botany, economics, forestry, meteorology, psychology, public health, and-above all-genetics, in which he is recognized as one of the leaders. Out of this varied scientific research and his skill in mathematics, he has evolved systematic principles for the interpretation of empirical data; and he has founded a science of experimental design. On the foundations he has laid down, there has been erected a structure of statistical techniques that are used whenever people attempt to learn about nature from experiment and observation.“

—  Ronald Fisher English statistician, evolutionary biologist, geneticist, and eugenicist 1890 - 1962

W. Allen Wallis (1952) at the University of Chicago while honoring Fisher with the Honorary degree of Doctor of Science; cited in: George E. P. Box (1976) " Science and Statistics http://www-sop.inria.fr/members/Ian.Jermyn/philosophy/writings/Boxonmaths.pdf" Journal of the American Statistical Association, Vol. 71, No. 356. (Dec., 1976), pp. 791-799.

Carl Schmitt photo
Aryabhata photo

„His work, called Aryabhatiya, is composed of three parts, in only the first of which use is made of a special notation of numbers. It is an alphabetical system in which the twenty-five consonants represent 1-25, respectively; other letters stand for 30, 40, …., 100 etc. The other mathematical parts of Aryabhatiya consists of rules without examples. Another alphabetic system prevailed in Southern India, the numbers 1-19 being designated by consonants, etc.“

—  Aryabhata Indian mathematician-astronomer 476 - 550

Florian Cajori in: A History of Mathematical Notations http://books.google.co.in/books?id=_byqAAAAQBAJ&pg=PT961&dq=Notations&hl=en&sa=X&ei=Wz65U5WYDIKulAW1qIGYDA&ved=0CBwQ6AEwAA#v=onepage&q=Notation&f=false, Courier Dover Publications, 26 September 2013, p. 47.

Matt Haig photo
Sam Harris photo
Robert A. Heinlein photo

„The 3-legged stool of understanding is held up by history, languages, and mathematics. Equipped with those three you can learn anything you want to learn. But if you lack any one of them you are just another ignorant peasant with dung on your boots.“

—  Robert A. Heinlein, book Expanded Universe

Source: "The Happy Days Ahead" in Expanded Universe (1980)
Context: I started clipping and filing by categories on trends as early as 1930 and my "youngest" file was started in 1945.
Span of time is important; the 3-legged stool of understanding is held up by history, languages, and mathematics. Equipped with these three you can learn anything you want to learn. But if you lack any one of them you are just another ignorant peasant with dung on your boots.

Zelda Fitzgerald photo

„Life has puffed and blown itself into a summer day, and clouds and spring billow over the heavens as if calendars were a listing of mathematical errors.“

—  Zelda Fitzgerald Novelist, wife of F. Scott Fitzgerald 1900 - 1948

Source: Dear Scott, Dearest Zelda: The Love Letters of F. Scott and Zelda Fitzgerald

Jodi Picoult photo
Albert Einstein photo

„As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.“

—  Albert Einstein German-born physicist and founder of the theory of relativity 1879 - 1955

Insofern sich die Sätze der Mathematik auf die Wirklichkeit beziehen, sind sie nicht sicher, und insofern sie sicher sind, beziehen sie sich nicht auf die Wirklichkeit. http://books.google.com/books?id=QF0ON71WuxEC&q=%22Insofern+sich+die+S%C3%A4tze+der+Mathematik+auf+die%22&pg=PA3#v=onepage

Geometrie and Erfahrung (1921) pp. 3-4 link.springer.com http://link.springer.com/chapter/10.1007%2F978-3-642-49903-6_1#page-1 as cited by Karl Popper, The Two Fundamental Problems of the Theory of Knowledge (2014) Tr. Andreas Pickel, Ed. Troels Eggers Hansen.
Ref: en.wikiquote.org - Albert Einstein / Quotes / 1920s

http://books.google.com/books?id=QF0ON71WuxEC&q=%22beziehen+sind+sie+nicht+sicher+und+insofern+sie+sicher+sind+beziehen+sie+sich+nicht+auf+die+Wirklichkeit%22&pg=PA4#v=onepage
1920s, Sidelights on Relativity (1922)

Graham Greene photo
Werner Heisenberg photo

„I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.“

—  Werner Heisenberg German theoretical physicist 1901 - 1976

Das Naturgesetz und die Struktur der Materie (1967), as translated in Natural Law and the Structure of Matter (1981), p. 34

Graham Greene photo
Anthony Doerr photo
Thomas Mann photo
Raymond Chandler photo
Bertrand Russell photo
Francis Bacon photo

„Histories make men wise; poets, witty; the mathematics, subtile; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend.“

—  Francis Bacon English philosopher, statesman, scientist, jurist, and author 1561 - 1626

Of Studies
Essays (1625)
Source: The Collected Works of Sir Francis Bacon

John Von Neumann photo

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

—  John Von Neumann Hungarian-American mathematician and polymath 1903 - 1957

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.

Jon Krakauer photo
Arthur Conan Doyle photo
Malcolm X photo
Louisa May Alcott photo
William Gibson photo

„Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts…“

—  William Gibson, book Neuromancer

Source: Neuromancer (1984)
Context: Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts… A graphic representation of data abstracted from banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data. Like city lights, receding...

Alan Moore photo

„Sexually progressive cultures gave us mathematics, literature, philosophy, civilization and the rest, while sexually restrictive cultures gave us the Dark Ages and the Holocaust.“

—  Alan Moore English writer primarily known for his work in comic books 1953

"BOG VENUS VERSUS NAZI COCK-RING: Some Thoughts Concerning Pornography" in Arthur magazine, Vol. 1, No. 25 (November 2006) http://www.arthurmag.com/magpie/?p=1685
Source: 25,000 Years of Erotic Freedom
Context: Sexually progressive cultures gave us mathematics, literature, philosophy, civilization and the rest, while sexually restrictive cultures gave us the Dark Ages and the Holocaust. Not that I’m trying to load my argument, of course.

Greg Egan photo
August Strindberg photo
Amy Chua photo

„As a purely mathematical fact, people who sleep less live more.“

—  Amy Chua, book Battle Hymn of the Tiger Mother

Source: Battle Hymn of the Tiger Mother

Barbara Kingsolver photo
Bertrand Russell photo

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

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970

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.

„Has anyone ever told you you’re sexy as hell when you’re mathematizing?“

—  Kresley Cole American writer

Source: Dark Desires After Dusk

H.L. Mencken photo
Michael Crichton photo
Robert A. Heinlein photo
Galileo Galilei photo

„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>.

Albert Einstein photo

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

—  Albert Einstein German-born physicist and founder of the theory of relativity 1879 - 1955

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