Math Quotations

< 32.7 Srinivasa Ramanujan | Topic Index | 32.9 Modular Arithmetic >

Here are a few quotations which show how mathematicians viewed their subject.

Mathematics

"Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty" - Archimedes

"Proof is an idol before which the mathematician tortures himself" - Arthur Eddington

"Mathematics does not grow through a monotonous increase of the number of indubitably established theorems, but through the incessant improvement of guesses by speculation and criticism" - Imre Lakatos

"I wanted certainty in the kind of way in which people want religious faith. I thought certainty is more likely to be found in mathematics than elsewhere. But after twenty years of arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable" - Bertrand Russel in 1959

“People think that mathematics is complicated. Mathematics is the simple bit, it’s the stuff we CAN understand. It’s cats that are complicated.” — John Horton Conway

"One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts." - Albert Einstein

"Either mathematics is too big for the human mind, or the human mind is more than a machine." - Kurt Gödel

"Pure mathematics is, in its way, the poetry of logical ideas"-Albert Einstein, in his obituary for Emmy Noether (1935)

“Mathematics is like oxygen. If it is there, you do not notice it. If it would not be there, you realize that you cannot do without.” - Lex Schrijver

Mathematics is the glory of the human mind - Liebnitz

“Mathematics is the music of reason.” - Paul Lockhart

"… the perpetuation of this “pseudo-mathematics,” this emphasis on the accurate yet mindless manipulation of symbols, creates its own culture and its own set of values. Those who have become adept at it derive a great deal of self-esteem from their success. The last thing they want to hear is that math is really about raw creativity and aesthetic sensitivity. Many a graduate student has come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions. Math is not about following directions, it’s about making new directions - Paul Lockhart in his piece, A Mathematician’s Lament

Mathematics is the most marvelous instrument created by the genius of man for the discovery of truth. - Laisant.

From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician -Sir James Jeans

Universe is written in the language of mathematics and its characters are triangles, circles and other geometrical figures – Galileo

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience -Emmanuel Kant

[Mathematics] is an independent world created out of pure intelligence -William Wordsworth

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning -John Locke

The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit – Alfred North Whitehead

Mathematics is not about numbers, equations, computations or algorithms, it is about understanding - William Paul Thurston

So Mathematical Truth prefers simple words since the language of Truth is itself simple - Tycho Brahe, Danish Astronomer (translated from Latin)

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 - Bertrand Russel

“Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as a sensible intelligible world.” - Bertrand Russell

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

“The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.” -Bertrand Russell

“Mathematics is the poetry of the universe.”- Jonathan David Farley

“Mathematics is the discipline dealing with nontrivial and interesting things.”-Jody Azzouni

“Mathematics is the queen of the sciences.”- Carl Friedrich Gauss

“Mathematics is a game played according to certain simple rules with meaningless marks on paper.” - David Hilbert

“All that is correct thinking is mathematics.”- Grigore Moisil

“How does the mathematician — closer to the artist than to the explorer — by turning away from nature, arrive at its most appropriate descriptions?” – Mark Steiner

“Mathematics is the door and key of the sciences.” - Roger Bacon

“Mathematics is the art of giving the same name to different things.” - Henri Poincaré

"Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose." - Henri Poincaré

“Mathematics is the tool especially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.” - Paul Dirac

“Mathematics is pure language — the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms- Alfred Adler

“Pure mathematics is, in its way, the poetry of logical ideas.”-Albert Einstein

“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

“Mathematics is not only real, but it is the only reality.” -Martin Gardner

“How does the mathematician — closer to the artist than to the explorer — by turning away from nature, arrive at its most appropriate descriptions?” – Mark Steiner

"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning" - Eugene Wigner

“Mathematical concepts turn up in entirely unexpected connections. Moreover, they often permit an unexpectedly close and accurate description of the phenomenon in these connections.” - Eugene Wigner

‘Mathematics is simultaneously a discipline, a method, and a language, applicable to other disciplines or methods of knowledge, but also to mathematics itself. It is a mode of organizing, validating, and communicating knowledge, which uses the principles of logic and gives it a field of manifestation and application that is “pure,” free from contingency, and free from the confusion of natural language, in which the truths of propositions are universally valid and do not depend on any interpretation. It is the only discipline entitled to investigate concepts of any nature and any degree of generality, but also to be self-referential and self-applicable, as is in fact human reason.’ - Dr. Catalin Barboianu is the author of the book What is Mathematics: School Guide to Conceptual Understanding of Mathematics

“Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.” ― Jordan Ellenberg, How Not to Be Wrong

“Mathematics is the extension of common sense by other means.” - ― Jordan Ellenberg, How Not to Be Wrong

"The heart of mathematics is its problems" - Paul Holmos

“The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization “ - John Kemeny

"Go down deep enough into anything and you will find mathematics" - Dean Schlicter

"Mathematics makes the invisible visible" – Keith Devlin

“Mathematics is the art of giving the same name to different things.” - – Henry Poincaré

"The essence of mathematics is not to make simple things complicated, but to make complicated things simple.” – Stan Gudder

"A mathematician is a maker of patterns, like a painter or poet." - G H Hardy

“The mathematician’s patterns, like the painter’s or poet’s, must be beautiful … Beauty is the first test: there is no permanent place in the world for ugly mathematics.” - G H Hardy

"Only by giving up math’s connection to reality, could it guide us to a deeper truth about the way the universe works" -Derek Muller

"Mathematics is about relationships, relationships & relationships' - Christina Tondewold

Arithmetic

God created the natural numbers. All the rest is the work of man - Leopold Kronecker; German mathematician and logician; 1823-1891.

God does arithmetic -Karl Friedrich Gauss

“Mathematics is the queen of sciences, and arithmetic is the queen of mathematics.” Karl Friedrich Gauss

Wherever there is number there is beauty - Proclus

“Why are numbers beautiful? It’s like asking why is Beethoven’s ninth symphony beautiful. If you don’t see why someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.” - Paul Erdos

"As far as I’m concerned, prime numbers constitute a more stable reality than the material reality that surrounds us" A.Connes

Place Value System

“The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. The importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius.” - Pierre Simon Laplace

Geometry

God geometrises continually - Plato

There is no royal road to Geometry - Euclid

All my physics is nothing else than geometry - Descartes

If the Greeks had not cultivated conic sections, Kepler would not have superseded Ptolemy - Whewell.

Geometry is nothing if it is not rigorous – H J S Smith

“Let no one unversed in geometry enter here” - Inscription at the gate of Plato's Academy

"There is geometry in the humming of the strings, there is music in the spacing of the spheres." - Pythagoras

Statistics

“Statistics is the grammar of science.” - Karl Pearson

Mathematics & Sciences

The universe is under no obligation to make sense to you - Neil deGrasse Tyson

The two eyes of exact science of mathematics and logic - De Morgan

Mathematics is the study of anything that obeys the rules of logic, using the rules of logic- Eugenia Cheng

All scientific education which does not commence with mathematics is, of necessity, defective at its foundation - Compte.

Mathematics is the indispensable instrument of all physical research - Berthelot

A natural science is a science only in so far as it is mathematical - Kant.

Mathematics is the gate and key to science – Roger Bacon

Mathematics is the queen of sciences She often condescends to render service to astronomy and other natural sciences, but in all relations, she is entitled to the first rank - Carl Friedrich Gauss; German mathematician, physicist, and prodigy; 1777-1855.

The great book of nature can be read-only by those who know the language in which it was written. And this language is mathematics- Galileo

There is no branch of mathematics, however abstract, which may not someday be applied to phenomena of the real world - Nikolai Lobatchevsky

Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore - Albert Einstein

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

“Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics" - Leonardo Da Vinci

No investigation can claim to be scientific if it does not pass the test of mathematical proof – Leonardo da Vinci

Math & AI in Biology - There’s an age-old adage in biology: structure determines function. In order to understand the function of the myriad proteins that perform vital jobs in a healthy body—or malfunction in a diseased one—scientists have to first determine these proteins’ molecular structure. But this is no easy feat: protein molecules consist of long, twisty chains of up to thousands of amino acids, chemical compounds that can interact with one another in many ways to take on an enormous number of possible three-dimensional shapes. Figuring out a single protein’s structure, or solving the “protein-folding problem,” can take years of finicky experiments - Google DeepMind CEO Demis Hassabis explains how its AlphaFold AI program predicted the 3-D structure of every known protein

Mathematics & Society

I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate -David Mumford

The progress &amp; the improvement of mathematics are linked to the prosperity of the state - Napoleon.

No subject loses more than mathematics by any attempt to dissociate it from its history - Glaisher.

A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator the smaller the fraction - Leo Tolstoy

The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head - G K Chesterton

The study of mathematics is the indispensable basis for all intellectual and spiritual progress — F.M. Cornford (1874–1943)

“Music is the pleasure the human mind experiences from counting without being aware that it is counting” - Gottfried Leibniz

“May not music be described as the mathematics of the senses, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.” - James Joseph Sylvester

The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization. -John Kemeny The essence of mathematics is not to make simple things complicated, but to make complicated things simple. -S. Gudder

Go down deep enough into anything and you will find mathematics. -Dean Schlicter Realizing that mathematics was developed with contributions from every race and culture helps students see mathematics as being more accessible – L Shirley (‘Using Ethnomathematics to Find Multicultural Mathematics Connections’)

”An equation for me has no meaning unless it expresses the mind of God.” - Ramanujan Srinivasa

Mathematics - Other Branches

A topologist is one who doesn't know the difference between a doughnut and a coffee cup -John Kelley

Statistics: the mathematical theory of ignorance -Morris Kline

Math & Humanities

"Poetry says more with fewer words. So does mathematics.” - Unknown

Music is the pleasure the human mind experiences from counting without being aware that it is counting. -Gottfried Leibniz

Doing Mathematics

“In mathematics, the art of proposing a question must be held of higher value than solving it.” - Georg Cantor.

“The yearning for and the satisfaction gained from mathematical insight brings the subject near to art.” - Olga Taussky-Todd

It (Math) can help us see the big picture and realize that we’re “just scratching the surface of something really profound.” Dr. Francis Su, the author of “Mathematics for Human Flourishing"

"Math does not mean that you have to do it all 'in your head'. Mental math means that you do it 'with your head'"– Cathy Fosnot

"One enters the first room of the mansion and it’s dark. One stumbles around bumping into furniture, but gradually you learn where each piece of furniture is. Finally, after six months of so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are the culmination of, and couldn’t exist without, the many months of stumbling around in the dark that precede them" - Andrew Wiles recalling his pursuit of a proof for Fermat's Last Theorem

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

“Every good mathematician is at least half a philosopher, and every good philosopher at least half a mathematician" - Gottlieb Frege

"In mathematics you don't understand things. You just get used to them." – John von Neumann

"I used to feel guilty in Cambridge that I spent all day playing games, while I was supposed to be doing mathematics. Then … I realized that playing games is math" - John Conway

Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, openness, visualization, and flexibility, the mathematics comes alive - Jo Boaler

 Imaginary Numbers

Square root of minus one in Schrödinger’s wave equation means that nature works with complex numbers and not with real numbers. Schrödinger put the square root of minus one into the equation, and suddenly it made sense. Suddenly, it became a wave equation instead of a heat conduction equation. And Schrödinger found, to his delight, that the equation has solutions corresponding to the quantized orbits in the Bohr model of the atom. It turns out that the Schrödinger equation describes correctly everything we know about the behaviour of atoms. It is the basis of all chemistry and most of physics. - Freeman Dyson, about the usage of imaginary numbers

< 32.7 Srinivasa Ramanujan | Topic Index | 32.9 Modular Arithmetic >