Quotes on the nature and scope of mathematics

Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.
Sofya Kovalevskaya

Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.
Shakuntala Devi

Mathematics is the most beautiful and most powerful creation of the human spirit.
Stefan Banach

Mathematics is the music of reason.
James Joseph Sylvester

The essence of mathematics lies in its freedom.
Georg Cantor

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Bertrand Russell

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 poetry.
Bertrand Russell

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.
Richard Courant

But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius.
Marston Morse

God used beautiful mathematics in creating the world.
Paul Dirac

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.
Andre Weil

Mathematics has beauty and romance. It’s not a boring place to be, the mathematical world. It’s an extraordinary place; it’s worth spending time there.
Marcus du Sautoy

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

I believe only in the mathematics.
Claudio Ranieri

Quotes on the relationship between mathematics and values

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

Mathematics allows for no hypocrisy and no vagueness.
Stendhal

The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.
Daniel Dennett

I became an atheist because, as a graduate student studying quantum physics, life seemed to be reducible to second-order differential equations. Mathematics, chemistry and physics had it all. And I didn’t see any need to go beyond that.
Francis Collins

Quotes on the communication of ideas in mathematics

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

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
Bertrand Russell

Language is remarkable, except under the extreme constraints of mathematics and logic, it never can talk only about what it’s supposed to talk about but is always spreading around.
Howard Nemerov

Logic and mathematics are nothing but specialised linguistic structures.
Jean Piaget

You can not apply mathematics as long as words still becloud reality.
Hermann Weyl

Film is one of the three universal languages, the other two: mathematics and music.
Frank Capra

Language is remarkable, except under the extreme constraints of mathematics and logic, it never can talk only about what it’s supposed to talk about but is always spreading around.
Howard Nemerov

The power of mathematics is often to change one thing into another, to change geometry into language.
Marcus du Sautoy

You can not apply mathematics as long as words still becloud reality.
Hermann Weyl

Quotes on mathematics, perspectives, and context

I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.
Maryam Mirzakhani

Mathematics allows for no hypocrisy and no vagueness.
Stendhal 

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 knows no races or geographic boundaries; for mathematics, the cultural world is one country.
David Hilbert

Quotes on the creation of new ideas in mathematics

I didn’t know what kinds of questions to ask in mathematics. In physics, I could see there were things that were known and things that weren’t.
Margaret Geller

Creativity is essential to particle physics, cosmology, and to mathematics, and to other fields of science, just as it is to its more widely acknowledged beneficiaries – the arts and humanities.
Lisa Randall

The mathematics is not there till we put it there.
Arthur Eddington 

For most people, the major hurdle in grasping modern insights into the nature of the universe is that these developments are usually phrased using mathematics.
Brian Greene

‘Obvious’ is the most dangerous word in mathematics.
E. T. Bell

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.
E. T. Bell

The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future.
E. T. Bell

The longer mathematics lives the more abstract – and therefore, possibly also the more practical – it becomes.
E. T. Bell

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
Felix Klein

I am interested in mathematics only as a creative art.
GH Hardy

Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty’s sake and pulls it down to earth.
Marston Morse

Quotes on becoming a discerning knower about mathematics

The beauty of mathematics only shows itself to more patient followers.
Maryam Mirzakhani

Mathematics is the most beautiful and most powerful creation of the human spirit.
Stefan Banach

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.
Felix Klein

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
Felix Klein

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

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