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Use the quotes to provide students with a quick access point into mathematics, prompt discussions and debates in your classroom, and introduce a range of influential thinkers.

We've arranged these quotes in a way that relates to our 5 Big Question framework for TOK, which is our favoured way of structuring the course. There are other ways to structure TOK, such as the Classic structure.

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Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.

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Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.

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Ada Lovelace

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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.

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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.

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Margaret Geller

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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.

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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.

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Lisa Randall

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The mathematics is not there till we put it there.

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The mathematics is not there till we put it there.

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Arthur Eddington

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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.

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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.

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Brian Greene

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I am interested in mathematics only as a creative art.

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I am interested in mathematics only as a creative art.

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GH Hardy

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

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

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E. T. Bell

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

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

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E. T. Bell

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

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

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E. T. Bell

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

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

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Felix Klein

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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.

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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.

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Marston Morse

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

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

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Maryam Mirzakhani

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Mathematics allows for no hypocrisy and no vagueness.

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Mathematics allows for no hypocrisy and no vagueness.

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Stendhal

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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.

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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.

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Albert Einstein

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

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

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David Hilbert

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Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.

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Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.

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Shakuntala Devi

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

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

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Bertrand Russell

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Logic and mathematics are nothing but specialised linguistic structures.

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Logic and mathematics are nothing but specialised linguistic structures.

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Jean Piaget

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

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

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Albert Einstein

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

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

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Hermann Weyl

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

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

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Frank Capra

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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.

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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.

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Howard Nemerov

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

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

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Marcus du Sautoy

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

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

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Hermann Weyl

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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.

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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.

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Daniel Dennett

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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.

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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.

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Francis Collins

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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.

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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.

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Bertrand Russell

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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.

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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.

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Sofya Kovalevskaya

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

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

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Stefan Banach

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James Joseph Sylvester

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The essence of mathematics lies in its freedom.

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The essence of mathematics lies in its freedom.

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Georg Cantor

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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.

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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.

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Bertrand Russell

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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.

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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.

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Bertrand Russell

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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.

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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.

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Richard Courant

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

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

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Marston Morse

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God used beautiful mathematics in creating the world.

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God used beautiful mathematics in creating the world.

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Paul Dirac

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

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

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Andre Weil

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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.

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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.

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Marcus du Sautoy

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

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

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Georg Cantor

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Claudio Ranieri

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Mathematics allows for no hypocrisy and no vagueness.

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Mathematics allows for no hypocrisy and no vagueness.

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Stendhal