Mathematical Quotes - Page 37

• I have no faith in political arithmetic.

  Adam Smith

  Faith, Math, Political

  "Wealth of Nations". Book by Adam Smith, March 9, 1776.

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• Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.

  John Locke

  Math, Proof, Diamond

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• Our teaching of mathematics revolves around a fundamental conflict. Rightly or wrongly, students are required to master a series of mathematical concepts and techniques, and anything that might divert them from doing so is deemed unnecessary. Putting mathematics into its cultural context, explaining what is has done for humanity, telling the story of its historical development, or pointing out the wealth of unsolved problems or even the existence of topics that do not make it into school textbooks leaves less time to prepare for the exam. So most of these things aren't discussed.

  Ian Stewart

  Education, Teaching, School

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• Mathematics is the science of patterns, and nature exploits just about every pattern that there is.

  Ian Stewart

  Patterns, Mathematics, Exploits

  Ian Stewart (2008). “Nature's Numbers: The Unreal Reality Of Mathematics”, p.18, Basic Books

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• Love was even more mathematical than poetry. It was the pure mathematics of the spirit.

  Charles Williams

  Spirit, Mathematics, Pure

  Charles Williams (2016). “Descent Into Hell”, p.65, Charles Williams

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• He who has heard the same thing told by 12,000 eye-witnesses has only 12,000 probabilities, which are equal to one strong probability, which is far from certain.

  Voltaire

  Strong, Eye, Math

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• Mathematicians are beginning to view order and chaos as two distinct manifestations of an underlying determinism. And neither state exists in isolation. The typical system can exist in a variety of states, some ordered, some chaotic. Instead of two opposed polarities, there is a continuous spectrum. As harmony and discord combine in musical beauty, so order and chaos combine in mathematical [and physical] beauty.

  Ian Stewart

  Beauty, Art, Views

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• ...a major triumph of mathematical imagination: the use of visual imagery to condense a large quantity of information into a single comprehensible picture... Mathematicians are just beginning to understand these basic building blocks of change and to analyze how they combine. The methodology involved has a very different spirit from traditional modeling with differential equations: it is more like chemistry than calculus, requiring careful counterpoint between analysis and synthesis.

  Ian Stewart

  Beauty, Art, Block

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• The social sciences, I thought, needed the same kind of rigor and the same mathematical underpinnings that had made the 'hard' sciences so brilliantly successful.

  Herbert Simon

  Successful, Kind, Social

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• I hope no man takes what I said about the living and dieing of men for mathematical demonstration.

  William Petty

  Men, Said, Demonstration

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• The history of art cannot be properly understood without some reference to the history of science. In both we are studying the symbols by which man affirms his mental scheme, and these symbols, be they pictorial or mathematical, a fable or formula, will reflect the same changes.

  Kenneth Clark

  Art, Men, Fables

  "How to Think Like Leonardo da Vinci: Seven Steps to Genius Every Day". Book by Michael J. Gelb (p. 127), October 21, 2009.

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• The nude gains its enduring value from the fact that it reconciles several contrary states. It takes the most sensual and immediately interesting object, the human body, and puts it out of reach of time and desire; it takes the most purely rational concept of which mankind is capable, mathematical order, and makes it a delight to the senses; and it takes the vague fears of the unknown and sweetens them by showing that the gods are like men and may be worshiped for their life-giving beauty rather than their death-dealing powers.

  Kenneth Clark

  Men, Order, Giving

  "The Nude: A Study in Ideal Form" by Kenneth Clark, (Ch. I), 1951.

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• "Nought usually comes at the beginning," Ralph said. "Not necessarily," said Sibyl. "It might come anywhere. Nought isn't a number at all. It's the opposite of number." Nancy looked up from the cards. "Got you, aunt," she said. "What about ten? Nought's a number there - it's part of ten." "Well, if you say that any mathematical arrangement of one and nought really makes ten - " Sibyl smiled. "Can it possibly be more than a way of representing ten?"

  Charles Williams

  Aunt, Opposites, Numbers

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• To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.

  Ian Stewart

  Technology, Ideas, Simplicity

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• For me, rhythm is a type of divine mathematics in a way. No matter where you're from, we can all understand the mathematics of rhythm. I try to apply this mathematical thinking to my playing.

  John McLaughlin

  Thinking, Trying, Matter

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• The problem with cinema nowadays is that it's a math problem. People can read a film mathematically; they know when this comes or that comes; in about 30 minutes, it's going to be over and have an ending. So film has become a mathematical solution. And that is boring, because art is not mathematical.

  Nicolas Winding Refn

  Art, Math, People

  Source: www.indiewire.com

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• Our inner weighing of evidence is not a careful mathematical calculation resulting in a probabilistic estimate of truth, but more like a whirlpool blending of the objective and the personal. The result is a set of beliefs - both conscious and unconscious - that guide us in interpreting all the events of our lives.

  Leonard Mlodinow

  Events, Belief, Conscious

  Deepak Chopra, Leonard Mlodinow (2011). “War of the Worldviews: Where Science and Spirituality Meet -- and Do Not”, p.270, Harmony

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• A mathematical idea should not be petrified in a formalised axiomatic setting, but should be considered instead as flowing as a river.

  James Joseph Sylvester

  Ideas, Rivers, Should

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• Strange! I don't understand how it is that we can write mathematical expressions and calculate what the thing is going to do without being able to picture it.

  Richard P. Feynman

  Writing, Expression, Able

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• If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither "number" nor "size", but always form. And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.

  Alexander Grothendieck

  Numbers, Faces, Size

  "Alexander Grothendieck, Math Enigma, Dies at 86" by Bruce Weber and Julie Rehmeyer, www.nytimes.com. November 14, 2014.

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• Nothing can be more fatal to progress than a too confident reliance on mathematical symbols; for the student is only too apt to take the easier course, and consider the formula not the fact as the physical reality.

  Lord Kelvin

  Reality, Progress, Facts

  "Treatise on Natural Philosophy". Book by Lord Kelvin and Peter Guthrie Tait, quod.lib.umich.edu. 1867.

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• Requirements in mathematical language are no use unless they are easier to read than the code.

  David Parnas

  Use, Requirements, Language

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• Absolute, true and mathematical time, of itself, and from its own nature flows equably without relation to anything external.

  Isaac Newton

  Flow, Relation, Absolutes

  Sir Isaac Newton, Florian Cajori (1946). “Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World”, p.6, Univ of California Press

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• It follows that the word probability, in its mathematical acceptance, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information 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. Probability is the expectation founded upon partial knowledge.

  George Boole

  Acceptance, Thinking, Expectations

  George Boole (2007). “An Investigation of the Laws of Thought”, p.244, Cosimo, Inc.

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• This harmony that human intelligence believes it discovers in nature - does it exist apart from that intelligence? No, without doubt, a reality completely independent of the spirit which conceives it, sees it or feels it, is an impossibility. A world so exterior as that, even if it existed, would be forever inaccessible to us. But what we call objective reality is, in the last analysis, that which is common to several thinking beings, and could be common to all; this common part, we will see, can be nothing but the harmony expressed by mathematical laws.

  Henri Poincare

  Believe, Independent, Reality

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