Math Quotes - Page 24

• Make your mistakes work for you by learning from them.

  Donald Trump

  Mistake, Teaching

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• Figures don't lie, but liars figure.

  Mark Twain

  Liars, Lying, Teaching

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• The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

  John von Neumann

  Teaching, Thinking, Achievement

  John Von Neumann, F. Bródy, Tibor Vámos (1995). “The Neumann Compendium”, p.620, World Scientific

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• Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.

  Hermann Weyl

  Teaching, Creative, Understanding

  Hermann Weyl (1968). “Gesammelte Abhandlungen”

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• The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific "truth." But what is the source of knowledge? Where do the laws that are to be tested come from? Experiment, itself, helps to produce these laws, in the sense that it gives us hints. But also needed is imagination to create from these hints the great generalizations--to guess at the wonderful, simple, but very strange patterns beneath them all, and then to experiment to check again whether we have made the right guess.

  Richard P. Feynman

  Science, Simple, Law

  Richard P. Feynman, Robert B. Leighton, Matthew Sands (2015). “The Feynman Lectures on Physics, Vol. I: The New Millennium Edition: Mainly Mechanics, Radiation, and Heat”, p.45, Basic Books

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• Next you'd see a raft sliding by, away off yonder, and maybe a galoot on it chopping. . . you'd see the ax flash and come down-you don't hear nothing; you see the ax go up again, and by the time it's above the man's head then you hear the k'chunk!-it had took all that time to come over the water.

  Mark Twain

  Science, Men, Water

  Mark Twain, General Press (2016). “The Complete Works of Mark Twain: All 13 Novels, Short Stories, Poetry and Essays”, p.475, GENERAL PRESS

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• To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.

  Arthur Eddington

  Cat, Would Be, Physics

  Arthur Eddington (1933). “The Expanding Universe: Astronomy's 'Great Debate', 1900-1931”, p.103, Cambridge University Press

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• Physics is much too hard for physicists.

  David Hilbert

  Physics, Physicist, Hard

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• We come now to the question: what is a priori certain or necessary, respectively in geometry (doctrine of space) or its foundations? Formerly we thought everything; nowadays we think nothing. Already the distance-concept is logically arbitrary; there need be no things that correspond to it, even approximately.

  Albert Einstein

  Distance, Thinking, Space

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• It can be shown that a mathematical web of some kind can be woven about any universe containing several objects. The fact that our universe lends itself to mathematical treatment is not a fact of any great philosophical significance.

  Bertrand Russell

  Kindness, Philosophical, Woven

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• How can a modern anthropologist embark upon a generalization with any hope of arriving at a satisfactory conclusion? By thinking of the organizational ideas that are present in any society as a mathematical pattern.

  Edmund Leach

  Hope, Thinking, Ideas

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• If "Number rules the universe" as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.

  Eric Temple Bell

  Numbers, Thrones, Ifs

  Eric Temple Bell (1945). “Men of Mathematics”

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• Teaching school is but another word for sure and not very slow destruction.

  Thomas Carlyle

  Teaching, School, Destruction

  Thomas Carlyle (1886). “Early Letters”, p.281, Georg Olms Verlag

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• I concluded that I might take as a general rule the principle that all things which we very clearly and obviously conceive are true: only observing, however, that there is some difficulty in rightly determining the objects which we distinctly conceive.

  Rene Descartes

  Principles, Might, Difficulty

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• When writing about transcendental issues, be transcendentally clear.

  Rene Descartes

  Writing, Issues, Transcendental

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• This has been done elegantly by Minkowski; but chalk is cheaper than grey matter, and we will do it as it comes.

  Albert Einstein

  Grey Matter, Done, Chalk

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• What is this frog and mouse battle among the mathematicians?

  Albert Einstein

  Battle, Frogs, Mice

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• I feel engulfed in the infinite immensity of spaces whereof I know nothing, and which know nothing of me, I am terrified The eternal silence of these infinite spaces alarms me.

  Blaise Pascal

  Space, Silence, Alarms

  "The Thoughts of Blaise Pascal". Book by Blaise Pascal, published by Kegan Paul. Chapter "The Misery of Man Without God", 1885.

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• The world of ideas is not revealed to us in one stroke; we must both permanently and unceasingly recreate it in our consciousness.

  Rene Thom

  Ideas, World, Consciousness

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• ... if one were to refuse to have direct, geometric, intuitive insights, if one were reduced to pure logic, which does not permit a choice among every thing that is exact, one would hardly think of many questions, and certain notions ... would escape us completely.

  Henri Lebesgue

  Thinking, Choices, Doe

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• What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises.

  Georg C. Lichtenberg

  Mind, Needs, Use

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• Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process - having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other's work.

  Paul Lockhart

  Teacher, Ideas, Focus

  "A Mathematician's Lament". Book by Paul Lockhart, www.huffingtonpost.com. 2009.

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• ... it can often be profitable to try a technique on a problem even if you know in advance that it cannot possibly solve the problem completely.

  Terence Tao

  Often Is, Trying, Technique

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• It's better to work with a nice category containing some nasty objects, than a nasty category containing only nice objects.

  John C. Baez

  Nice, Nasty, Categories

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• Geometry is the art of correct reasoning from incorrectly drawn figures.

  Henri Poincare

  Art, Figures, Geometry

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