Math Quotes - Page 28

• Gauss replied, when asked how soon he expected to reach certain mathematical conclusions, that he had them long ago, all he was worrying about was how to reach them!

  Rene Dubos

  Long Ago, Worry, Certain

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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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• To your care and recommendation am I indebted for having replaced a half-blind mathematician with a mathematician with both eyes, which will especially please the anatomical members of my Academy.

  Frederick The Great

  Eye, Half, Care

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• A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.

  Gottlob Frege

  Giving, Foundation, Letters

  Note in the appendix of "Grundlagen der Arithmetik" (Vol. 2), after Frege had received a letter of Bertrand Russell in which Russell had explained his discovery of, what is now known as, Russell's paradox, 1903.

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• [Statistics are] the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of Man.

  Francis Galton

  Cutting, Men, Bars

  Natural Inheritance Normal Variability (pp. 62-3)

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• I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

  Carl Friedrich Gauss

  Science, Mechanic, Conviction

  "Solid Shape". Book by Jan J. Koenderink, 1990.

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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 mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe.

  Karl Pearson

  May, Results, Description

  Karl Pearson (1900). “The grammar of science”, p.505, Рипол Классик

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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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• If one must choose between rigour and meaning, I shall unhesitatingly choose the latter.

  Rene Thom

  Rigour, Latter, Ifs

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• Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.

  William Thurston

  Thinking, Errors, Ideas

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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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• The years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving until one breaks through to clarity and understanding, are known only to him who has experienced them himself.

  Albert Einstein

  Dark, Years, Break Through

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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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• The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.

  David Hilbert

  Figures, Diagrams, Formulas

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• ... commutative algebra is a lot like topology, only backwards.

  John C. Baez

  Topology, Algebra, Backwards

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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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• Mathematical objects are determined by - and understood by - the network of relationships they enjoy with all the other objects of their species.

  Barry Mazur

  Determined, Enjoy, Understood

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• All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

  G. H. Hardy

  Hunting, Use, Half

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• The real irony is that the view of infinity as some forbidden zone or road to insanity - which view was very old and powerful and haunted math for 2000+ years - is precisely what Cantor's own work overturned. Saying that infinity drove Cantor mad is sort of like mourning St. George's loss to the dragon: it's not only wrong but insulting.

  David Foster Wallace

  Powerful, Real, Loss

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• Topology is precisely the mathematical discipline that allows the passage from local to global.

  Rene Thom

  Discipline, Topology, Passages

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