Mathematical Quotes - Page 24

• [The] humanization of mathematical teaching, the bringing of the matter and the spirit of mathematics to bear not merely upon certain fragmentary faculties of the mind, but upon the whole mind, that this is the greatest desideratum is. I assume, beyond dispute.

  Cassius Jackson Keyser

  Teaching, Science, Mind

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• I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics.

  Balfour Stewart

  Philosophy, Exercise, Science

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• Imagination is the Discovering Faculty, pre-eminently ... It is that which feels & discovers what is, the REAL which we see not, which exists not for our senses... Mathematical science shows what is. It is the language of unseen relations between things... Imagination too shows what is ... Hence she is or should be especially cultivated by the truly Scientific, those who wish to enter into the worlds around us!

  Ada Lovelace

  Real, Science, Discovery

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• Like Molière's M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole's The Mathematical Analysis of Logic.

  Ernest Nagel

  Nature, Real, Science

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• Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.

  Chen-Ning Yang

  Beautiful, Nature, Science

  Chen Ning Yang (2013). “Selected Papers of Chen Ning Yang II: With Commentaries”, p.260, World Scientific

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• All the effects of Nature are only the mathematical consequences of a small number of immutable laws.

  Pierre-Simon Laplace

  Beauty, Art, Nature

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• It is probably no exaggeration to suppose that in order to improve such an organ as the eye at all, it must be improved in ten different ways at once. And the improbability of any complex organ being produced and brought to perfection in any such way is an improbability of the same kind and degree as that of producing a poem or a mathematical demonstration by throwing letters at random on a table.

  Joseph Murray

  Eye, Science, Order

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• Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly-yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.

  Robert Kanigel

  Nature, Science, Years

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• The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little inquiry into its nature and purpose as a deliberate human activity. Doubtless this is due to the inevitable drawback that mathematical study is saturated with technicalities from beginning to end.

  Herbert Turnbull

  Science, Experts, Purpose

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• The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.

  Cassius Jackson Keyser

  Independent, World, Matter

  Cassius Jackson Keyser (1929). “The pastures of wonder: the realm of mathematics and the realm of science”

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• When the difficulty of a problem lies only in finding out what follows from certain fixed premises, mathematical methods furnish invaluable wings for flying over intermediate obstructions.

  Arthur M. Wellington

  Lying, Science, Wings

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• [Before the time of Benjamin Peirce it never occurred to anyone that mathematical research] was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood alone-a mountain peak whose absolute height might be hard to measure, but which towered above all the surrounding country.

  Julian Coolidge

  Country, Science, Mountain Peaks

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• [In the Royal Society, there] has been, a constant Resolution, to reject all the amplifications, digressions, and swellings of style: to return back to the primitive purity, and shortness, when men deliver'd so many things, almost in an equal number of words. They have exacted from all their members, a close, naked, natural way of speaking; positive expressions; clear senses; a native easiness: bringing all things as near the Mathematical plainness, as they can: and preferring the language of Artizans, Countrymen, and Merchants, before that, of Wits, or Scholars.

  Thomas Sprat

  Men, Numbers, Expression

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• How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

  Clifford Truesdell

  Science, Years, Swim

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• There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot successfully be put into equations, because it is nonsense.

  Clifford Truesdell

  Funny, Fear, Science

  Clifford Truesdell (1966). “Six lectures on modern natural philosophy”, Springer

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• A child is born on that day and at that hour when the celestial rays are in mathematical harmony with his individual karma.

  Sri Yukteswar Giri

  Karma, Children, Astrology

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• Mathematics is the queen of science, and arithmetic the queen of mathematics.

  Carl Friedrich Gauss

  Queens, Math, Arithmetic

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• No employment can be managed without arithmetic, no mechanical invention without geometry.

  Benjamin Franklin

  Math, Employment, Invention

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• It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak.

  Gottlob Frege

  Knowledge, Thinking, Names

  Gottlob Frege, J. L. Austin (1980). “The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number”, p.4, Northwestern University Press

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• Who would not rather have the fame of Archimedes than that of his conqueror Marcellus?

  William Rowan Hamilton

  Math, Fame, Conqueror

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• The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results.

  Carl Gustav Hempel

  Queens, Math, Doubt

  Carl Gustav Hempel (2001). “The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality”, p.18, Oxford University Press on Demand

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• Ex-Professor Moriarty of mathematical celebrity... is the Napoleon of crime, Watson.

  Arthur Conan Doyle

  Crime, Professors, Watson

  Memoirs of Sherlock Holmes (1894) "The Final Problem"

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• Six is a number perfect in itself, and not because God created the world in six days; rather the contrary is true. God created the world in six days because this number is perfect, and it would remain perfect, even if the work of the six days did not exist.

  Saint Augustine

  God, Work, Math

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• All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics.

  John D. Barrow

  God, Spiritual, Littles

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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, Math, Thinking

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

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