Mathematical Quotes - Page 22

• Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.

  Carl Friedrich Gauss

  Science, Discovery, Woods

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• Our present work sets forth mathematical principles of philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces. It is to these ends that the general propositions in books 1 and 2 are directed, while in book 3 our explanation of the system of the world illustrates these propositions.

  Isaac Newton

  Nature, Philosophy, Book

  Sir Isaac Newton (2014). “Newton: Philosophical Writings”, p.60, Cambridge University Press

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• Perspective is a most subtle discovery in mathematical studies, for by means of lines it causes to appear distant that which is near, and large that which is small.

  Leonardo da Vinci

  Mean, Science, Discovery

  Leonardo (da Vinci) (1965). “Leonardo Da Vinci on Painting: A Lost Book (Libro A)”, p.39, Univ of California Press

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• Le Verrier-without leaving his study, without even looking at the sky-had found the unknown planet [Neptune] solely by mathematical calculation, and, as it were, touched it with the tip of his pen!

  Camille Flammarion

  Discovery, Sky, Leaving

  Camille Flammarion (1914). “Astronomy”

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• Kant, discussing the various modes of perception by which the human mind apprehends nature, concluded that it is specially prone to see nature through mathematical spectacles. Just as a man wearing blue spectacles would see only a blue world, so Kant thought that, with our mental bias, we tend to see only a mathematical world.

  James Jeans

  Nature, Science, Men

  Sir James Hopwood Jeans (2017). “The Mysterious Universe [New Revised Edition]”, p.115, Pickle Partners Publishing

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• So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality.

  Henri Poincare

  Eye, Science, Reality

  "Statistical Mechanics of Disordered Systems: A Mathematical Perspective". Book by Anton Bovier, p. 3, 2006.

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• A mathematical point is the most indivisble and unique thing which art can present.

  John Donne

  Art, Unique, Mathematics

  "The science of poetry, the poetry of science" by Ruth Padel, www.theguardian.com. December 9, 2011.

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• All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.

  James Clerk Maxwell

  Determination, Science, Law

  James Clerk Maxwell, W. D. Niven (2003). “The Scientific Papers of James Clerk Maxwell”, p.156, Courier Corporation

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• Another characteristic of mathematical thought is that it can have no success where it cannot generalize.

  Charles Sanders Peirce

  Success, Science, Thinking

  Charles Sanders Peirce (1933). “Collected Papers of Charles Sanders Peirce: Exact logic (Published papers).. The Simplest mathematics”, Harvard University Press

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• As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

  G. H. Hardy

  History, Achievement, Mathematics

  G. H. Hardy, C. P. Snow (2012). “A Mathematician's Apology”, p.80, Cambridge University Press

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• Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

  Hermann Weyl

  Substance, Mathematics

  "Mind and Nature: Selected Writings on Philosophy, Mathematics, and Physics".

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• Distrust even Mathematics; albeit so sublime and highly perfected, we have here a machine of such delicacy it can only work in vacuo, and one grain of sand in the wheels is enough to put everything out of gear. One shudders to think to what disaster such a grain of sand may bring a Mathematical brain. Remember Pascal.

  Anatole France

  Science, Thinking, Sublime

  Anatole France (1920). “The garden of Epicurus”

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• I also ask you my friends not to condemn me entirely to the mill of mathematical calculations, and allow me time for philosophical speculations, my only pleasures.

  Johannes Kepler

  Philosophy, Philosophical, Science

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• I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world... Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.

  G. H. Hardy

  Differences, Creating, Escaping

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• In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.

  Carl Friedrich Gauss

  Two, One Direction, Interesting

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• It seems perfectly clear that Economy, if it is to be a science at all, must be a mathematical science. There exists much prejudice against attempts to introduce the methods and language of mathematics into any branch of the moral sciences. Most persons appear to hold that the physical sciences form the proper sphere of mathematical method, and that the moral sciences demand some other method-I know not what.

  William Stanley Jevons

  Science, Spheres, Prejudice

  William Stanley Jevons (1871). “The Theory of Political Economy”, p.3

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• Laplace would have found it child's-play to fix a ratio of progression in mathematical science between Descartes, Leibnitz, Newton and himself

  Henry Adams

  Children, Science, Play

  Benjamin Franklin, Ulysses S Grant, Andrew Carnegie, Henry Adams (2016). “Great American Lives: The Autobiography of Benjamin Franklin, Personal Memoirs of Ulysses S. Grant, Autobiography of Andrew Carnegie, and The Education of Henry Adams”, p.1699, Open Road Media

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• The Mathematics are Friends to Religion, inasmuch as they charm the Passions, restrain the Impetuosity of the Imagination, and purge the Mind from Error and Prejudice. Vice is Error, Confusion, and false Reasoning; and all Truth is more or less opposite to it. Besides, Mathematical Studies may serve for a pleasant Entertainment for those Hours which young Men are apt to throw away upon their Vices; the Delightfulness of them being such as to make Solitude not only easy, but desirable.

  John Arbuthnot

  Passion, Science, Men

  Martin Strong, John Arbuthnot (1745). “An Essay on the Usefulness of Mathematical Learning: In a Letter from a Gentleman in the City, to His Friend at Oxford”, p.8

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• The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.

  Kurt Gödel

  Simple, Two, Development

  "Kurt Gödel: Collected Works: Volume I: Publications 1929-1936".

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• The proof given by Wright, that non-adaptive differentiation will occur in small populations owing to "drift," or the chance fixation of some new mutation or recombination, is one of the most important results of mathematical analysis applied to the facts of neo-mendelism. It gives accident as well as adaptation a place in evolution, and at one stroke explains many facts which puzzled earlier selectionists, notably the much greater degree of divergence shown by island than mainland forms, by forms in isolated lakes than in continuous river-systems.

  Julian Huxley

  Science, Rivers, Lakes

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• The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. ... It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wilderness lies in wait.

  Gilbert K. Chesterton

  Real, Lying, Waiting

  "Orthodoxy". Chapter VI: "The Paradoxes of Christianity". Book by Gilbert K. Chesterton, 1908.

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• The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

  Benoit Mandelbrot

  Powerful, Science, Tools

  Benoit B. Mandelbrot (2013). “Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E”, p.16, Springer Science & Business Media

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• The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence.

  Paul Dirac

  Science, Law, Simplicity

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• A theory is just a mathematical model to describe the observations.

  Karl Popper

  Religion, Atheism, Theory

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• There are good reasons to believe in God, including the existence of mathematical principles and order in creation. They are positive reasons, based on knowledge, rather than default assumptions based on a temporary lack of knowledge.

  Francis Collins

  Believe, Order, Atheism

  Francis Collins (2008). “The Language of God: A Scientist Presents Evidence for Belief”, p.62, Simon and Schuster

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