Mathematics Quotes - Page 24

• Theory attracts practice as the magnet attracts iron.

  Carl Friedrich Gauss

  Math, Practice, Iron

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• [In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.

  Gian-Carlo Rota

  Mistake, Science, Two

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• Sir Arthur Eddington deduces religion from the fact that atoms do not obey the laws of mathematics. Sir James Jeans deduces it from the fact that they do.

  Bertrand Russell

  Science, Law, Jeans

  Bertrand Russell (2009). “The Scientific Outlook”, p.77, Routledge

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• How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

  Henri Poincare

  Science, Skeletons, Understanding

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• Modern mathematics, that most astounding of intellectual creations, has projected the mind's eye through infinite time and the mind's hand into boundless space.

  Nicholas Murray Butler

  Eye, Science, Hands

  Nicholas Murray Butler (1895). “What Knowledge is of Most Worth? ...”

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• As regards authority I so proceed. Boetius says in the second prologue to his Arithmetic, 'If an inquirer lacks the four parts of mathematics, he has very little ability to discover truth.' And again, 'Without this theory no one can have a correct insight into truth.' And he says also, 'I warn the man who spurns these paths of knowledge that he cannot philosophize correctly.' And Again, 'It is clear that whosoever passes these by, has lost the knowledge of all learning.'

  Roger Bacon

  Truth, Men, Path

  Roger Bacon (2016). “Opus Majus, Volumes 1 and 2”, p.117, University of Pennsylvania Press

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• If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.

  Carl Friedrich Gauss

  Truth, Science, Discovery

  "The World of Mathematics". Book by J. R. Newman, 1956.

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• Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.

  Bertrand Russell

  Encouragement, Truth, Teaching

  Bertrand Russell (2015). “Mysticism and Logic and Other Essays: Top Philosophy Collections”, p.45, 谷月社

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• [I]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error.

  Roger Bacon

  Truth, Science, Errors

  Opus Majus bk. 1, ch. 4 (ca. 1267) (translation by Robert Burke)

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• Angling may be said to be so like the Mathematics that it can never be fully learnt; at least not so fully but that there will still be more new experiments left for the trial of other men that succeed us.

  Izaak Walton

  Learning, Science, Men

  Izaak Walton, Charles Cotton (1824). “The Complete Angler of Izaak Walton and Charles Cotton: Estensively Embellished with Engravings on Copper and Wood, from Original Paintings and Drawings, by First-rate Artists, to which are Added, an Introductory Essay, the Linnœan Arangement of the Various River Fish Delineated in the Work, and Illustrative Notes”, p.57

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• If physics leads us today to a world view which is essentially mystical, it returns, in a way, to its beginning, 2,500 years ago... This time, however, it is not only based on intuition, but also on experiments of great precision and sophistication, and on a rigorous and consistent mathematical formalism.

  Fritjof Capra

  Science, Views, Years

  "The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism". Book by Fritjof Capra, 1975.

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• Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future... If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them... My own belief is that this is a more likely line of progress than trying to guess at physical pictures.

  Paul Dirac

  Science, Discovery, People

  "The Evolution of the Physicist's Picture of Nature" by Paul Dirac, blogs.scientificamerican.com. May 1963.

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• 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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• 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.

  G. H. Hardy

  Science, Discovery, Differences

  G. H. Hardy (2012). “A Mathematician's Apology”, p.150, Cambridge University Press

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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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• Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

  Henri Poincare

  Nature, Philosophical, Science

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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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• For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

  Henri Poincare

  Science, Ideas, Long

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• A chemist who does not know mathematics is seriously handicapped.

  Irving Langmuir

  Doe, Chemist, Handicapped

  Irving Langmuir (1962). “The Collected Works of Irving Langmuir: Langmuir, the man and the scientist, including a biography by Albert Rosenfield”

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• A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.

  G. H. Hardy

  Beautiful, Moving, Mean

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• A great deal of my work is just playing with equations and seeing what they give.

  Paul Dirac

  Science, Giving, Biographies

  Howard Baer, Paul Adrien Maurice Dirac, Alexander Belyaev (2003). “Proceedings of the Dirac Centennial Symposium: Florida State University, Tallahassee, USA, 6-7 December 2002”, p.45, World Scientific

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

  John Donne

  Art, Unique, Mathematical

  "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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