Mathematical Quotes - Page 32

• There is (gentle reader) nothing (the works of God only set apart) which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences . Many arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called mathematical , unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of Geometry.

  John Dee

  Art, Men, Perfect

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• Wisdom is not mathematical, nor astronomical, nor zoological; when it talks too much of any one thing it ceases to be itself. There are wise physicists, but wisdom is not physical; there are wise physicians, but wisdom is not medical.

  George Sarton

  Wise, Physicians, Too Much

  George Sarton (1964). “A History of Science: Ancient Science Through the Golden Age of Greece”

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• Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures:;; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind. It's chief attribute is clearness; it has no marks to express confused notations. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them.

  Joseph Fourier

  Confused, Errors, Space

  Joseph Fourier (2007). “The Analytical Theory of Heat”, p.7, Cosimo, Inc.

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• The effects of heat are subject to constant laws which cannot be discovered without the aid of mathematical analysis. The object of the theory is to demonstrate these laws; it reduces all physical researches on the propagation of heat, to problems of the integral calculus, whose elements are given by experiment. No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it influences the processes of the arts, and occurs in all the phenomena of the universe.

  Joseph Fourier

  Art, Law, Progress

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• An uniformity of weights and measures, arranged upon mathematical principles, would be a benefit to the whole commercial world, if it were wise enough to adopt such an expedient.

  Jean-Baptiste Say

  Wise, Weight, Principles

  Jean Baptiste Say, Charles Robert Prinsep (1857). “A Treatise on Political Economy; Or, The Production, Distribution, and Consumption of Wealth”, p.433

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• The word 'definition' has come to have a dangerously reassuring sound, owing no doubt to its frequent occurrence in logical and mathematical writings.

  Willard Van Orman Quine

  Writing, Doubt, Sound

  Willard Van Orman Quine (1961). “From a Logical Point of View: 9 Logico-philosophical Essays”, p.26, Harvard University Press

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• For many years I was the youngest among my mathematical friends. It makes me melancholy to realize that I now have become the oldest in most groups of scientists.

  Stanislaw Ulam

  Years, Groups, Realizing

  "Adventures of a Mathematician" by Stanislaw Ulam, Third Edition, (p. 37), 1991.

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• The mathematical forms of order which the mind of a physicist manipulates coincides "miraculously" with experimental measurements.

  Marie-Louise von Franz

  Order, Mind, Measurement

  Marie-Louise Von Franz (2001). “Psyche and Matter”, p.260, Shambhala Publications

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• I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other mathematical formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future.

  Benjamin Peirce

  Profound, Satisfaction, Cold

  "Linear Associative Algebra" by Benjamin Peirce, (Preface), 1882.

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• What seems certain is that Pythagoras developed the idea of mathematical logic. He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths which were independent of opinion of prejudice and which were more absolute than any previous knowledge.

  Simon Singh

  Independent, Mathematical Logic, Ideas

  "Fermat's Last Theorem". Book by Simon Singh, 1997.

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• If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.

  George Dantzig

  Alternatives, Use, Schedules

  George Dantzig (2016). “Linear Programming and Extensions”, p.2, Princeton University Press

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• As soon as a thought or word becomes a tool, one can dispense with actually 'thinking' it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of mathematics - the model of all neo-positivistic thinking - lies in just this 'intellectual economy.' Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based. ... Reason ... becomes a fetish, a magic entity that is accepted rather than intellectually experienced.

  Max Horkheimer

  Lying, Thinking, Intellectual

  "Eclipse of Reason" by Max Horkheimer, (pp. 24-25), 1947.

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• I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen's, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell's equations.

  Kenneth E. Iverson

  Queens, Taken, Years

  "Kenneth E. Iverson with Donald B. McIntyre". Autobiographical sketch from an unfinished work, keiapl.info. (ca. 2004).

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• Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.

  Kenneth E. Iverson

  Would Be, Tools, Littles

  "Notation as a Tool of Thought". Cvommunications of the ACM, 23 (8), (pp. 444 - 465), August 1980.

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• The properties of executability and universality associated with programming languages can be combined, in a single language, with the well-known properties of mathematical notation which make it such an effective tool of thought.

  Kenneth E. Iverson

  Tools, Language, Well Known

  "Notation as a Tool of Thought". Cvommunications of the ACM, 23 (8), (pp. 444 - 465), August 1980.

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• Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows no more uniformity than mathematics. Nevertheless, programming languages do bring a different perspective. [...] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation.

  Kenneth E. Iverson

  Perspective, Different, Topics

  "Math for the Layman" by Kenneth E. Iverson, Ch. 10, §D, www.cs.trinity.edu. 1999.

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• The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical] notation.

  Kenneth E. Iverson

  Confusion, Execution, Language

  "Math for the Layman" by Kenneth E. Iverson, Ch. 10, §D, www.cs.trinity.edu. 1999.

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• With the computer and programming languages, mathematics has newly-acquired tools, and its notation should be reviewed in the light of them. The computer may, in effect, be used as a patient, precise, and knowledgeable "native speaker" of mathematical notation.

  Kenneth E. Iverson

  Light, Tools, May

  "Math for the Layman" by Kenneth E. Iverson, Ch. 10, §D, www.cs.trinity.edu. 1999.

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• Now, the velocity of wave propagation can be seen, without the aid of any mathematical analysis, to depend on the elasticity of the medium and its density; for we can see that if a medium is highly elastic the disturbance would be propagated at a great speed.

  Albert A. Michelson

  Velocity, Would Be, Density

  "Light Waves and Their Uses". Book by Albert A. Michelson. Published by The University of Chicago Press, pp. 23-25, 1903.

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• The next grand extensions of mathematical physics will, in all likelihood, be furnished by quaternions.

  Peter Tait

  Next, Physics, Extensions

  "Note on a Quaternion Transformation", Communication read on Monday, 6th April, 1863, Proceedings of the Royal Society of Edinburgh, p. 117, 1866.

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• A mathematical equation stands forever.

  Albert Einstein

  Mathematical Equations, Forever, Equations

  "Brighter than a Thousand Suns: A Personal History of the Atomic Scientists". Book by Robert Jungk (p. 249), 1958.

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• As far as I know, Clifford Pickover is the first mathematician to write a book about areas where math and theology overlap. Are there mathematical proofs of God? Who are the great mathematicians who believed in a deity? Does numerology lead anywhere when applied to sacred literature? Pickover covers these and many other off-trail topics with his usual verve, humor, and clarity. And along the way the reader will learn a great deal of serious mathematics.

  Martin Gardner

  Book, Writing, Math

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• Fancy what a game of chess would be if all the chessmen had passions and intellects, more or less small and cunning; if you were not only uncertain about your adversary's men, but a little uncertain also about your own. You would be especially likely to be beaten, if you depended arrogantly on your mathematical imagination, and regarded your passionate pieces with contempt. Yet this imaginary chess is easy compared with a game a man has to play against his fellow-men with other fellow-men for instruments.

  George Eliot

  Passion, Men, Games

  "Felix Holt, the Radical". Book by George Eliot. Chapter 29, 1866.

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• If we have dwelled on Godel's work at some length, is it because we see it in the mathematical analogy of what we would call the the ultimate paradox of man's existence. Man is ultimately subject and object of his quest. While the question whether the mind can be considered to be anything like a formalized system, as defined in the preceding paragraph, is probably unanswerable, his quest for an understanding of the meaning of his existence is an attempt at formalization.

  Paul Watzlawick

  Men, Understanding, Mind

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• According to PhD astrophysicists and qualified American science professors, the odds of the more than 2,500 prophecies found in the Bible being fulfilled by chance are 1 with 2,000 zeros after it. According to the mathematical science of probability, if a number has more than 50 zeros after it, the odds of that happening by chance is virtually impossible. This is irrefutable proof that the Bible is inspired by God!

  Hugh Ross

  Odds, Numbers, Phds

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