Mathematical Quotes - Page 38

• It is indeed a surprising and fortunate fact that nature can be expressed by relatively low-order mathematical functions.

  Rudolf Carnap

  Order, Facts, Lows

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• Human beings, from a mathematical perspective, are fairly limited. Two and three dimensions, maybe five, and we're OK.

  Usama Fayyad

  Two, Perspective, Three

  Interview with Joshuah Bearman, believermag.com. September 2003.

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• The classes of problems which are respectively known and not
  known to have good algorithms are of great theoretical interest. [...]
  I conjecture that there is no good algorithm for the traveling
  salesman problem. My reasons are the same as for any mathematical
  conjecture: (1) It is a legitimate mathematical possibility, and
  (2) I do not know.

  Jack Edmonds

  Class, Algorithms, Problem

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• My reasons are the same as for any mathematical conjecture: (1) It is a legitimate mathematical possibility, and (2) I do not know.

  Jack Edmonds

  Reason, Possibility, Conjecture

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• It has long been my personal view that the separation of practical and theoretical work is artificial and injurious. Much of the practical work done in computing, both in software and in hardware design, is unsound and clumsy because the people who do it have not any clear understanding of the fundamental design principles of their work. Most of the abstract mathematical and theoretical work is sterile because it has no point of contact with real computing.

  Christopher Strachey

  Real, Views, Long

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• It's the vision of the composer that we have to determine, and not the absolute mathematical adherence of the score. In my experience, there have been occasions where I feel that a composer has not notated something as they meant to have it represented.

  Marc-Andre Hamelin

  Vision, Adherence, Score

  Interview with Elijah Ho, www.thecounterpoints.com. November 8, 2013.

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• Why are we willing to accept a new mathematical formula we don't understand as the product of a brilliant mind, while rejecting a new art form we don't understand as the product of a deranged mind?

  Sydney J. Harris

  Art, Mind, Brilliant

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• [F]or academic men to be happy, the universe would have to take shape. All of philosophy has no other goal: it is a matter of giving a frock coat to what is, a mathematical frock coat. On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit.

  Georges Bataille

  Philosophy, Men, Hands

  Georges Bataille (1985). “Visions of Excess: Selected Writings, 1927-1939”, p.31, U of Minnesota Press

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• Poverty is a mathematical proof of the fact that mankind is a big failure!

  Mehmet Murat Ildan

  Poverty, Facts, Proof

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• Our external physical reality is a mathematical structure.

  Max Tegmark

  Reality, Structure

  "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality". Book by Max Tegmark, January 7, 2014.

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• In short, absolute, so-called mathematical, factors never find a firm basis in military calculations. From the very start, there is an interplay of possibilities, probabilities, good luck and bad, that weaves its way throughout the length and breadth of the tapestry. In the whole range of human activities, war most closely resembles a game of cards.

  Carl von Clausewitz

  Military, War, Good Luck

  On War Chapter 1, 21 (p. 86)

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• I am allowed to use plain English because everybody knows that I could use mathematical logic if I chose.

  Bertrand Russell

  Mathematical Logic, Use, Plain English

  Bertrand Russell (2009). “Bertrand Russell's Best”, p.66, Routledge

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• In mathematical science, more than in all others, it happens that truths which are at one period the most abstract, and apparently the most remote from all useful application, become in the next age the bases of profound physical inquiries, and in the succeeding one, perhaps, by proper simplification and reduction to tables, furnish their ready and daily aid to the artist and the sailor.

  Charles Babbage

  Artist, Profound, Age

  Charles Babbage, Peter Mark Roget (1989). “Reflections on the decline of science in England and on some of its causes: with a new appendix of correspondence by Charles Babbage & Peter M. Roget from the Philosophical magazine”

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• For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.

  Lynn Steen

  Real, People, Intuition

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• Because of mathematics precise, formal character, mathematical arguments remain sound even when they are long and complex. In contast, common sense arguments can generally be trusted only if they remain short; even moderately long nonmathematical arguments rapidly becomes farfetched an dubious.

  Jacob T. Schwartz

  Character, Long, Common Sense

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• You feed yourself. Make sure you have all the information, whether it's aesthetic, scientific, mathematical, I don't care what it is. Then you walk away from it and let it ferment. You ignore it and pretend you don't care. Next thing you know, the answer comes.

  Ray Bradbury

  Answers, Care, Information

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• Are mathematical ideas invented or discovered? This question has been repeatedly posed by philosophers through the ages and will probably be with us forever.

  Gian-Carlo Rota

  Ideas, Forever, Age

  Gian-Carlo Rota (2008). “Indiscrete Thoughts”, p.89, Springer Science & Business Media

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• We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.

  David Hilbert

  Theory, Masters, Kernel

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• The practical man demands an appearance of reality at least. Always dealing in the concrete, he regards mathematical terms not as symbols or thought but as images of reality. A system acceptable to the mathematician because of its inner consistency may appear to the practical man to be full of contradictions because of the incomplete manner in which it represents reality.

  Tobias Dantzig

  Reality, Men, Consistency

  Tobias Dantzig (1954). “Number, the Language of Science: A Critical Survey Written for the Cultured Non-mathematician”

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• However gemlike mathematical truths may be, research is but a human endeavor.

  H. David Burton

  Research, May, Endeavor

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• Two factors explain our success. One, MIT's renaissance after World War II as a federally supported research resource. Two, the mathematical revolution in macro- and micro-economic theory and statistics. This was overdue and inevitable, MIT was the logical place for it to flourish.

  Paul Samuelson

  War, Two, Mit

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• A physical law must possess mathematical beauty.

  Paul Dirac

  Law, Mathematical Beauty

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• The world of physics is essentially the real world construed by mathematical abstractions, and the world of sense is the real world construed by the abstractions which the sense-organs immediately furnish. To suppose that the "material mode" is a primitive and groping attempt at physical conception is a fatal error in epistemology.

  Susanne Katherina Langer

  Real, Errors, World

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• In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.

  Ada Lovelace

  Independent, Peculiar, Analysis

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• One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used in mathematical notation. First, the symbols of operation are frequently also the symbols of the results of operations.

  Ada Lovelace

  Littles, Shifting, Firsts

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