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Principles Quotes

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Principles Quotes

“I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded.”

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Author:Jim Sanborn

“Our design, not respecting arts, but philosophy, and our subject, not manual, but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena.”

Source: Newton's Principia: The Mathematical Principles of Natural Philosophy

“Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.”

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Author:David Hilbert

“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.”

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Author:John Dee

“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.”

Source: The Analytical Theory of Heat

“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.”

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Book:A Treatise on Political Economy; Or, The Production, Distribution, and Consumption of Wealth

Source: A Treatise on Political Economy; Or, The Production, Distribution, and Consumption of Wealth

“What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.”

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Book:Mathematics

Source: Mathematics

“Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.”

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Author:Leonhard Euler

“In accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up the double octave.”

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Author:Marcus Vitruvius Pollio

“I have presented principles of philosophy that are not, however, philosophical but strictly mathematical-that is, those on which the study of philosophy can be based. These principles are the laws and conditions of motions and of forces, which especially relate to philosophy.”

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Book:The Principia: Mathematical Principles of Natural Philosophy

Source: The Principia: Mathematical Principles of Natural Philosophy

“The material which a scientist actually has at his disposal, his laws, his experimental results, his mathematical techniques, his epistemological prejudices, his attitude towards the absurd consequences of the theories which he accepts, is indeterminate in many ways, ambiguous, and never fully separated from the historical background . This material is always contaminated by principles which he does not know and which, if known, would be extremely hard to test.”

Source: Against Method

“The method of differences is, in fact, a method of additions; and as it includes within its means a larger number of results attainable by addition simply, than any other mathematical principle, it was very appropriately selected as the basis on which to construct an Adding Machine, so as to give to the powers of such a machine the widest possible range.”

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Author:Ada Lovelace

“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.”

“It is however pretty evident, on general principles, that in devising for mathematical truths a new form in which to record and throw themselves out for actual use, views are likely to be induced, which should again react on the more theoretical phase of the subject.”

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Author:Ada Lovelace