Best mathematics & reasoning Quotes | Short & Famous Sayings

“The increased abstraction in mathematics that took place during the early part of this century was paralleled by a similar trend in the arts. In both cases, the increased level of abstraction demands greater effort on the part of anyone who wants to understand the work.”

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Author:Keith Devlin

“It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.”

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Book:The Evanston Colloquium: Lectures on Mathematics Delivered from Aug. 28 to Sept. 9, 1893 Before Members of the Congress of Mathematics Held in Connection with the World's Fair in Chicago at Northwestern University, Evanston, Ill

Source: The Evanston Colloquium: Lectures on Mathematics Delivered from Aug. 28 to Sept. 9, 1893 Before Members of the Congress of Mathematics Held in Connection with the World's Fair in Chicago at Northwestern University, Evanston, Ill

“Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.”

“Mathematics is purely hypothetical: it produces nothing but conditional propositions.”

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Book:Collected papers of Charles Sanders Peirce

Source: Collected papers of Charles Sanders Peirce

“The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it.”

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Book:Philosophical Reflections and Syntheses

Source: Philosophical Reflections and Syntheses

“Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems-general and specific statements-can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.”

“Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning. The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.”

“We find sects and parties in most branches of science; and disputes which are carried on from age to age, without being brought to an issue. Sophistry has been more effectually excluded from mathematics and natural philosophy than from other sciences. In mathematics it had no place from the beginning; mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly, we find no parties among mathematicians, and hardly any disputes.”

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Author:Thomas Reid

“As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond mathematics itself. He knew his technical abilities; his virtuosity in following complicated reasoning and his insights were supreme; yet he lacked absolute self confidence.”

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Author:Stanislaw Ulam

“The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. ... Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.”

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Author:George Polya

“To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation. Not activity Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know.”

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Author:George Spencer-Brown

“The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.”

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Author:IU?. I. Manin

“Theoretically, I grant you, there is no possibility of error in necessary reasoning. But to speak thus "theoretically," is to uselanguage in a Pickwickian sense. In practice, and in fact, mathematics is not exempt from that liability to error that affects everything that man does.”

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Book:Reasoning and the logic of things: the Cambridge conferences lectures of 1898

Source: Reasoning and the logic of things: the Cambridge conferences lectures of 1898

“The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.”

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Author:George Polya

“Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.”

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Author:Alfred North Whitehead

“As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment.”

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Book:The Essays ... Revised ... by Thomas Markby ... Second Edition

Source: The Essays ... Revised ... by Thomas Markby ... Second Edition

“Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.”

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Author:John Locke

“Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.”

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Author:Bertrand Russell

“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.”

“But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.”

May Values Process Subjects Logic Mathematics Operations Abstract Reasoning Peculiar

Author:Ada Lovelace

“Actually, most mathematics courses do not teach reasoning of any kind. Students are so baffled by the material that they are obliged to memorize in order to pass examinations.”

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Author:Morris Kline

“Mathematics is the art of accurate reasoning on inaccurately-drawn figures... let that be our motto.”

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Author:Arthur Mattuck

“In general, I'm in support of promoting art and science in public schools. I think music and science are probably the most important factors for the human brain developing. Even more so than any other fields, because music covers mathematics, cognitive reasoning, motor skills, coordination, like, it's kind of everything.”

“If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.”

“Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.”

Language Tools Logic Mathematics Reasoning Plus

Author:Richard P. Feynman

“Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion - thus: Major Premise: Sixty men can do a piece of work sixty times as quickly as one man. Minor Premise: One man can dig a post-hole in sixty seconds; Therefore- Conclusion: Sixty men can dig a post-hole in one second. This may be called syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.”

“Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.”

Source: What is Mathematics?: An Elementary Approach to Ideas and Methods

“The Reader may here observe the Force of Numbers, which can be successfully applied, even to those things, which one would imagine are subject to no Rules. There are very few things which we know, which are not capable of being reduc'd to a Mathematical Reasoning, and when they cannot, it's a sign our Knowledge of them is very small and confus'd; and where a mathematical reasoning can be had, it's as great folly to make use of any other, as to grope for a thing in the dark when you have a Candle standing by you.”

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Author:John Arbuthnot

“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.”

Source: An Essay on the Usefulness of Mathematical Learning: In a Letter from a Gentleman in the City, to His Friend at Oxford

“Mathematics is a form of poetry which transcends poetry in that it proclaims a truth; a form of reasoning which transcends reasoning in that it wants to bring about the truth it proclaims; a form of action, of ritual behavior, which does not find fulfilment in the act but must proclaim and elaborate a poetic form of truth.”

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Book:Collected Papers of Salomon Bochner

Source: Collected Papers of Salomon Bochner

“Anyone who has had actual contact with the making of the inventions that built the radio art knows that these inventions have been the product of experiment and work based on physical reasoning, rather than on the mathematicians' calculations and formulae. Precisely the opposite impression is obtained from many of our present day text books and publications.”

“The moving power of mathematical invention is not reasoning but imagination.”

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Author:Augustus De Morgan

“Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications.”

“I have hardly ever known a mathematician who was capable of reasoning.”

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Book:The Complete Works of Plato (Unabridged): From the greatest Greek philosopher, known for The Republic, Symposium, Apology, Phaedrus, Laws, Crito, Phaedo, Timaeus, Meno, Euthyphro, Gorgias, Parmenides, Protagoras, Statesman and Critias

Source: The Complete Works of Plato (Unabridged): From the greatest Greek philosopher, known for The Republic, Symposium, Apology, Phaedrus, Laws, Crito, Phaedo, Timaeus, Meno, Euthyphro, Gorgias, Parmenides, Protagoras, Statesman and Critias

“The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.”

Whole Process Imagination Organization Mathematics Series Math Aids Reasoning

Book:A Treatise on Universal Algebra with Applications

Source: A Treatise on Universal Algebra with Applications

“Logic, like whiskey, loses its beneficial effect when taken in too large quantities.”