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Subjects Quotes

“If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.”

Ifs Might Subjects Transformation Mathematical Contrast

Book:The Neumann Compendium

Source: The Neumann Compendium

“We shall see that the mathematical treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.”

Has Beens Two Term Results Subjects Theory Evidence Experiments Doctrine Being True Data Mathematical Treatment Peculiar Electricity Fluid Verification

Book:A Treatise on Electricity and Magnetism

Source: A Treatise on Electricity and Magnetism

“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

“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.”

“How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon.”

“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.”

Ifs Men Mind Understanding Existence Atheism Subjects Objects Ultimate Positive Atheism Defined Mathematical Length Paradox Quests Analogies Paragraph

Author:Paul Watzlawick

“The knowledge that is suited to our situation and powers, the whole compass of moral, natural, and mathematical science, was neglected by the new Platonists; whilst they exhausted their strength in the verbal disputes of metaphysics, attempted to explore the secrets of the invisible world, and studied to reconcile Aristotle with Plato, on subjects of which both these philosophers were as ignorant as the rest of mankind.”

Source: The History of the Decline and Fall of the Roman Empire

“Mathematical demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick are the only truths that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth according as their Subjects are more or less capable of Mathematical Demonstration.”

Men Mind Subjects Capable Built Mathematics Foundation Mathematical Uncertainty Void Discourse Demonstration Geometry

Book:Sir Christopher Wren and his times. With illustrative sketches and anecdotes of the most distinguished personages in the seventeenth century

Source: Sir Christopher Wren and his times. With illustrative sketches and anecdotes of the most distinguished personages in the seventeenth century

“In my own professional work I have touched on a variety of different fields. I've done work in mathematical linguistics, for example, without any professional credentials in mathematics; in this subject I am completely self-taught, and not very well taught.”

Wells Different Self Done My Own Subjects Example Fields Taught Mathematics Variety Mathematical Touched Linguistics Credentials Self Taught Professional Work

Book:The Chomsky-Foucault Debate: On Human Nature

Source: The Chomsky-Foucault Debate: On Human Nature

“[Lord Brougham's writings on the bee's cell contain] as striking examples of bad reasoning as are often to be met with in writings related to mathematical subjects.”

Writing Lord Subjects Example Mets Cells Mathematical Related Reasoning Bees

Author:James Whitbread Lee Glaisher

“I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn about and gather together. Then there is a sort of inevitable development in those fields. You get to the point where a certain theorem is bound to be proved, independent of any particular individual, because it is just in the path of development.”

People Thinking Together Certain Individual Path Subjects Fields Particular Development Civilization Mathematics Independent Bounds Mathematical Inevitable Territory Theorems

Author:William Thurston

“It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine.”

“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.”

Should Use Form Views Principles Records Subjects Mathematical Phases Evident Theoretical Devising

Author:Ada Lovelace