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Independent Quotes

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Independent Quotes

“The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.”

World Mind Firsts Form Order Three Numbers Type Logic Thirds Absolutes Infinite Independent Arise Certainty Mathematical Uncertainty Reasoning Magnitude Ontology Finite Number

Author:Georg Cantor

“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.”

World Ideas Seems Certain Numbers Opinion Study Perception Logic Prejudice Absolutes Independent Mathematical Tangible Mathematical Logic

Author:Simon Singh

“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.”

Doe Matter Shows Certain Left Principles Independent Philosopher Proof Conclusion Mathematical Premises Validity Irrationality Mathematical Proof

Book:Mathematics

Source: Mathematics

“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.”

“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.”

Action Results Study Objects Independent Defined Mathematical Operations Analysis Consideration Peculiar Engines Distinguished Mathematical Analysis

Author:Ada Lovelace

“The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it places in a true and just light the mutual relations and connexion of the various steps of mathematical analysis; how clearly it separates those things which are in reality distinct and independent, and unites those which are mutually dependent.”

Reality Light Process Results Steps Relation Independent Various Mathematical Perceive Analysis Dependent Mutual Engines Connexion Mathematical Analysis

Author:Ada Lovelace

“The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.”

Ideas Numbers Effort Mathematics Independent Mathematical Elegance Theorems

Author:George Polya

“How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

Humans Reality Science Objects Products Mathematics Independent Mathematical Appropriate Human Thought Independent Thought Mathematics And Science

Book:A Stubbornly Persistent Illusion: The Essential Scientific Works of Albert Einstein

Source: A Stubbornly Persistent Illusion: The Essential Scientific Works of Albert Einstein

“The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.”

Ifs World Matter Subjects Eternal Logic Mathematics Independent Mathematical Propositions Subject Matter Validity

Book:The pastures of wonder: the realm of mathematics and the realm of science

Source: The pastures of wonder: the realm of mathematics and the realm of science

“It is the invaluable merit of the great Basle mathematician Leonard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.”

Leadership Fields Mathematics Independent Independence Bounds Math Mathematical Analysis Merit Mathematician Invaluable Calculus Geometric Euler

Author:Thomas Reid

“There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation.”

Ifs World Mind Reality Truth Mistake Creation Divine Mathematics Independent Math Access Mathematical Mistaken Totality

Author:Charles Hermite

“I have a mathematical certainty that the future will confirm my assertion that aerial warfare will be the most important element in future wars, and that in consequence not only will the importance of the Independent Air Force rapidly increase, but the importance of the army and navy will decrease in proportion.”

Important War Force Air Elements Consequence Importance Increase Army Independent Certainty Mathematical Proportion Aviation Warfare Navy Assertion Decrease Air Force Air Power Airpower

Book:Command Of The Air

Source: Command Of The Air