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Results Quotes

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Results Quotes

“All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.”

Form Simple Results Mathematics Property Mathematical Investigation Integers

Author:Leopold Kronecker

“I have had my results for a long time: but I do not yet know how I am to arrive at them.”

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Author:Carl Friedrich Gauss

“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 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

“Mathematics may be the only exception in the sciences that leaves no room for skepicism. But, if mathematical results are exact as no empirical law can ever be, philosophers have discovered that they are not absolutely novel - instead, they are tautological.”

Ifs May Law Rooms Results Novel Mathematics Philosopher Mathematical Exception

Author:Luigi Luca Cavalli-Sforza

“Unlike mathematical theorems, scientific results can't be proved. They can only be tested again and again, until only a fool would not believe them. I cannot prove that electrons exist..........if you don't believe in them I have a high voltage cattle prod I'm willing to apply as an argument on their behalf. Electrons speak for themselves.”

Ifs Believe Speak Results Willing Fool Prove Argument Don't Believe Mathematical Again And Again Tested Behalf Cattle Theorems Electrons Voltage

Author:Seth Lloyd

“Logical investigations can obviously be a useful tool for philosophy. They must, however, be informed by a sensitivity to the philosophical significance of the formalism and by a generous admixture of common sense, as well as a thorough understanding both of the basic concepts and of the technical details of the formal material used. It should not be supposed that the formalism can grind out philosophical results in a manner beyond the capacity of ordinary philosophical reasoning. There is no mathematical substitute for philosophy.”

“The physicist may be satisfied when he has the mathematical scheme and knows how to use for the interpretation of the experiments. But he has to speak about his results also to non-physicists who will not be satisfied unless some explanation is given in plain language. Even for the physicist the description in plain language will be the criterion of the degree of understanding that has been reached.”

“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.”

Giving Mean Facts Differences Results Numbers Principles Machines Bases Method Mathematical Range Constructs Selected

Author:Ada Lovelace

“[On Archimedes mathematical results:] It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanation... No investigation of yours would succeed in attaining the proof, and yet, once seen you immediately believe you would have discovered it.”

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Author:Proclus

“Black holes result from God dividing the universe by zero.”

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Author:Steven Wright

“Our inner weighing of evidence is not a careful mathematical calculation resulting in a probabilistic estimate of truth, but more like a whirlpool blending of the objective and the personal. The result is a set of beliefs - both conscious and unconscious - that guide us in interpreting all the events of our lives.”

Belief Results Our Lives Events Conscious Evidence Careful Guides Objectives Mathematical Unconscious Calculations Interpreting Weighing Conscious And Unconscious Whirlpools

Book:War of the Worldviews: Where Science and Spirituality Meet -- and Do Not

Source: War of the Worldviews: Where Science and Spirituality Meet -- and Do Not