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Principles Quotes

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Principles Quotes

“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.”

“Three principles - the conformability of nature to herself, the applicability of the criterion of simplicity, and the utility of certain parts of mathematics in describing physical reality - are thus consequences of the underlying law of the elementary particles and their interactions. Those three principles need not be assumed as separate metaphysical postulates. Instead, they are emergent properties of the fundamental laws of physics.”

“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.”

“And so matching by itself is incapable of creating an art of reckoning. Without our ability to arrange things in ordered succession little progress could have been made. Correspondence and succession, the two principles that permeate all mathematics - nay, all realms of exact thought - are woven into the very fabric of our number system.”

“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.”

“... fain would I turn back the clock and devote to French or some other language the hours I spent upon algebra, geometry, and trigonometry, of which not one principle remains with me. Stay! There is one theorem painfully drummed into my head which seems to have inhabited some corner of my brain since that early time: "The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides!" There it sticks, but what of it, ye gods, what of it?”