God does not care about our mathematical difficulties. He integrates empirically.
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Attributed to Einstein by his colleague Léopold Infeld in his book Quest: An Autobiography (1949), p. 279.Albert Einstein
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If I have had any success in mathematical physics, it is, I think, because I have been able to dodge mathematical difficulties.
Josiah Willard Gibbs
Reductionism (ultimately, the empirical explanability of everything and a cornerstone of science), has uses that are appropriate, and it also can be used inappropriately. It is appropriately used as a way (one way) of understanding what is empirically known or empirically knowable. When it becomes merely an intellectual "position" confronting what is not empirically known or knowable, then it becomes very quickly absurd, and also grossly desensitizing and false.
Wendell Berry
If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
George Dantzig
There's a tremendous popular fallacy which holds that significant research can be carried out by trying things. Actually it is easy to show that in general no significant problem can be solved empirically, except for accidents so rare as to be statistically unimportant. One of my jests is to say that we work empirically — we use bull's eye empiricism. We try everything, but we try the right thing first!
Edwin H. Land
The first intellectual operation in which I arrived at any proficiency, was dissecting a bad argument, and finding in what part the fallacy lay; and though whatever capacity of this sort I attained was due to the fact that it was an intellectual exercise in which I was most perseveringly drilled by my father, yet it is also true that the school logic, and the mental habits acquired in studying it, were among the principal instruments of this drilling. I am persuaded that nothing, in modern education, tends so much, when properly used, to form exact thinkers, who attach a precise meaning to words and propositions, and are not imposed on by vague, loose, or ambiguous terms. The boasted influence of mathematical studies is nothing to it; for in mathematical processes, none of the real difficulties of correct ratiocination occur.
John Stuart Mill
Einstein, Albert
Eisenhower, Dwight D.
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