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Produce Quotes

“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.”

“Of the properties of mathematics, as a language, the most peculiar one is that by playing formal games with an input mathematical text, one can get an output text which seemingly carries new knowledge. The basic examples are furnished by scientific or technological calculations: general laws plus initial conditions produce predictions, often only after time-consuming and computer-aided work. One can say that the input contains an implicit knowledge which is thereby made explicit.”

“What is the use of aesthetics if they can neither teach how to produce beauty nor how to appreciate it in good taste? It exists because it behooves rational human beings to provide reasons for their actions and assessments. Even if aesthetics are not the mathematics of beauty, they are the proof of the calculation.”

“I used to be surprised and even depressed when I met someone I had admired and discovered him or her to be a jerk or, perhaps worse, rather common. Now I half expect this reaction and even find it a little reassuring, maybe even uplifting. Isn't it amazing that somebody like that could produce such and such.”

“The scientists from Franklin to Morse were clear thinkers and did not produce erroneous theories. The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite insane. Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.”