Home » (Quotes) » A Passage. Some Thoughts. Of Language. Of Mathematical Physics.

A Passage. Some Thoughts. Of Language. Of Mathematical Physics.

The opening paragraph of Klein’s Greek Mathematical Thought and the Origin of Algebra (tr. Evan Brann):

The creation of a formal mathematical language was of decisive significance for the constitution of modern mathematical physics. If the mathematical presentation is regarded as a mere device, preferred only because the insights of natural science can be expressed by “symbols” in the simplest and most exactly manner possible, the meaning of the symbolism as well as of the special methods of the physical disciplines will be misunderstood. True, in the seventeenth and eighteenth century it was still possible to express and communicate discoveries concerning the “natural” relations of objects in nonmathematical terms, yet even then—or, rather, particularly then—it was precisely the mathematical form, the mos geometricus, which secured their dependability and trustworthiness. After three centuries of intensive development, it has finally become impossible to separate the content of mathematical physics from its form. The fact that elementary presentations of physical science which are to a certain degree nonmathematical and appear quite free of presuppositions in their derivations of fundamental concepts . . . are still in vogue should not deceive about the fact that it is impossible, and has always been impossible, to grasp the meaning of what we nowadays call physics independently of its mathematical form. Thence arise the insurmountable difficulties in which discussions of modern physical theories become entangled as soon as physicist or nonphysicist attempt to disregard the mathematical apparatus and to present the results of scientific research in popular form. The intimate connection of the formal mathematical language with the content of mathematical physics stems from the special kind of conceptualization which is concomitant of modern science and which was of fundamental importance in its formation.

Not all languages are equal. We sometimes cannot teach in one language what has been learned in another. In order to teach what we have learned, should we not begin with the language behind it?

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