An excerpt from a book by Lanczos
In one of the (unfortunately lost) comedies of Aristophanes the Voice of the Mathematician appeared, as it descended from a snow-capped mountain peak, pronouncing in a ponderous sing-song-and words which to the audience sounded like complete gibberish-his eternal Theorems, Lemmas, and Corollaries. The laughter of the listeners was enhanced by the implication that in fifty years' time another Candidate of Eternity would pronounce from the same snow-capped mountain peak exactly the same theorems, although in a modified but scarcely less ponderous and in-comprehensible language.
Since the days of antiquity it has been the privilege of the mathematician to engrave his conclusions, expressed in a rarefied and esoteric language, upon the rocks of eternity. While this method is excellent for the codification of mathematical results, it is not so acceptable to the many addicts of mathematics, for whom the science of mathematics is not a logical game, but the language in which the physical universe speaks to us, and whose mastery is inevitable for the comprehension of natural phenomena.
In his previous books the author endeavoured to establish a more discursive manner of presentation in which the esoteric shorthand formulation of mathematical deductions and results was replaced by a more philosophic exposition, putting the emphasis on ideas and concepts and their mutual interrelations, rather than on the mere manipulation of formulae. Our symbolic mechanism is eminently useful and powerful, but the danger is ever-present that we become drowned in a language which has its well-defined grammatical rules but eventually loses all content and becomes a nebulous sham. Hence the author's constant desire to penetrate below the manipulative surface and comprehend the hidden springs of mathematical equations.
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When is the last time you open up some "math book", see only Greek, and close it as if you just have opened some gateway to hell? Such a book is like a computer science book with nothing but one huge program listing. Completely unreadable and completely useless.
Since the days of antiquity it has been the privilege of the mathematician to engrave his conclusions, expressed in a rarefied and esoteric language, upon the rocks of eternity. While this method is excellent for the codification of mathematical results, it is not so acceptable to the many addicts of mathematics, for whom the science of mathematics is not a logical game, but the language in which the physical universe speaks to us, and whose mastery is inevitable for the comprehension of natural phenomena.
In his previous books the author endeavoured to establish a more discursive manner of presentation in which the esoteric shorthand formulation of mathematical deductions and results was replaced by a more philosophic exposition, putting the emphasis on ideas and concepts and their mutual interrelations, rather than on the mere manipulation of formulae. Our symbolic mechanism is eminently useful and powerful, but the danger is ever-present that we become drowned in a language which has its well-defined grammatical rules but eventually loses all content and becomes a nebulous sham. Hence the author's constant desire to penetrate below the manipulative surface and comprehend the hidden springs of mathematical equations.
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When is the last time you open up some "math book", see only Greek, and close it as if you just have opened some gateway to hell? Such a book is like a computer science book with nothing but one huge program listing. Completely unreadable and completely useless.