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The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.
-David Hilbert
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The Arithmetical Symbols Are Written Diagrams And

David Hilbert
The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.
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Math Figures Diagrams

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Philosophy [nature] is written in that great book which ever is before our eyes -- i mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. the book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.
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I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. disgusted at my want of success, i went away to spend a few days at the seaside, and thought of entirely different things. one day, as i was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-euclidian geometry.
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Do you think it interests me that this painting represents two figures? these two figures existed, they exist no more. the sight of them gave me an initial emotion, little by little their real presence grew indistinct they became a fiction for me, then they disappeared, or rather, were turned into problems of all kinds. for me they are no longer two figures but shapes and colours, don't misunderstand me, shapes and colours, though, that sum up the idea of the two figures and preserve the vibration of their existence.
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The more we progress the more we tend to progress. we advance not in arithmetical but in geometrical progression. we draw compound interest on the whole capital of knowledge and virtue which has been accumulated since the dawning of time.
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