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Mathematical Analysis Quotes (12 quotes)

Il ne peut y avoir de langage plus universel et plus simple, plus exempt d’erreurs et d’obscurités, c'est-à-dire plus digne d'exprimer les rapports invariables des êtres naturels.
There cannot be a language more universal and more simple, more free from errors and obscurities, … more worthy to express the invariable relations of all natural things. [About mathematical analysis.]
From Théorie Analytique de la Chaleur (1822), xiv, translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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L’analyse mathématique … dans l’étude de tous les phénomènes; elle les interprète par le même langage, comme pour attester l’unité et la simplicité du plan de l’univers, et rendre encore plus manifeste cet ordre immuable qui préside à toutes les causes naturelles.
Mathematical analysis … in the study of all phenomena, interprets them by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), xv, translated by Alexander Freeman in The Analytical Theory of Heat (1878), 8.
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Art is an expression of the world order and is, therefore, orderly, organic, subject to mathematical law, and susceptible to mathematical analysis.
In 'The Theosophic View of the Art of Architecture', The Beautiful Necessity, Seven Essays on Theosophy and Architecture (2nd ed., 1922), Preface to the Second Edition, 11.
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I remember my first look at the great treatise of Maxwell’s when I was a young man… I saw that it was great, greater and greatest, with prodigious possibilities in its power… I was determined to master the book and set to work. I was very ignorant. I had no knowledge of mathematical analysis (having learned only school algebra and trigonometry which I had largely forgotten) and thus my work was laid out for me. It took me several years before I could understand as much as I possibly could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly… It will be understood that I preach the gospel according to my interpretation of Maxwell.
From translations of a letter (24 Feb 1918), cited in Paul J. Nahin, Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age (2002), 24. Nahin footnotes that the words are not verbatim, but are the result of two translations. Heaviside's original letter in English was quoted, translated in to French by J. Bethenode, for the obituary he wrote, "Oliver Heaviside", in Annales des Posies Telegraphs (1925), 14, 521-538. The quote was retranslated back to English in Nadin's book. Bethenode footnoted that he made the original translation "as literally as possible in order not to change the meaning." Nadin assures that the retranslation was done likewise. Heaviside studyied Maxwell's two-volume Treatise on Electricity and Magnetism.
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In mathematical analysis we call x the undetermined part of line a: the rest we don’t call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language.
Lichtenberg: A Doctrine of Scattered Occasions: Reconstructed From: Reconstructed From His Aphorisms and Reflections (1959), 158.
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Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.
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Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind.
From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7. From the original French, “L’analyse mathématique est aussi étendue que la nature elle-même; elle définit tous les rapports sensibles, mesure les temps y les espaces, les forces, les températures; cette science difficile se forme avec lenteur, mais elle conserve tous les principes quelle a une fois acquis; elle s’accroît et s’affermit sans cesse au milieu de tant de variations et d’erreurs de l’esprit humain.”
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Objections … inspired Kronecker and others to attack Weierstrass’ “sequential” definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.
In Men of Mathematics (1937), 431-432.
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The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
In 'The Mathematician', Works of the Mind (1947), 1, No. 1. Collected in James Roy Newman (ed.), The World of Mathematics (1956), Vol. 4, 2055.
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There is inherent in nature a hidden harmony that reflects itself in our minds under the image of simple mathematical laws. That then is the reason why events in nature are predictable by a combination of observation and mathematical analysis. Again and again in the history of physics this conviction, or should I say this dream, of harmony in nature has found fulfillments beyond our expectations.
…...
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Those skilled in mathematical analysis know that its object is not simply to calculate numbers, but that it is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression.
In Antoine-Augustin Cournot and Nathaniel T. Bacon (trans.), Mathematical Theory of the Principles of Wealth (1897), Preface, 3.
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We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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