"All of mathematics can be deduced from the sole notion of an integer; here we have a fact universally acknowledged today." (Émile Borel, "Contribution a l'analyse arithmetique du continu", 1903)
"A mathematical theorem and its demonstration are prose. But if the mathematician is overwhelmed with the grandeur and wondrous harmony of geometrical forms, of the importance and universal application of mathematical maxims, or, of the mysterious simplicity of its manifold laws which are so self-evident and plain and at the same time so complicated and profound, he is touched by the poetry of his science; and if he but understands how to give expression to his feelings, the mathematician turns poet, drawing inspiration from the most abstract domain of scientific thought." (Paul Carus," Friedrich Schiller: A Sketch of His Life and an Appreciation of His Poetry", 1905)
"Without doubt one of the most characteristic features of mathematics in the last century is the systematic and universal use of the complex variable. Most of its great theories received invaluable aid from it, and many owe their very existence to it." (James Pierpont, "History of Mathematics in the Nineteenth Century", Congress of Arts and Sciences Vol. 1, 1905)
"For thought raised on specialization the most potent objection to the possibility of a universal organizational science is precisely its universality. Is it ever possible that the same laws be applicable to the combination of astronomic worlds and those of biological cells, of living people and the waves of the ether, of scientific ideas and quanta of energy? [...] Mathematics provide a resolute and irrefutable answer: yes, it is undoubtedly possible, for such is indeed the case. Two and two homogenous separate elements amount to four such elements, be they astronomic systems or mental images, electrons or workers; numerical structures are indifferent to any element, there is no place here for specificity." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)
"[…] there is a special relationship, a profound affinity between mathematics and tektology. Mathematical laws do not refer to a particular area of natural phenomena, as the laws of the other, special, sciences do, but to each and all phenomena, considered merely in their quantitative aspect; mathematics is in its own way universal, like tektology." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)
"Numbers constitute the only universal language." (Nathanael West, "Miss Lonelyhearts", 1933)
"[…] the merit of mathematics, in all its forms, consists in its truth; truth conveyed to the understanding, not directly by words but by symbols which serve as the world’s only universal written language." (David Eugene Smith, "The Poetry of Mathematics and Other Essays", 1934)
"[...] our knowledge of the external world must always consist of numbers, and our picture of the universe - the synthesis of our knowledge - must necessarily be mathematical in form. All the concrete details of the picture, the apples, the pears and bananas, the ether and atoms and electrons, are mere clothing that we ourselves drape over our mathematical symbols - they do not belong to Nature, but to the parables by which we try to make Nature comprehensible." (Sir James H Jeans, "The New World-Picture of Modern Physics", Supplement to Nature, Vol. 134 (3384), 1934)
"Given any domain of thought in which the fundamental objective is a knowledge that transcends mere induction or mere empiricism, it seems quite inevitable that its processes should be made to conform closely to the pattern of a system free of ambiguous terms, symbols, operations, deductions; a system whose implications and assumptions are unique and consistent; a system whose logic confounds not the necessary with the sufficient where these are distinct; a system whose materials are abstract elements interpretable as reality or unreality in any forms whatsoever provided only that these forms mirror a thought that is pure. To such a system is universally given the name Mathematics." (Samuel T Sanders, "Mathematics", National Mathematics Magazine, 1937)
"Mathematical research can lend its organisational characteristics to poetry, whereby disjointed metaphors take on a universal sense. Similarly, the axiomatic foundations of group theory can be assimilated into a larger moral concept of a unified universe. Without this, mathematics would be a laborious Barbary." (Dan Barbilian,"The Autobiography of the Scientist", 1940)
"Here, then, in mathematics we have a universal language, valid, useful, intelligible everywhere in place and in time - in banks and insurance companies, on the parchments of the architects who raised the Temple of Solomon, and on the blueprints of the engineers who, with their calculus of chaos, master the winds. Here is a discipline of a hundred branches, fabulously rich, literally without limit in its sphere of application, laden with honors for an unbroken record of magnificent accomplishment. Here is a creation of the mind, both mystic and pragmatic in appeal. Austere and imperious as logic, it is still sufficiently sensitive and flexible to meet each new need." (Edward Kasner & James R Newman, "Mathematics and the Imagination", 1940)
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