„[T]he application of algebra to geometry… far more than any of his metaphysical speculations, has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.“
An Examination of Sir William Hamilton's Philosophy (1865) as quoted in 5th ed. (1878) p. 617. https://books.google.com/books?id=ojQNAQAAMAAJ&pg=PA617
„More than any of his predecessors Plato appreciated the scientific possibilities of geometry... By his teaching he laid the foundations of the science, insisting upon accurate definitions, clear assumptions, and logical proof. His opposition to the materialists, who saw in geometry only what was immediately useful to the artisan and the mechanic is… clear. …That Plato should hold the view… is not a cause for surprise. The world's thinkers have always held it. No man has ever created a mathematical theory for practical purposes alone. The applications of mathematics have generally been an afterthought.“
— David Eugene Smith American mathematician 1860 - 1944
Quelle: History of Mathematics (1923) Vol.1, p. 90
„The absolute requisites for the study of this work… are a knowledge of algebra to the binomial at least, plane and solid geometry, plane trigonometry, and the most simple part of the usual applications of algebra to geometry.
…A. De Morgan. London July 1, 1836“
— Augustus De Morgan British mathematician, philosopher and university teacher (1806-1871) 1806 - 1871
The Differential and Integral Calculus (1836)
„Descartes… complained that Greek geometry was so much tied to figures "that is can exercise the understanding only on condition of greatly fatiguing the imagination." Descartes also deplored that the methods of Euclidean geometry were exceedingly diverse and specialized and did not allow for general applicability. Each theorem required a new kind of proof… What impressed Descartes especially was that algebra enables man to reason efficiently. It mechanizes thought, and hence produces almost automatically results that may otherwise be difficult to establish…. historically it was Descartes who clearly perceived and called attention to this feature. Whereas geometry contained the truth about the universe, algebra offered the science of method. It is… paradoxical that great thinkers should be enamored with ideas that mechanize thought. Of course, their goal is to get at more difficult problems, as indeed they do.“
— Morris Kline American mathematician 1908 - 1992
Quelle: Mathematics for the Nonmathematician (1967), pp. 255-256.
„As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection.“
— Joseph Louis Lagrange Italian mathematician and mathematical physicist 1736 - 1813
Dans Les Leçons Élémentaires sur les Mathématiques (1795) Leçon cinquiéme,Tr. McCormack, cited in Robert Edouard Moritz, Memorabilia mathematica or, The philomath's quotation-book (1914) Ch. V The teaching of mathematics, p. 81. https://archive.org/stream/memorabiliamathe00moriiala#page/80/mode/2up
„It is odd that the last twenty-five years which have witnessed the greatest progress ever made in physical science—the greatest victories ever achieved by mind over matter—should have produced hardly a volume that will be remembered in 1900.“
— Thomas Babington Macaulay, 1st Baron Macaulay British historian and Whig politician 1800 - 1859
Diary entry (9 March 1850)
„The modern poet has no essential alliance with regular schemes of any sorts. He reserves the right to adapt his rhythm to his mood, to modulate his metre as he progresses. Far from seeking freedom and irresponsibility (implied by the unfortunate term free verse) he seeks a stricter discipline of exact concord of thought and feeling.“
— Herbert Read English anarchist, poet, and critic of literature and art 1893 - 1968
Collected Essays in Literary Criticism (1938)
„It was my lot to plant the harpoon of algebraic topology into the body of the whale of algebraic geometry.“
— Solomon Lefschetz American mathematician 1884 - 1972
[Carl C. Gaither, Alma E. Cavazos-Gaither, Gaither's Dictionary of Scientific Quotations: A Collection of Approximately 27,000 Quotations Pertaining to Archaeology, Architecture, Astronomy, Biology, Botany, Chemistry, Cosmology, Darwinism, Engineering, Geology, Mathematics, Medicine, Nature, Nursing, Paleontology, Philosophy, Physics, Probability, Science, Statistics, Technology, Theory, Universe, and Zoology, https://books.google.com/books?id=zQaCSlEM-OEC&pg=PA29, 5 January 2012, Springer Science & Business Media, 978-1-4614-1114-7, 29]
„Politics I conceive to be nothing more than the science of the ordered progress of society along the lines of greatest usefulness and convenience to itself.“
— Woodrow Wilson American politician, 28th president of the United States (in office from 1913 to 1921) 1856 - 1924
“What is Pan-Americanism?” http://books.google.com/books?id=_VYEIml1cAkC&pg=PA97&dq=%22Politics+I+conceive+to+be+nothing+more+than+the+science+of+the+ordered+progress+of+society+along+the+lines+of+greatest+usefulness+and+convenience+to+itself%22, Address to Pan American Scientific Congress (6 January 1916)
„Let us calculate the motion of bodies, but also consult the plans of the Intelligence that makes them move.
It seems that the ancient philosophers made the first attempts at this sort of science, in looking for metaphysical relationships between numbers and material bodies. When they said that God occupies himself with geometry, they surely meant that He unites in that science the works of His power with the perspectives of His wisdom.
From the all too few ancient geometers who undertook such studies, we have little that is intelligible or well-founded. The perfection which geometry has acquired since their time puts us in a better position to succeed, and may more than compensate for the advantages that those great minds had over us.“
— Pierre Louis Maupertuis French mathematician, philosopher and man of letters 1698 - 1759
Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles (1744)
„History has borne out the case against him; for no State has ever constituted itself on his principles or made it possible to live according to his commandments: those States who have taken his name have taken it as an alias to enable them to persecute his followers more plausibly.“
— George Bernard Shaw Irish playwright 1856 - 1950
Preface, Leading Case of Jesus Christ
1930s, On the Rocks (1933)
Kontext: I dislike cruelty, even cruelty to other people, and should therefore like to see all cruel people exterminated. But I should recoil with horror from a proposal to punish them. Let me illustrate my attitude by a very famous, indeed far too famous, example of the popular conception of criminal law as a means of delivering up victims to the normal popular lust for cruelty which has been mortified by the restraint imposed on it by civilization. Take the case of the extermination of Jesus Christ. No doubt there was a strong case for it. Jesus was from the point of view of the High Priest a heretic and an impostor. From the point of view of the merchants he was a rioter and a Communist. From the Roman Imperialist point of view he was a traitor. From the commonsense point of view he was a dangerous madman. From the snobbish point of view, always a very influential one, he was a penniless vagrant. From the police point of view he was an obstructor of thoroughfares, a beggar, an associate of prostitutes, an apologist of sinners, and a disparager of judges; and his daily companions were tramps whom he had seduced into vagabondage from their regular trades. From the point of view of the pious he was a Sabbath breaker, a denier of the efficacy of circumcision and the advocate of a strange rite of baptism, a gluttonous man and a winebibber. He was abhorrent to the medical profession as an unqualified practitioner who healed people by quackery and charged nothing for the treatment. He was not anti-Christ: nobody had heard of such a power of darkness then; but he was startlingly anti-Moses. He was against the priests, against the judiciary, against the military, against the city (he declared that it was impossible for a rich man to enter the kingdom of heaven), against all the interests, classes, principalities and powers, inviting everybody to abandon all these and follow him. By every argument, legal, political, religious, customary, and polite, he was the most complete enemy of the society of his time ever brought to the bar. He was guilty on every count of the indictment, and on many more that his accusers had not the wit to frame. If he was innocent then the whole world was guilty. To acquit him was to throw over civilization and all its institutions. History has borne out the case against him; for no State has ever constituted itself on his principles or made it possible to live according to his commandments: those States who have taken his name have taken it as an alias to enable them to persecute his followers more plausibly.
It is not surprising that under these circumstances, and in the absence of any defence, the Jerusalem community and the Roman government decided to exterminate Jesus. They had just as much right to do so as to exterminate the two thieves who perished with him.
„But by far the greatest obstacle to the progress of science and to the undertaking of new tasks and provinces therein is found in this — that men despair and think things impossible.“
— Francis Bacon, buch Novum Organum
Novum Organum (1620), Book I
„The method of the science not being practiced much nowadays, except what logic prescribes to all sciences generally, that fitted for the peculiar nature of metaphysics being simply ignored, it is no wonder that those who everlastingly turn the Sisyphean stone of this inquiry do not seem so far to have made much progress. Though here I neither can nor will expatiate upon so important and extensive a subject, I shall briefly shadow forth what constitutes no despicable part of this method, namely, the infection between sensuous and intellectual cognition, not only as creeping in on those incautious in the application of principles, but even producing spurious principles under the appearance of axioms.“
— Immanuel Kant German philosopher 1724 - 1804
Section V On The Method Respecting The Sensuous And The Intellectual In Metaphysics
— Mr. T American actor and retired professional wrestler 1952
World of Warcraft Advert (2007)
„Ultimately, progress in applications is not deterministic, but opportunistic, exploiting for new applications whatever new science and technology happen to be coming along.“
— Herbert Kroemer Nobel laureate in physics 1928
in his Nobel Lecture http://nobelprize.org/nobel_prizes/physics/laureates/2000/kroemer-lecture.html, Quasi-Electric Fields and Band Offsets: Teaching Electrons New Tricks, 8 December 2000, at Aula Magna, Stockholm University.
— Aryabhata Indian mathematician-astronomer 476 - 550
His rule is stated as: dn^2+(2a-d)n=2s, which implies the approximation 3.1416 which is correct to the last decimal place.
In, p. 245.
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures
„There is proof enough furnished by every science, but by none more than geometry, that the world to which we have been allotted is peculiarly adapted to our minds, and admirably fitted to promote our intellectual progress.“
— Benjamin Peirce American mathematician 1809 - 1880
Ben Yamen's Song of Geometry (1853)
Kontext: There is proof enough furnished by every science, but by none more than geometry, that the world to which we have been allotted is peculiarly adapted to our minds, and admirably fitted to promote our intellectual progress. There can be no reasonable doubt that it was part of the Creator's plan. How easily might the whole order have been transposed! How readily might we have been assigned to some complicated system which our feeble and finite powers could not have unravelled!
— Henry David Thoreau, buch Über die Pflicht zum Ungehorsam gegen den Staat
Quelle: Civil Disobedience (1849)
— William Thomson British physicist and engineer 1824 - 1907
Statement of 1896, as quoted in Prodigal Genius : The Life of Nikola Tesla (2007) by James J. O'Neill
„Galileo, perhaps more than any other single person, was responsible for the birth of modern science.“
— Stephen Hawking, buch A Brief History of Time
Quelle: A Brief History of Time (1988), p. 179