“The new art must be based upon science — in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences.”

— Albrecht Dürer

As quoted in Dictionary of Scientific Biography (1970 - 1990) edited by M Steck.

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Albrecht Dürer 6

German painter, printmaker, mathematician, and theorist 1471–1528

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“Logic is not only an exact science, but is the most simple and elementary of all sciences; it ought therefore undoubtedly to find some place in every course of education.”

William Stanley Jevons (1835–1882) English economist and logician

Preface.
Elementary Lessons on Logic (1870)

“I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially of nature, requires a pure portion, lying at the foundation of the empirical, and based upon à priori knowledge of natural things. …the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.”

Immanuel Kant book Metaphysical Foundations of Natural Science

Preface, Tr. https://books.google.com/books?id=OCJLAAAAMAAJ Ernest Belfort Bax (1883)
Metaphysical Foundations of Natural Science (1786)

“Logic is the most useful tool of all the arts. Without it no science can be fully known.”

William of Ockham book Sum of Logic

Summa Logicae (c. 1323), Prefatory Letter, as translated by Paul Vincent Spade (1995) http://www.pvspade.com/Logic/docs/ockham.pdf
Context: Logic is the most useful tool of all the arts. Without it no science can be fully known. It is not worn out by repeated use, after the manner of material tools, but rather admits of continual growth through the diligent exercise of any other science. For just as a mechanic who lacks a complete knowledge of his tool gains a fuller [knowledge] by using it, so one who is educated in the firm principles of logic, while he painstakingly devotes his labor to the other sciences, acquires at the same time a greater skill at this art.

“Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic.”

Robert Chambers (publisher, born 1802) (1802–1871) Scottish publisher and writer

Robert Chambers, Chambers's Information for the People (1875) Vol. 2 https://books.google.com/books?id=vNpTAAAAYAAJ

“It is clear that economics, if it is to be a science at all, must be a mathematical science.”

William Stanley Jevons The Theory of Political Economy

Source: The Theory of Political Economy (1871), Chapter I, Introduction, p. 38.

“Our delight in any particular study, art, or science rises and improves in proportion to the application which we bestow upon it. Thus, what was at first an exercise becomes at length an entertainment.”

Joseph Addison (1672–1719) politician, writer and playwright

No. 447 (2 August 1712).
The Spectator (1711–1714)

“"Normal science" means research firmly based upon one or more past scientific achievements, achievements that some particular scientific community acknowledges for a time as supplying the foundation for its further practice”

Thomas Kuhn book The Structure of Scientific Revolutions

Source: The Structure of Scientific Revolutions (1962), II. The Route to Normal Science, p. 10

“Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.”

David Hilbert Mathematical Problems

Mathematical Problems (1900)
Context: Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

“We had principles in mathematics that were granted to be absolute in mathematics for over 800 years, but new science has gotten rid of those absolutism, gotten — forward other different logics of looking at mathematics, and sort of turned the way we look at it as a science altogether after 800 years.”

Mahmoud Ahmadinejad (1956) 6th President of the Islamic Republic of Iran

Columbia University speech, 24 September 2007
[24 September 2007, http://www.azstarnet.com/sn/hourlyupdate/202820.php, "Iran's president at Columbia University - a transcript", azstarnet.com, 2007-09-25]
2007

“Logic is neither a science nor an art, but a dodge.”

Benjamin Jowett (1817–1893) Theologian, classical scholar, and academic administrator

Letters

“The new art must be based upon science — in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences.”

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Albrecht Dürer 6

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