“The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!”

Mathematical Problems (1900)

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David Hilbert30

German prominent mathematician 1862–1943

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“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) <br class="br">Metaphysical Foundations of Natural Science (1786)

“For the mathematician the important consideration is that the foundations of mathematics and a great portion of its content are Greek. The Greeks laid down the first principles, invented the methods ab initio, and fixed the terminology. Mathematics in short is a Greek science, whatever new developments modern analysis has brought or may bring.”

Thomas Little Heath (1861–1940) British civil servant and academic

Preface p. v
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

“And if the experience of natural science is any guide, then as the science of administration advances, we may reasonably expect it to take on an increasingly deterministic character. As research, scientific societies, and the exchanges of knowledge and hypotheses by natural scientists have advanced the exactness of knowledge in the domain of natural science, so we may expect research, administrative societies, and the exchanges among administrators to advance the exactness of knowledge in the domain of administration.”

Charles A. Beard (1874–1948) American historian

661-2
Philosophy, Science and Art of Public Administration (1939)

“A model may be pictorial, descriptive, qualitative, or generally approximate in nature, or it may be mathematical and quantitative in nature and reasonably precise.”

Harold Chestnut (1917–2001) American engineer

Source: Systems Engineering Tools, (1965), p. 108

“[The mathematical character of Descartes' physics lies in its methodological nature, namely, the] axiomatic structure of the whole system, in the establishment of indubitable foundations and the deduction of the phenomena.”

Eduard Jan Dijksterhuis (1892–1965) Dutch historian

Source: The mechanization of the world picture, 1961, p. 414; as cited in: ‎Marleen Rozemond (2009), Descartes's Dualism. p. 235

“As a science mathematics has been adapted to the description of natural phenomena, and the great practitioners in this field… have never concerned themselves with the logical foundations of mathematics, but have boldly taken a pragmatic view of mathematics as an intellectual machine which works successfully. Description has been verified by further observation, still more strikingly be prediction, and sometimes, more ominously, by control of natural forces. Happily, unresolved problems… still remain as challenges.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“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

“This civilization is the work of man, who high-handedly and ignorant of the true workings of Nature, has created a world without meaning or foundation, which now threatens to destroy him, for through his behavior and his activities, he, who should be her master, has disturbed Nature's inherent unity.”

Viktor Schauberger (1885–1958) austrian philosopher and inventor

Callum Coats: Water Wizard
Viktor Schauberger: Our Senseless Toil (1934)

“This [experimentation] is the custom—and properly so—in those sciences where mathematical demonstrations are applied to natural phenomena, as is seen in the case of perspective, astronomy, mechanics, music, and others where the principles, once established by well-chosen experiments, become the foundations of the entire superstructure.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

Salviati, Third Day. Change of Position
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)

“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 (1471–1528) German painter, printmaker, mathematician, and theorist

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

“The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!”

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David Hilbert30

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