„If we compare. e. g. the systems of classical mathematics and of intuitionistic mathematics, we find that the first is much simpler and technically more efficient, while the second is more safe from surprising occurences, e. g. contradictions. At the present time, any estimation of the degree of safety of the system of classical mathematics, in other words, the degree of plausibility of its principles, is rather subjective. The majority of mathematicians seem to regard this degree as sufficiently high for all practical purposes and therefore prefer the application of classical mathematics to that of intuitionistic mathematics. The latter has not, so far as I know, been seriously applied in physics by anybody.“

Rudolf Carnap (1939; 51), as cited in: Paul van Ulsen. Wetenschapsfilosofie http://www.illc.uva.nl/Research/Publications/Inaugurals/IV-10-Arend-Heyting.text.pdf, 6 november 2017.

Übernommen aus Wikiquote. Letzte Aktualisierung 3. Juni 2021. Geschichte
Rudolf Carnap Foto
Rudolf Carnap
deutscher Philosoph 1891 - 1970

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George Pólya Foto
Eduard Jan Dijksterhuis Foto
Thomas Little Heath Foto
John Von Neumann Foto
Paul Bernays Foto
John Nash Foto

„For the great majority of mathematicians, mathematics is“

—  George Frederick James Temple British mathematician 1901 - 1992

100 Years of Mathematics: a Personal Viewpoint (1981)
Kontext: For the great majority of mathematicians, mathematics is... a whole world of invention and discovery—an art. The construction of a new theorem, the intuition of some new principle, or the creation of a new branch of mathematics is the triumph of the creative imagination of the mathematician, which can be compared to that of a poet, the painter and the sculptor.

Benjamin Peirce Foto

„The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics.“

—  Benjamin Peirce, Linear Associative Algebra

§ 2.
Linear Associative Algebra (1882)
Kontext: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.

Johannes Kepler Foto
Hans Reichenbach Foto
G. H. Hardy Foto
David Deutsch Foto
René Descartes Foto

„With me, everything turns into mathematics.
More closely translated as: but in my opinion, all things in nature occur mathematically.“

—  René Descartes French philosopher, mathematician, and scientist 1596 - 1650

""Mais"" is French for ""but"" and the ""but in my opinion"" comes from the context of the original conversation. apud me omnia fiunt Mathematicè in Natura is in latin.
Sometimes the Latin version is incorrectly quoted as Omnia apud me mathematica fiunt.
Sources: Correspondence with Mersenne http://fr.wikisource.org/wiki/Page%3aDescartes_-_%C5%92uvres,_%C3%A9d._Adam_et_Tannery,_III.djvu/48 note for line 7 (1640), page 36, Die Wiener Zeit http://books.google.com/books?id=9Xh3fVZLCycC&pg=PA532&lpg=PA532&dq=%22Omnia+apud+me+mathematica+fiunt%22+original+zitat&source=bl&ots=CgQOrveRiM&sig=WFHwIK20r5vRZ66FwCaxo857LCU&hl=de&sa=X&ei=_Wf2UcHlJYbfsgaf1IHABg#v=onepage&q=%22Omnia%20apud%20me%20mathematica%20fiunt%22%20original%20zitat&f=false page 532 (2008); StackExchange Math Q/A Where did Descartes write... http://math.stackexchange.com/questions/454599/where-did-descartes-write-with-me-everything-turns-into-mathematics?noredirect=1#comment978229_454599
Original: (la) Mais apud me omnia fiunt Mathematicè in Natura

E. W. Hobson Foto

„Much of the skill of the true mathematical physicist and of the mathematical astronomer consists in the power of adapting methods and results carried out on an exact mathematical basis to obtain approximations sufficient for the purposes of physical measurements. It might perhaps be thought that a scheme of Mathematics on a frankly approximative basis would be sufficient for all the practical purposes of application in Physics, Engineering Science, and Astronomy, and no doubt it would be possible to develop, to some extent at least, a species of Mathematics on these lines. Such a system would, however, involve an intolerable awkwardness and prolixity in the statements of results, especially in view of the fact that the degree of approximation necessary for various purposes is very different, and thus that unassigned grades of approximation would have to be provided for. Moreover, the mathematician working on these lines would be cut off from the chief sources of inspiration, the ideals of exactitude and logical rigour, as well as from one of his most indispensable guides to discovery, symmetry, and permanence of mathematical form. The history of the actual movements of mathematical thought through the centuries shows that these ideals are the very life-blood of the science, and warrants the conclusion that a constant striving toward their attainment is an absolutely essential condition of vigorous growth. These ideals have their roots in irresistible impulses and deep-seated needs of the human mind, manifested in its efforts to introduce intelligibility in certain great domains of the world of thought.“

—  E. W. Hobson British mathematician 1856 - 1933

Quelle: Presidential Address British Association for the Advancement of Science, Section A (1910), pp. 285-286; Cited in: Moritz (1914, 229): Mathematics and Science.

Bertrand Russell Foto

„Physics is mathematical not because we know so much about the physical world, but because we know so little“

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970

An Outline of Philosophy Ch.15 The Nature of our Knowledge of Physics (1927)
1920s
Kontext: Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover.

Bernard Le Bovier de Fontenelle Foto

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