„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)
Contexto: 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.

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Benjamin Peirce Foto
Benjamin Peirce
matemático estadounidense 1809 - 1880

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Benjamin Peirce Foto

„Mathematics, under this definition, belongs to every enquiry, moral as well as physical.“

—  Benjamin Peirce, Linear Associative Algebra

§ 1.
Linear Associative Algebra (1882)
Contexto: The sphere of mathematics is here extended, in accordance with the derivation of its name, to all demonstrative research, so as to include all knowledge strictly capable of dogmatic teaching. Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics. It deduces from a law all its consequences, and develops them into the suitable form for comparison with observation, and thereby measures the strength of the argument from observation in favor of a proposed law or of a proposed form of application of a law.
Mathematics, under this definition, belongs to every enquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by, observation.

Eugene Paul Wigner Foto

„The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.“

—  Eugene Paul Wigner, La Irrazonable Eficacia de la Matemática en las Ciencias Naturales

"The Unreasonable Effectiveness of Mathematics in the Natural Sciences," Communications in Pure and Applied Mathematics, February 1960, final sentence.

Max Horkheimer Foto
William Thomson Foto

„Now I think hydrodynamics is to be the root of all physical science, and is at present second to none in the beauty of its mathematics.“

—  William Thomson British physicist and engineer 1824 - 1907

Fuente: In a letter addressed to George Stokes dated December 20, 1857, as quoted in Fluid Mechanics in the Next Century https://doi.org/10.1115/1.3101925 (1996), by Mohamed Gad-el-Hak and Mihir Sen.

Hermann Weyl Foto
Leonardo Da Vinci Foto

„There is no certainty in sciences where one of the mathematical sciences cannot be applied, or which are not in relation with these mathematics.“

—  Leonardo Da Vinci Italian Renaissance polymath 1452 - 1519

The Notebooks of Leonardo da Vinci (1883), XIX Philosophical Maxims. Morals. Polemics and Speculations.

E. W. Hobson Foto

„A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.“

—  E. W. Hobson British mathematician 1856 - 1933

Fuente: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 286; Cited in: Moritz (1914, 106): Modern mathematics.

William John Macquorn Rankine Foto
George Pólya Foto

„Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.“

—  George Pólya Hungarian mathematician 1887 - 1985

[Jon Fripp, Michael Fripp, Deborah Fripp, Speaking of Science: Notable Quotes on Science, Engineering, and the Environment, https://books.google.com/books?id=44ihCUS1XQMC&pg=PA45, 2000, Newnes, 978-1-878707-51-2, 45]

Donald Ervin Knuth Foto
Hermann Grassmann Foto
Hans Reichenbach Foto
Ian McDonald Foto
Benjamin Peirce Foto
George Klir Foto

„Among the various paradigmatic changes in science and mathematics in this century, one such change concerns the concept of uncertainty.“

—  George Klir American computer scientist 1932 - 2016

In science, this change has been manifested by a gradual transition from the traditional view, which insists that uncertainty is undesirable in science and should be avoided by all possible means, to an alternative view, which is tolerant of uncertainty and insists that science cannot avoid it. According to the traditional view, science should strive for certainty in all its manifestations (precision, specificity, sharpness, consistency, etc.); hence, uncertainty (imprecision, nonspecificity, vagueness, inconsistency,etc.) is regarded as unscientific. According to the alternative (or modem) view, uncertainty is considered essential to science; it is not only an unavoidable plague, but it has, in fact, a great utility.
Fuente: Fuzzy sets and fuzzy logic (1995), p. 1.

Arthur Stanley Eddington Foto

„It is to this background that our own personality and consciousness belong, and those spiritual aspects of our nature not to be described by any symbolism… to which mathematical physics has hitherto restricted itself.“

—  Arthur Stanley Eddington British astrophysicist 1882 - 1944

Science and the Unseen World (1929)
Contexto: It remains a real world if there is a background to the symbols—an unknown quantity which the mathematical symbol x stands for. We think we are not wholly cut off from this background. It is to this background that our own personality and consciousness belong, and those spiritual aspects of our nature not to be described by any symbolism... to which mathematical physics has hitherto restricted itself.<!--III, p.37-38

Bernard Le Bovier de Fontenelle Foto

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