„It is not true, out of geometry, that the mathematical sciences are, in all their parts those models of finished accuracy which many suppose. The extreme boundaries of analysis have always been as imperfectly understood as the tract beyond the boundaries was absolutely unknown. But the way to enlarge the settled country has not been by keeping within it, but by making voyages of discovery, and I am perfectly convinced that the student should be exercised in this manner; that is, that he should be taught how to examine the boundary, as well as how to cultivate the interior. …allowing all students whose capacity will let them read on the higher branches of applied mathematics, to have each his chance of being led to the cultivation of those parts of analysis on which rather depends its future progress than its present use in the sciences of matter.“

The Differential and Integral Calculus (1836)

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Augustus De Morgan Foto
Augustus De Morgan8
1806 - 1871

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„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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„Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.“

—  David Hilbert German prominent mathematician 1862 - 1943

Quoted in Mathematical Circles Revisited (1971) by Howard Whitley Eves

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„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.

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Tracey Ullman Foto

„I love John Waters. There's stuff in it that's beyond the boundaries of my taste, but his movies have always been like that.“

—  Tracey Ullman English-born actress, comedian, singer, dancer, screenwriter, producer, director, author and businesswoman 1959

"Q&A: Tracey Ullman" http://www.newsweek.com/newsmakers-127011 (Newsweek, 19 September 2004)

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„Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics…. The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible…. I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s “Algebra” published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.“

—  James Whitbread Lee Glaisher English mathematician and astronomer 1848 - 1928

Fuente: "Presidential Address British Association for the Advancement of Science," 1890, p. 466 : On the need of text-books on higher mathematics

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Tilopa Foto

„No thought, no reflection, no analysis, No cultivation, no intention; Let it settle itself.“

—  Tilopa Indian philosopher 928 - 1009

"Six Precepts" of Tilopa, quoted in Powell Zen and Reality (1975), p. 72

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