“It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained…. I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject”

— James Whitbread Lee Glaisher

Source: "Presidential Address British Association for the Advancement of Science," 1890, p. 466 : On the expansion of the field of mathematics, and on the importance of a well-chosen notation

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its f…" by James Whitbread Lee Glaisher?

James Whitbread Lee Glaisher 6

English mathematician and astronomer 1848–1928

Related quotes

“The Glass Bead Game, formerly the specialized entertainment of mathematicians in one era, philologists or musicians in another era, now more and more cast its spell upon all true intellectuals.”

Hermann Hesse book The Glass Bead Game

The Glass Bead Game (1943)
Context: The Glass Bead Game, formerly the specialized entertainment of mathematicians in one era, philologists or musicians in another era, now more and more cast its spell upon all true intellectuals. Many an old university, many a lodge, and especially the age-old League of Journeyers to the East, turned to it. Some of the Catholic Orders likewise scented a new intellectual atmosphere and yielded to its lure. At some Benedictine abbeys the monks devoted themselves to the Game so intensely that even in those early days the question was hotly debated — it was subsequently to crop up again now and then — whether this game ought to be tolerated, supported, or forbidden by Church and Curia.

“Out of fifty mathematical papers presented in brief at such a meeting, it is a rare mathematician indeed who really understands what more than half a dozen are about.”

Eric Temple Bell (1883–1960) mathematician and science fiction author born in Scotland who lived in the United States for most of his li…

Source: Mathematics: Queen and Servant of Science (1938), p. 7

“It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.”

Richard Courant (1888–1972) German American mathematician (1888-1972)

Richard Courant, "Mathematics in the Modern World", Scientific American, Vol 211, (Sep 1964), p. 42

“Pure mathematics is much more than an armoury of tools and techniques for the applied mathematician. On the other hand, the pure mathematician has ever been grateful to applied mathematics for stimulus and inspiration. From the vibrations of the violin string they have drawn enchanting harmonies of Fourier Series, and to study the triode valve they have invented a whole theory of non-linear oscillations.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“When this book was first conceived (more than 25 years ago) few mathematicians outside the Soviet Union recognized probability as a legitimate branch of mathematics.”

William Feller (1906–1970) Croatian-American mathematician

Preface to the Third Edition, p. vii.
An Introduction To Probability Theory And Its Applications (Third Edition)

“The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work”

James Whitbread Lee Glaisher (1848–1928) English mathematician and astronomer

Source: "Presidential Address British Association for the Advancement of Science," 1890, p. 467 : On the importance of broad training

“It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

Gauss-Schumacher Briefwechsel (1862)
Context: It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation. So there are mere philologists, mere jurists, mere soldiers, mere merchants, etc. To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.

“We must understand that the fact of error, demonstrated in subsequent work, does not suggest that ethical lapses are responsible. It is more likely that the source of error is, as the advertisement says, a reflection of the fact that "its dangerous to trifle with Mother Nature."”

Lewis M. Branscomb (1926) physicist and science policy advisor

1994, p. 45
Integrity in Science (1985)

“As far as the use of mathematics in economics is concerned, there is an abundance of formulas where such are not needed. They are frequently introduced, one fears, in order to show off. The more difficult the mathematical theorem, the more esoteric the name of the mathematician quoted, the better.”

Oskar Morgenstern (1902–1977) austrian economist

Oskar Morgenstern, " Limits of the Use of Mathematics in Economics https://www.princeton.edu/~erp/ERParchives/archivepdfs/M49.pdf," in: James C. Charlesworth (Hg.), Mathematics and the Social Science. The Utility and Inutility of Mathematics in the Study of Economics, Political Sciences and Sociology, Philadelphia 1963, S. 12-29, hier S. 18.

“…there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, […] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as ‘real’, but […] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics.”

G. H. Hardy book A Mathematician's Apology

A Mathematician's Apology (1941)

Help us to complete the source, original and additional information

James Whitbread Lee Glaisher 6

Related quotes

Related topics