“Many of the greatest masters of the mathematical sciences were first attracted to mathematical inquiry by problems relating to numbers, and no one can glance at the periodicals of the present day which contain questions for solution without noticing how singular a charm such problems still continue to exert. The interest in numbers seems implanted in the human mind, and it is a pity that it should not have freer scope in this country. The methods of the theory of numbers 271 are peculiar to itself, and are not readily acquired by a student whose mind has for years been familiarized with the very different treatment which is appropriate to the theory of continuous magnitude; it is therefore extremely desirable that some portion of the theory should be included in the ordinary course of mathematical instruction at our University. From the moment that Gauss, in his wonderful treatise of 1801, laid down the true lines of the theory, it entered upon a new day, and no one is likely to be able to do useful work in any part of the subject who is unacquainted with the principles and conceptions with which he endowed it.”

—  James Whitbread Lee Glaisher

Source: "Presidential Address British Association for the Advancement of Science," 1890, p. 467 : On the theory of numbers

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 "Many of the greatest masters of the mathematical sciences were first attracted to mathematical inquiry by problems rela…" by James Whitbread Lee Glaisher?
James Whitbread Lee Glaisher photo
James Whitbread Lee Glaisher6
English mathematician and astronomer 1848–1928

Related quotes

Ernst Mach photo

“There is no problem in all mathematics that cannot be solved by direct counting. But with the present implements of mathematics many operations can be performed in a few minutes which without mathematical methods would take a lifetime.”

Ernst Mach (1838–1916) Austrian physicist and university educator

Source: 19th century, Popular Scientific Lectures [McCormack] (Chicago, 1898), p. 197; On mathematics and counting.

David Hilbert photo

“It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning.”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

Justus von Liebig photo

“To investigate the essence of a natural phenomenon, three conditions are necessary: We must first study and know the phenomenon itself, from all sides; we must then determine in what relation it stands to other natural phenomena; and lastly, when we have ascertained all these relations, we have to solve the problem of measuring these relations and the laws of mutual dependence—that is, of expressing them in numbers. In the first period of chemistry, all the powers of men's minds were devoted to acquiring a knowledge of the properties of bodies; it was necessary to discover, observe, and ascertain their peculiarities. This is the alchemistical period. The second period embraces the determination of the mutual relations or connections of these properties; this is the period of phlogistic chemistry. In the third period, in which we now are, we ascertain by weight and measure and express in numbers the degree in which the properties of bodies are mutually dependent. The inductive sciences begin with the substance itself, then come just ideas, and lastly, mathematics are called in, and with the aid of numbers, complete the work.”

Justus von Liebig (1803–1873) German chemist

Familiar Letters on Chemistry, Tr. Blythe, 4th ed., London, 1859, p. 60 as quoted by John Theodore Merz, A History of European Thought in the Nineteenth Century Vol.1 http://books.google.com/books?id=xqwQAAAAYAAJ (1903).

Nicholas Murray Butler photo

“1. The human mind is so constructed that it must see every perception in a time-relation—in an order—and every perception of an object in a space-relation—as outside or beside our perceiving selves.
2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra.
3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry.
Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.”

Nicholas Murray Butler (1862–1947) American philosopher, diplomat, and educator

Editor's Introduction, The Teaching of Elementary Mathematics https://books.google.com/books?id=NKoAAAAAMAAJ (1906) by David Eugene Smith

David Eugene Smith photo

“1. The human mind is so constructed that it must see every perception in a time-relation—in an order—and every perception of an object in a space-relation—as outside or beside our perceiving selves.
2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra.
3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry.
Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.”

David Eugene Smith (1860–1944) American mathematician

David Eugene Smith, "Editor's Introduction," in: The Teaching of Elementary Mathematics https://books.google.com/books?id=NKoAAAAAMAAJ (1906)

Henry John Stephen Smith photo

“The problem of the direct determination of the primitive roots of a prime number is one of the 'cruces' of the Theory of Numbers. Euler, who first observed the peculiarity of these numbers, has yet left us no rigorous proof of their existence; though assuming their existence, he succeeded in accurately determining their number. The defect in his demonstration was first supplied by Gauss, who has also proposed an indirect method for finding a primitive root.”

Henry John Stephen Smith (1826–1883) mathematician

Report on the Theory of Numbers (1859) Part I, p. 49.
The Collected Mathematical Papers of Henry John Stephen Smith (1894) Vol. 1

Wilhelm Von Humboldt photo

“If we glance at the most important revolutions in history, we are at no loss to perceive that the greatest number of these originated in the periodical revolutions of the human mind.”

Wilhelm Von Humboldt (1767–1835) German (Prussian) philosopher, government functionary, diplomat, and founder of the University of Berlin

Source: The Limits of State Action (1792), Ch. 16

“Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 495

Marcus du Sautoy photo

“I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe.
Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.”

Marcus du Sautoy (1965) British professor of mathematics

In "Life lessons" http://www.theguardian.com/science/2005/apr/07/science.highereducation?fb_ref=desktop The Guardian (7 April 2005)

Carl Gustav Jacob Jacobi photo

“It is true that M. Fourier had the opinion that the principal end of mathematics was the public utility and the explanation of natural phenomena; but such a philosopher as he is should have known that the unique end of science is the honor of the human mind, and that from this point of view a question of number is as important as a question of the system of the world.”

Carl Gustav Jacob Jacobi (1804–1851) German mathematician

Letter to Legendre (July 2, 1830) in response to Fourier's report to the Paris Academy Science that mathematics should be applied to the natural sciences, as quoted in Science (March 10, 1911) Vol. 33 https://books.google.com/books?id=4LU7AQAAMAAJ&pg=PA359, p.359, with additional citations and dates from H. Pieper, "Carl Gustav Jacob Jacobi," Mathematics in Berlin (2012) p.46

Related topics