“I have endeavoured, in the following treatise, to convey as complete an account of the present state of knowledge on the subject of Differential Equations, as was consistent with the idea of a work intended, primarily, for elementary instruction. It was my object, first of all, to meet the wants of those who had no previous acquaintance with the subject, but I also desired not quite to disappoint others who might seek for more v advanced information. These distinct, but not inconsistent - aims determined the plan of composition.”

Source: 1850s, A treatise on differential equations (1859), p. v; Lead paragraph of the preface

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George Boole39

English mathematician, philosopher and logician 1815–1864

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“My specific… object has been to contain, within the prescribed limits, the whole of the student's course, from the confines of elementary algebra and trigonometry, to the entrance of the highest works on mathematical physics. A learner who has a good knowledge of the subjects just named, and who can master the present treatise, taking up elementary works on conic sections, application of algebra to geometry, and the theory of equations, as he wants them, will, I am perfectly sure, find himself able to conquer the difficulties of anything he may meet with; and need not close any book of Laplace, Lagrange, Legendre, Poisson, Fourier, Cauchy, Gauss, Abel, Hindenburgh and his followers. or of any one of our English mathematicians, under the idea that it is too hard for him.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

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“A subject interests me and holds my attention only so long as it presents me with difficulties, only so long as I am at odds with it and have, as it were, to struggle with it; but once I have mastered it I hurry on to something else, to a new subject; for my interest is not confined to any particular field or subject; it extends to everything human. This does not mean that I am an intellectual miser or egoist, who amasses knowledge for himself alone; by no means! What I do and think for myself, I must also think and do for others. But I feel the need of instructing others in a subject only so long as, while instructing others, I am also instructing myself.”

Ludwig Feuerbach (1804–1872) German philosopher and anthropologist

Lecture I, , R. Manheim, trans. (1967), p. 2 <br class="br"> Lectures on the Essence of Religion http://www.marxists.org/reference/archive/feuerbach/works/lectures/index.htm (1851)

“The researches of the last thirty or forty years into the history of mathematics (I need only mention such names as those of [Carl Anton] Bretschneider, Hankel, Moritz Cantor, [Friedrich] Hultsch, Paul Tannery, Zeuthen, Loria, and Heiberg) have put the whole subject upon a different plane. I have endeavoured in this edition to take account of all the main results of these researches up to the present date. Thus, so far as the geometrical Books are concerned, my notes are intended to form a sort of dictionary of the history of elementary geometry, arranged according to subjects; while the notes on the arithmetical Books VII.-IX. and on Book X follow the same plan.”

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“I am far from saying that this Treatise will be easy; the subject is a difficult one, as all know who have tried it.”

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“This work… was designed in the first instance to be a second edition of a Treatise on Algebra, published in 1830, and which has been long out of print; but I have found it necessary, in carrying out the principles developed in that work, to present the subject in so novel a form, that I could not with propriety consider it in any other light than as an entirely new treatise.”

George Peacock (1791–1858) Scottish mathematician

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“Not many years had elapsed after the first edition of this work, when it became known to all with whom Mr. Malthus had the opportunity of communicating on the subject, or who were acquainted with his last publications, that his opinions on the subject of value had undergone some change.”

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“…the strongest part of a picture is the sensation and the feeling which it creates, this being done through the agency of certain familiar objects more or less accurately depicted and represented with more or less completeness.
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Alfred Horsley Hinton (1863–1908) British photographer

Source: Practical Pictorial Photography, 1898, The application of the foregoing principles, p. 12

“It is the lone worker who makes the first advance in a subject: the details may be worked out by a team, but the prime idea is due to the enterprise, thought, and perception of an individual.”

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biographyonline.net http://www.biographyonline.net/scientists/alex-fleming.html

“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 (1848–1928) English mathematician and astronomer

Source: "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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Jacob Leupold (1674–1727) German multidisciplinary scientist

Jacob Leupold (1724-39) Theatrium machinarum, as quoted in: Biography of Jacob Leupold (1674–1727) http://history-computer.com/People/LeupoldBio.html on history-computer.com, 2013

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George Boole39

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