“It has always appeared to me that we sacriﬁce many of the advantages and more of the pleasures of studying any science by omitting all reference to the history of its progress: I have therefore occasionally introduced historical notices of those problems which are interesting either from the nature of the questions involved, or from their bearing on the history of the Calculus. …[T]hese digressions may serve to relieve the dryness of a mere collection of Examples.”

— Duncan Gregory

p. vi http://books.google.com/books?id=h7JT-QDuAHoC&pg=PR6, as cited in: Patricia R. Allaire and Robert E. Bradley. " Symbolical algebra as a foundation for calculus: DF Gregory's contribution http://poncelet.math.nthu.edu.tw/disk5/js/history/gregory.pdf." Historia Mathematica 29.4 (2002): p. 409. <br class="br">Examples of the processes of the differential and integral calculus, (1841)

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Duncan Gregory4

British mathematician 1813–1844

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Those conceptions were ones I had previously drawn partly from scientific training itself and partly from a long-standing avocational interest in the philosophy of science. Somehow, whatever their pedagogic utility and their abstract plausibility, those notions did not at all fit the enterprise that historical study displayed. Yet they were and are fundamental to many discussions of science, and their failures of verisimilitude therefore seemed thoroughly worth pursuing. The result was a drastic shift in my career plans, a shift from physics to history of science and then, gradually, from relatively straightforward historical problems back to the more philosophical concerns that had initially led me to history.”

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“Historical studies of the sciences tend to adopt one of two rather divergent points of view. One of these typically looks at historical developments in a discipline from the inside. It is apt to take for granted many of the presuppositions that are currently popular among members of the discipline and hence tends to view the past in terms of gradual progress toward a better present. The second point of view does not adopt its framework of issues and presuppositions from the field that is the object of study but tends nowadays to rely heavily on questions and concepts derived from studies in the history, philosophy, and sociology of science. A history written from the insider's point of view always conveys a strong sense of being "our" history. That is not the case with the second type of history, whose tone is apt to be less celebratory and more critical.
In the case of the older sciences, histories of the second type have for many years been the province of specialists in the history, philosophy, or sociology of science. This is not, or perhaps not yet, the case for psychology, whose history has to a large extent been left to psychologists to pursue. Accordingly, insiders' histories have continued to have a prominence they have long lost in the older sciences. Nevertheless, much recent work in the history of psychology has broken with this tradition.”

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“A society has many pasts from which it chooses those that go into the creation of its history. The choice is made by those in authority—the authority being of various kinds—although occasionally the voice of others may be heard.”

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“I came into history from a primary concern with mathematics and science. This has been a tremendous help to me as a person and as a historian, although it must be admitted it has served to make my historical interpretations less conventional than may be acceptable of many of my colleagues in the field.”

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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.”

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

“If the question be raised, why such an apparently special problem as the quadrature of the circle, is deserving of the sustained interest which has attained to it, and which it still possesses, the answer is only to be found in a scrutiny of the history of the problem, and especially in the closeness of the connection of that history with the general history of Mathematical Science.”

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“But History was against me. History is right, objectively speaking. I'm just a historical dead end. I hope at least that my fate will serve as an example to you all and to posterity.”

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