“It is true that in recent years a number of attractive histories of mathematics have been published in England and America, but these have only dealt with Greek mathematics as part of the larger subject, and in consequence the writers have been precluded… from presenting the work of the Greeks in suflicient detail. The same remark applies to the German histories of mathematics, even to the great work of Moritz Cantor…”

—  Thomas Little Heath

Preface p. vi
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

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Thomas Little Heath 46
British civil servant and academic 1861–1940

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Thomas Little Heath photo

“Dr. James Gow did a great service by the publication in 1884 of his Short History of Greek Mathematics, a scholarly and useful work which has held its own and has been quoted with respect and appreciation by authorities on the history of mathematics in all parts of the world. At the date when he wrote, however, Dr. Gow had necessarily to rely upon the works of the pioneers Bretschneider, Hankel, Allman, and Moritz Cantor (first edition). Since then the subject has been very greatly advanced… scholars and mathematicians… have thrown light on many obscure points. It is therefore high time for the complete story to be rewritten.”

Thomas Little Heath (1861–1940) British civil servant and academic

A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

“The history of Greek mathematics is, for the most part, only the history of such mathematics as are learnt daily in all our public schools. …If it was not wanted, as it ought to have been, by our classical professors and our mathematicians, it would have served at any rate to quicken, with some human interest, the melancholy labours of our schoolboys.”

James Gow (scholar) (1854–1923) scholar

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“The sciences we are familiar with have been installed in a number of great 'continents'. Before Marx, two such continents had been opened up to scientific knowledge: the continent of Mathematics and the continent of Physics. The first by the Greeks (Thales), the second by Galileo. Marx opened up a third continent to scientific knowledge: the continent of History.”

Louis Althusser book Lenin and Philosophy and Other Essays

Source: Lenin and Philosophy and Other Essays (1968), "Philosophy as a Revolutionary Weapon", p. 4

“A student of history, who cares little for Greek or mathematics in particular, but who likes to watch how things grow, will be able to extract from these pages a notion of the whole history of mathematical science down to Newton's time…”

James Gow (scholar) (1854–1923) scholar

Preface
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Freeman Dyson photo

“Anyone who compares the bibliography with the reprinted papers will notice that mathematics and physics have not been given equal treatment. There is a strong bias in favor of mathematics. The bias arises from the fact that mathematical papers, provided that are correct and not trivial, have permanent value, whereas most papers in physics journals are ephemeral. For this reason, it is customary to publish complete collected works of mathematicians but only selected works of physicists.”

Freeman Dyson (1923) theoretical physicist and mathematician

Selected Papers of Freeman Dyson with Commentary. https://books.google.com/books?id=nnyNUidX1OMC&pg=PA1 American Mathematical Soc. (1996) p. 1

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“I have said that mathematics is the oldest of the sciences; a glance at its more recent history will show that it has the energy of perpetual youth. The output of contributions to the advance of the science during the last century and more has been so enormous that it is difficult to say whether pride in the greatness of achievement in this subject, or despair at his inability to cope with the multiplicity of its detailed developments, should be the dominant feeling of the mathematician. Few people outside of the small circle of mathematical specialists have any idea of the vast growth of mathematical literature. The Royal Society Catalogue contains a list of nearly thirty-nine thousand papers on subjects of Pure Mathematics alone, which have appeared in seven hundred serials during the nineteenth century. This represents only a portion of the total output, the very large number of treatises, dissertations, and monographs published during the century being omitted.”

E. W. Hobson (1856–1933) British mathematician

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 283; Cited in: Moritz (1914, 108-9): Modern mathematics.

“The unnaturalness of mathematical symbolism is attested to by history. The algebra of the Egyptians, the Babylonians, the Greeks, the Hindus, and the Arabs was what is commonly called rhetorical algebra. …on the whole they used ordinary rhetoric to describe their mathematical work. Symbolism is a relatively modern invention of the sixteenth and seventeenth centuries…”

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 59

Thomas Little Heath photo

“It is to be feared that few who are not experts in the history of mathematics have any acquaintance with the details of the original discoveries in mathematics of the greatest mathematician of antiquity, perhaps the greatest mathematical genius that the world has ever seen.”

Thomas Little Heath (1861–1940) British civil servant and academic

Source: Achimedes (1920), Ch. I. Archimedes, p.1

Thomas Little Heath photo

“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.”

Thomas Little Heath (1861–1940) British civil servant and academic

p, 125
The Thirteen Books of Euclid's Elements (1908)

Thomas Little Heath photo

“The best history of Greek mathematics which exists at present is undoubtedly that of Gino Loria under the title Le scienze esatte nell' antica Grecia (second edition 1914…) …the arrangement is chronological …they raise the question whether in a history of this kind it is best to follow chronological order or to arrange the material according to subjects…
I have adopted a new arrangement, mainly according to subjects…”

Thomas Little Heath (1861–1940) British civil servant and academic

A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

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