“The history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several preceding centuries.”

— James Gow (scholar)

Preface
A Short History of Greek Mathematics (1884)

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scholar 1854–1923

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“Another feature of Alexandrian algebra is the absence of any explicit deductive structure. The various types of numbers… were not defined. Nor was there any axiomatic basis on which a deductive structure could be erected. The work of Heron, Nichomachus, and Diophantus, and of Archimedes as far as his arithmetic is concerned, reads like the procedural texts of the Egyptians and Babylonians… The deductive, orderly proof of Euclid and Apollonius, and of Archimedes' geometry is gone. The problems are inductive in spirit, in that they show methods for concrete problems that presumably apply to general classes whose extent is not specified. In view of the fact that as a consequence of the work of the classical Greeks mathematical results were supposed to be derived deductively from an explicit axiomatic basis, the emergence of an independent arithmetic and algebra with no logical structure of its own raised what became one of the great problems of the history of mathematics. This approach to arithmetic and algebra is the clearest indication of the Egyptian and Babylonian influences… Though the Alexandrian Greek algebraists did not seem to be concerned about this deficiency… it did trouble deeply the European mathematicians.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p.144

“It is a remarkable fact in the history of geometry, that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences.”

Florian Cajori book A History of Mathematics

Source: A History of Mathematics (1893), p. 30 Reported in Memorabilia mathematica or, The philomath's quotation-book by Robert Edouard Moritz. Published 1914.

“When we speak of the early history of algebra it is necessary to consider… the meaning of the term. If… we mean the science that allows us to solve the equation ax^2 + bx + c = 0, expressed in these symbols, then the history begins in the 17th century; if we remove the restriction as to these particular signs, and allow for other and less convenient symbols, we might properly begin the history in the 3rd century; if we allow for the solution of the above equation by geometric methods, without algebraic symbols of any kind, we might say that algebra begins with the Alexandrian School or a little earlier; and if we say that we should class as algebra any problem that we should now solve with algebra (even though it was as first solved by mere guessing or by some cumbersome arithmetic process), the the science was known about 1800 B. C., and probably still earlier.<”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, Ch. 6: Algebra, p. 378

“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

“In the history of mathematics, the "how" always preceded the "why," the technique of the subject preceded its philosophy.”

Tobias Dantzig (1884–1956) American mathematician

Number: The Language of Science (1930)

“He moved to Egypt and supported himself by teaching and by copying Arabic translations of Greek mathematical classics such as Euclid’s Elements and Ptolemy’s Almagest.”

Alhazen (965–1038) Arab physicist, mathematician and astronomer

Abdelhamid I. Sabra, in “Ibn al-Haytham Brief life of an Arab mathematician: died circa 1040 (September-October 2003)”

“Mathematics as an Element in the History of Thought.”

Alfred North Whitehead (1861–1947) English mathematician and philosopher

1920s, Science and the Modern World (1925)

“Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him.”

Florian Cajori book A History of Mathematics

Source: A History of Mathematics (1893), p. 30, Reported in Moritz (1914)

“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.”

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

Source: Squaring the Circle (1913), p. 2

“Euclid's work will live long after all the text books of the present day are superseded and forgotten. It is one of the noblest monuments of antiquity; no mathematician worthy of the name can afford not to know Euclid, the real Euclid as distinct from any revised or rewritten versions which will serve for schoolboys or engineers. And, to know Euclid, it is necessary to know his language, and, so far as it can be traced, the history of the "elements" which he collected in his immortal work.”

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

The Thirteen Books of Euclid's Elements (1908)

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