James Gow (scholar) quote: “With Diophantus the history of Greek arithmetic comes to an end. No original work, that we know of, was done afterwards.”

“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

“To give here an elaborate account of Pappus would be to create a false impression. His work is only the last convulsive effort of Greek geometry which was now nearly dead and was never effectually revived. It is not so with Ptolemy or Diophantus. The trigonometry of the former is the foundation of a new study which was handed on to other nations indeed but which has thenceforth a continuous history of progress. Diophantus also represents the outbreak of a movement which probably was not Greek in its origin, and which the Greek genius long resisted, but which was especially adapted to the tastes of the people who, after the extinction of Greek schools, received their heritage and kept their memory green. But no Indian or Arab ever studied Pappus or cared in the least for his style or his matter. When geometry came once more up to his level, the invention of analytical methods gave it a sudden push which sent it far beyond him and he was out of date at the very moment when he seemed to be taking a new lease of life.”

James Gow (scholar) (1854–1923) scholar

p, 125
A Short History of Greek Mathematics (1884)

“To give here an elaborate account of Pappus would be to create a false impression. His work is only the last convulsive effort of Greek geometry which was now nearly dead and was never effectually revived. It is not so with Ptolemy or Diophantus. The trigonometry of the former is the foundation of a new study which was handed on to other nations indeed but which has thenceforth a continuous history of progress.”

Ptolemy (100–170) Greco-Egyptian writer and astronomer of Alexandria

James Gow, A Short History of Greek Mathematics https://books.google.com/books?id=9d8DAAAAMAAJ (1884) p.308.

“Here we have seen that their early history is still largely an open question. They may have had Greek origins: Whatever process produced the Greek-speakers (of that is how one defines "Greek") who lived south of Olympus may have also produced the Makedones who wandered out of the western mountains to establish a home and a kingdom in Pieria.”

Eugene N. Borza (1935) American historian

Source: In the Shadow of Olympus: The Emergence of Macedon (1990), pp. 277-278

“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) (1854–1923) scholar

Preface
A Short History of Greek Mathematics (1884)

“Some of these things seem as if it’s a lot of hard work, and it is. But it’s to an end—toward a richer, deeper understanding of a phenomenon that I was seeking to bring to life…The term narrative comes from Greek for the word knowing. And I think that that’s a powerful message because it means you cannot tell a story until you know the story.”

Isabel Wilkerson (1961) American journalist

On how she hopes The Warmth of Other Suns led to a deeper understanding in “Isabel Wilkerson” https://www.neh.gov/humanities/2016/fall/feature/isabel-wilkerson in Humanities (Fall 2016)

“The more original a discovery the more obvious it seems afterwards.”

Arthur Koestler book The Act of Creation

The Act of Creation (1970).

“Probably Greek logistic, or calculation, extended to more difficult operations… and… probably Greek arithmetic, or theory of numbers, owed much more to induction than is permitted to appear by its first and chief professors.”

James Gow (scholar) (1854–1923) scholar

p, 125
A Short History of Greek Mathematics (1884)

“It appears, accordingly, from the experience of all ages and nations, I believe, that the work done by freemen comes cheaper in the end than that performed by slaves.”

Adam Smith (1723–1790) Scottish moral philosopher and political economist

Source: (1776), Book I, Chapter VIII.

“For Beatrice--When we met, my life began. Soon afterwards, yours ended”

Daniel Handler book The Ersatz Elevator

Lemony Snicket
The Ersatz Elevator (2001)

“With Diophantus the history of Greek arithmetic comes to an end. No original work, that we know of, was done afterwards.”

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