- GREEK AND ROMAN MATHEMATICS 47
indeed I had put down everything just as it occurred to me, post-
poning revision until the end. [Book II]Ptolemy. Claudius Ptolemy was primarily an astronomer and physicist, although
these subjects were hardly distinct from mathematics in his time. He lived in
Alexandria during the second century, as is known from the astronomical observa-
tions that he made between 127 and 141 CE. He created an intricate and workable
Earth-centered mathematical system of explaining the motion of the planets and
systematized it in a treatise known as the Syntaxis, which, like Euclid's, consisted
of 13 books. Also like Euclid's treatise, Ptolemy's Syntaxis became a classic refer-
ence and was used for well over a thousand years as the definitive work on math-
ematical astronomy. It soon became known as the "greatest" work (megistos in
Greek) and when translated into Arabic became al-megista or the Almagest, as we
know it today.
Diophantus. Little is known about this author of a remarkable treatise on what
we now call algebra and number theory. He probably lived in the third century
CE, although some experts believe he lived earlier than that. His treatise is of no
practical value in science or commerce, but its problems inspired number theorists
during the seventeenth century and led to the long-standing conjecture known as
Fermat's last theorem. The 1968 discovery of what may be four books from this
treatise that were long considered lost was the subject of a debate among the
experts, some of whom believed the books might be commentaries, perhaps written
by the late fourth-century commentator Hypatia. If so, they would be the only-
work by Hypatia still in existence.
Pappus. Pappus, who is known to have observed a solar eclipse in Alexandria in
320 CE, was the most original and creative of the later commentators on Greek
geometry and arithmetic. His Synagoge (Collection) consists of eight books of
insightful theorems on arithmetic and geometry, as well as commentary on the
works of other authors. In some cases where works of Euclid, Apollonius, and
others have been lost, this commentary tells something about these works. Pappus
usually assumes that the reader is interested in what he has to say, but sometimes
he gives in addition a practical justification for his study, as in Book 8:
The science of mechanics, my dear Hermodorus, has many impor-
tant uses in practical life, and is held by philosophers to be worthy
of the highest esteem, and is zealously studied by mathematicians,
because it takes almost first place in dealing with the nature of the
material elements of the universe. [Thomas, 1941, p. 615]As a commentator, Pappus was highly original, and the later commentators
Theon of Alexandria (late fourth century) and his daughter Hypatia (ca. 370-
415) produced respectable work, including a standard edition of Euclid's Elements.
Several of Theon's commentaries still exist, but nothing authored by Hypatia has
been preserved, unless the books of Diophantus mentioned above were written by
her. Very little of value can be found in Greek mathematics after the fourth century.
As Gow (1884, P- 308) says:The Collection of Pappus is not cited by any of his successors, and
none of them attempted to make the slightest use of the proofs
and aperQus in which the book abounds... His work is only the