40 A History ofMathematics
Although he has been criticized since for the way in which he used his often unreliable sources,
Tannéry was on the whole careful and many of his successors have been less so. Writing before
the Babylonian and Egyptian contributions had come to light, he saw the Greeks as the earliest
known mathematicians, and as such particularly important. But even today, the importance, and
the difficulties of source material, remain much the same.
The works of Euclid and his successors have been ‘classics’ for three major civilizations—their
own, the medieval Islamic, and the modern European. They have the advantage of being readable
(in a language which is related to a modern European language), often accessible in libraries
and now, at least in extracts, on the Internet, and clearly central to any history of mathematics;
whatever reservations one may have about Eurocentrism, and the role of the Greeks as overvalued
‘Europeans’, their methods and discoveries have had a decisive influence. However, as Tannéry
pointed out, their study needs supplementing to give us a ‘history’, and the construction of such
a history raises serious questions of method and approach.
In the first place, Greek mathematics is supposed to have started in the early sixth centurybce
At this time, the Greek world consisted of what is now Greece, western Turkey, and a few colonies,
particularly Sicily. However, there are no surviving mathematical texts earlier than the discussions
in Plato’s dialogues (say about 380bce) and no substantial writings before those of Euclid, about
70 years later. By Euclid’s time, the Greek world had changed completely as a result of Alexander the
Great’s conquests, and included what we now call the Middle East; and the centre of learning had
shifted from Athens to Alexandria in Egypt. While there are a number of substantial mathematical
texts from Euclid onwards (see table given below), there are still major gaps in the record before
it comes to an end, about 600ceSome works said to have been written are lost, and many
well-known mathematicians have no surviving works, known or not. Here is a list, with dates, of
the main ‘important’ Greek mathematicians and one rather arbitrarily chosen memorable work for
each, where known. Euclid, Archimedes, Ptolemy, and others wrote a number of works, some lost,
some not; the table is simply there as a rough guide. An entry in italics means that the work(s) have
not survived.
Mathematician Works Rough DateThales None known 480 bce
Pythagoras None known 500 bce
Democritus None known 450 bce
Hippocrates Elements 420 bce
Plato Dialogues 380 bce
Eudoxus Phaenomena 350 bce
Euclid Elements 310 bce
Archimedes Sphere and cylinder 240 bce
Apollonius Conics 210 bce
Hipparchus Star catalogue 150 bce
Heron Metrics 50 ce
Ptolemy Syntaxis (‘almagest’) 150 ce
Pappus Collection 200 ceSecond, as Tannéry recognized, our sources for most of what happened are of two kinds.
The first, of course, is the works themselves; the second is descriptive material about the works