When it comes to a figure like Thales of Miletus, historians face a conundrum. Thales is mentioned repeatedly in ancient sources, often as the founder of Greek mathematics. But the distance between the man and the sources is so large that we wonder whether we can trust them.
Proclus, for example, says about geometry that
Thales, who had travelled to Egypt, was the first to introduce this science into Greece. He made many discoveries himself and taught the principles for many others to his successors, Attacking some problems in a general way and others more empirically. (from Glenn R. Morrow’s translation of Proclus’s Commentary on the First Book of Euclid’s Elements, page 52).
Many scholars believe that Proclus is here quoting or transcribing an earlier account of the history of geometry written by Eudemus, a student of Aristotle.
And there is the problem: Proclus’s Commentary is presumably based on lectures he gave in Athens in the fifth century CE. Thales is said to have lived in the sixth century BCE, so there are at least one thousand years between the man and this report. If we believe that the source is Eudemus, the distance becomes smaller: Eudemus lived in the fourth century BCE, so some two hundred years after the time of Thales. But no copy of Eudemus has survived, so we can only know him through the lens of Proclus.
As far as we know, Thales left no writings, so if we want to understand his mathematical achievements were are entirely dependent on such reports, which we often receive second-hand, as in the case of Eudemus. The claim, however, is that those achievements are monumental: Thales, says Proclus, was the first to think seriously about geometry. He is supposed to have been the discoverer of some basic geometrical facts:
- The circle is bisected by its diameter.
- The angles at the base of an isosceles triangle are equal.
- Vertical and opposite angles are equal.
- The side-angle-side criterion for congruence of triangles.
What’s more, some of the sources say he “demonstrated” these things, making Thales the first person of whom it is claimed that he gave proofs of geometrical facts. We yearn to know more, but all our sources seem quite distant from the man himself.
Can we trust what Proclus says? He was as far from Thales as I am from, say, Gerbert of Aurillac (Pope Sylvester II). Worse, I have access to texts that I’m pretty sure were written by Gerbert, but Proclus had no writings from Thales. One option, then, is to decide that everything we are told about Thales should be treated as legend. He was remembered as the founder of Greek philosophy. He must have done important things, but we have no hard facts; given his reputation, it was natural to attribute to him the beginning of many things, including geometry and proof. But we can’t say any more than that.
The skeptical approach is attractive in some ways, but it can be overdone. (There is a famous parody of this kind of history called Did Napoleon Ever Exist?) Another option is to find all the sources that mention Thales, extract from each the small amount of information they provide, and try to integrate all those infinitesimal pieces to construct a portrait of the man. Any such portrait will, of course, be conjectural, but perhaps there are certain solid things we can say.
This book offers the preliminary spadework for that project: it collects every reference to Thales in ancient sources, ranging from hearsay (“Himerios says Alcaeus sang about Thales”) to actual text (the earliest is a passage from Herodotus). The latest reference included is from the 14th century. Texts are given both in the original (Greek, Latin, and Arabic) and in German translation.
This is, of course, a resource for scholars, the fruit of an amazing amount of work. The compiler deserves our thanks.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College and Editor of MAA Reviews.