Abstract

There are a number of ways in which Greek mathematics can be seen to be radically original. First, at the level of mathematical contents: many objects and results were first discovered by Greek mathematicians. Second, Greek mathematics was original at the level of logical form: it is arguable that no form of mathematics was ever axiomatic independently of the influence of Greek mathematics. Finally, third, Greek mathematics was original at the level of form, of presentation: Greek mathematics is written in its own specific, original style. This style may vary from author to author, as well as within the works of a single author, but it is still always recognizable as the Greek mathematical style. This style is characterized by the use of the lettered diagram, a specific technical terminology, and a system of short phrases. I believe this third aspect of the originality—the style—was responsible, indirectly, for the two other aspects of the originality. The style was a tool, with which Greek mathematicians were able to produce results of a given kind, and to produce them in a special, compelling way. This tool, I claim, emerged organically, and reflected the communication-situation in which Greek mathematics was conducted. For all this I have argued elsewhere.