The Origin of Mathematics 16: The Origin of the Elements

Abstract

Heiberg, the modern editor of the Greek original of the Elements and the most eminent Euclid scholar of his time, thought in 1904 that it was nearly impossible to reconstruct earlier versions of Greek mathematics from the Elements (Heiberg [1904], p. 4). Mathematical and stylistic analyses over the last 100 years have disproved Heiberg’s claim and revealed a great deal about the prehistory of this monumental compendium of Greek mathematics. Our present, fairly complete, picture of the different contributions of pre-Euclidean mathematicians to the Elements is to a large extent due to the detailed studies begun by Becker in the 1930s, and continued by Neuenschwander on the geometrical books and by Mueller on the Elements as a whole. Heath and the other translators of the Elements provide valuable commentaries, but they are primarily concerned with individual definitions, theorems, and proofs. The global picture emerges from the investigation of the mathematical architecture of the Elements in combination with the study of other ancient sources.