Abstract:
The Archimedes Palimpsest, otherwise known as Codex C, contains two new treatises of the
great mathematician and mechanical engineer, Archimedes of Syracuse. The first treatise, The Method
of Mechanical Theorems, was read in part by J.L. Heiburg in 1906, but its critically important
proposition 14 was first read in the last decade using modern imaging techniques. Proposition 14
indicates that Archimedes knew certain principles of infinite summation, calculated with actual
infinity, and foresaw modern Set Theory. These are critical concepts to the development of calculus
and advanced mathematics, and they also undermine the nature of what historians of science have
long believed of ancient Greek mathematics. The second treatise found in the palimpsest is the
Stomachion in which Archimedes relies on a 14 piece tangram puzzle to perform pure calculations and
use combinatorics. The content of these two treatises create a new and more developed role for
Archimedes within the history of science as they show him to be both the father of calculus and the
father of combinatorics. This paper assesses the content of these treatises, their importance within
the history of science, and how they alter our perception of Archimedes.
