The Method
The most extraordinary discovery gained through the Palimpsest is the Method - because this is the most amazing treatise of all the amazing works of Archimedes. It will not be an exaggeration to say that, even now, more than ninety years after its original discovery, scholars and mathematicians still can not quite explain what Archimedes did in the Method - or how he managed to make it such a mathematical success.
There are two main features to the Method, each of which, on its own, is an astonishing breakthrough.
Archimedes combines in this work pure mathematics and physical considerations. By putting segments of geometrical objects on a balance, Archimedes manages to measure the area and volume of the geometrical objects. In other words, geometrical discoveries are made by a physical thought-experiment.
Archimedes is able to perform infinite sums: he takes a sphere, for instance, and calculates its volume as the infinite sum of the circles from which it is made. But how can you add up infinitely many objects, and still come up with a finite sum? This was Archimedes' breakthrough, comparable to the modern integral calculus.
Both breakthroughs are essential features of modern science. Modern science is based on the discovery that mathematics and physics go hand in hand; and its prime tool is the differential and integral calculus, dealing with infinite sums and divisions. The Method can be truly said to have been two thousand years ahead of its time.
Comments by DR. DEVIEL NETZ
