Overview: The Importance
of the Palimpsest to the Study of Archimedes
By Reviel Netz of Stanford University

In discussing the importance of the Palimpsest for our knowledge of Archimedes, care should be taken to distinguish the significance of what Heiberg read in 1906 (call this The 1906 Discovery) from that of the further readings we make now (call this The 1998 Discovery).

For both discoveries, one is tempted to say that it is difficult to exaggerate their importance – only that their importance is often exaggerated. Some reports on the web suggest that nothing was known of Archimedes prior to 1906, or that entire treatises came to light in 1998. The reality is no less spectacular, but much more complicated. Here are the major facts.

First, we did possess the bulk of Archimedes' writings even prior to the 1906 Discovery, based mostly on a group of Renaissance manuscripts, all of them copied from a single Byzantine manuscript known as The Valla Codex, or Codex A. (The Valla Codex itself disappeared in the 16th century). Another important source was a Latin translation made from another Byzantine manuscript known as the Codex Mechanicorum, or Codex B. (This was lost probably in the 14th century).

Still, The 1906 Discovery was a major event, for several reasons. First, note that Codices A and B overlapped for a single work at most. The Palimpsest, on the other hand, overlaps with codices A and B for several works: together with Codex A, it has a text of Spiral Lines, Sphere and Cylinder and Measurement of the Circle; together with Codex B, it has a text of Floating Bodies. While it is of course especially exciting to discover totally fresh works that are unattested elsewhere, there is great value in having more than a single source for a given work: by the comparison between the two copies, our reconstruction of the original text can be made more precise. Thus The 1906 Discovery substantially furthered the precise establishment of the original text of Archimedes. Further, The Palimpsest did contain fresh, unattested works: the Method, as well as (in fragmentary form) the Stomachion. Indeed, many think of the Method as Archimedes' most interesting work. A special romantic aspect of this discovery lies in Archimedes' statement (which however should be taken with a grain of salt) that the Method contains what was, in some sense, his method of discovery. In other words, The 1906 Discovery appeared to provide a glimpse into the hidden process leading to Archimedes' Eureka moments. Finally, while the extant Latin translation of Floating Bodies is very precise, we could never know that this was indeed the case prior to the discovery of The Archimedes Palimpsest. The Archimedes Palimpsest thus settled the text of Floating Bodies, and it is only thanks to The 1906 Discovery that we can have the original formulation, in the Greek, of this treatise by Archimedes.

The 1998 Discovery is important for at least five reasons.

• First, because it is there. To do any work on an ancient author, one needs to know that all the evidence is available. The state of affairs following the disappearance of the Palimpsest in the 20th century was especially uncomfortable: we knew that a major source of evidence was (proably) extant, we knew that it was edited, partly – and we knew that it was no longer accessible. And so, for every statement one made concerning Archimedes, this worry returned: who knows, perhaps a close reading of the relevant passage of the Palimpsest could refute us? This state of affairs impeded all study of Archimedes and so of ancient science in general.
• Second, we now find that there are many corrections – numbering in the hundreds, if not thousands - to the text as printed by Heiberg. Perhaps the majority of these are small errors, undetected by Heiberg, made by the Byzantine scribe. These, then, do not change the text of Archimedes himself. In a good number of cases, however, such corrections add detail to the text of Archimedes. Sometimes such details are of great historical value (To take a single example: in Heiberg's text Eudoxus was the first to "discover" a certain proof; we know now the text has Eudoxus as the first to "publish" it). All of those details are important for our understanding of the mind of Archimedes at work.
• Third, while Heiberg had full access to the diagrams in the Palimpsest, he did not comment on them or publish them. Had it not been for The 1998 Discovery, then, the diagrams would have been simply lost. This is of special significance, as recent research has shown the importance of diagrams to science in general and to Greek mathematics in particular. The rediscovery of the diagrams in The Archimedes Palimpsest is probably the most important single contribution The 1998 Discovery makes to our knowledge of Archimedes. (See: The Diagrams as Floating Bodies).
• Fourth, the text of the Method was to a large extent established by Heiberg. This achievement, given what we now know of his task, is truly incredible. Even so, certain gaps were left in his text, especially where Archimedes' own thought was especially original and therefore unpredictable. One of these gaps was found to contain a use, by Archimedes, of actual infinity. This passage is unique in ancient mathematics, and surely counts as one of the most original and important passages in the entire corpus of Archimedes. (See: Methods of Infinity).
• Fifth, Heiberg's reading of the fragment of the Stomachion was so fragmentary that no conclusions could be made concerning its content. Recent and better readings, together with more recent developments in the scholarship of Greek mathematics, allow us now to provide a guess concerning the nature of the Stomachion. Possibly, this was a treatise in combinatorics – the first written, ever. (See: How Many Ways can you have a Stomach Ache?)

All in all, The 1998 Discovery is the most important event in the study of ancient science since – well, since The 1906 Discovery.