Reviel Netz

A long-standing puzzle in the interpretation of Epicurean philosophy of science is the contradiction between Epicurus’ wholesale rejection of mathematical science, and the evidence for later Epicurean mathematicians. This chapter resolves the puzzle in a simple way: there were no Epicurean mathematicians and the evidence for their existence is spurious. A reconsideration of the evidence for Zeno of Sidon as well as for Demetrius of Lacon shows that they likely argued not merely that mathematics did not refute Epicureanism but, in a much stronger vein, that Euclid’s Elements could not be made logically sound. The Epicurean interest in such an argument may be related to the adoption of Euclid’s Elements into the elementary school curriculum, sometime in the Hellenistic era. The evidence for other purported Epicurean mathematicians—Basilides, Protarchus, and Philonides—is much weaker than often thought, and should on balance be rejected. These observations have consequences for the chronology of Hellenistic science and philosophy but, more centrally, the chapter argues throughout for a more probabilistic approach in the study of ancient history.

Reviews in Common Knowledge generally seek to be more cool and edgy than their subjects, an impossibility in this case. Ording takes a mathematical statement and reaches it in ninety-nine different ways. This book is quite literally a page-turner: most of the arguments take the recto page, with comments on their verso. One keeps cycling back and forth between the mathematical inventiveness of the recto and the philosophical elegance of the verso. The ambition is huge—to construct a mathematical counterpart to Queneau's masterpiece Exercises de Style—and, remarkably, this ambition is fulfilled.It is interesting that Queneau's variations are much closer to each other than Ording's are. Queneau often feels free to provide, as a variation, the very same text with a fundamentally grammatical transformation (switching the order of the descriptions, changing their tenses, and so forth). Most of the time, Ording feels obliged to come up with a significantly different argument. Indeed, his fixed core is less constraining: instead of following the same narrative arc in different forms, he merely has to reach the same endpoint. Ording's book is rather like ninety-nine different jokes leading to the same punch line. To be clear: it is perfectly possible to produce the precise same narrative arc, in mathematics, via different forms. Switching the order is a normal way in which such exercises in mathematical style are actually produced (mathematicians do have to decide whether to write “P, therefore Q” or to write “Q, since P”). Evidently, Ording felt that producing many such purely grammatical and formal transformations would feel tedious, which is fair enough but is not precisely a contrast between mathematics and literature. Queneau's variations are, indeed, tedious; delightfully tedious; delightful in their tediousness. Joyce as a tasting menu. Some readers of modernist literature can take delight in a certain tediousness, but Ording has no illusions concerning the audience for mathematics, and, to make his own variations appealing, he had to make them much more interesting than Queneau's. The result is brilliant and should be read by anyone interested in mathematics, literature, and their many parallels and variations.

The ancient Greeks played a fundamental role in the history of mathematics and their ideas were reused and developed in subsequent periods all the way down to the scientific revolution and beyond. In this, the first complete history for a century. Reviel Netz offers a panoramic view of the rise and influence of Greek mathematics and its significance in world history. He explores the Near Eastern antecedents and the social and intellectual developments underlying the subject's beginnings in Greece in the fifth century BCE. He leads the reader through the proofs and arguments of key figures like Archytas, Euclid and Archimedes, and considers the totality of the Greek mathematical achievement which also includes, in addition to pure mathematics, such applied fields as optics, music, mechanics and, above all, astronomy. This is the story not only of a major historical development, but of some of the finest mathematics ever created.

ZusammenfassungDer Artikel stellt die Methodik zur Erforschung einer „Bibliosphäre“ vor, also der Gesamtheit der literarischen Dokumente einer bestimmten Kultur. In diesem Fall geht es um die Bibliosphäre der Antike, und hierbei insbesondere um deren wissenschaftlich-philosophischen Bereich. Es wird die Auffassung vertreten, dass wir die Inhalte von Werken durch ihre Position in der Bibliosphäre begreifen können. Der Gegensatz zwischen Mathematik und Literatur wird detailliert dargestellt und der Übergangscharakter der Medizin hervorgehoben.

Greek culture matters because its unique pluralistic debate shaped modern discourses. This ground-breaking book explains this feature by retelling the history of ancient literary culture through the lenses of canon, space and scale. It proceeds from the invention of the performative 'author' in the archaic symposium through the 'polis of letters' enabled by Athenian democracy and into the Hellenistic era, where one's space mattered and culture became bifurcated between Athens and Alexandria. This duality was reconfigured into an eclectic variety consumed by Roman patrons and predicated on scale, with about a thousand authors active at any given moment. As patronage dried up in the third century CE, scale collapsed and literary culture was reduced to the teaching of a narrower field of authors, paving the way for the Middle Ages. The result is a new history of ancient culture which is sociological, quantitative, and all-encompassing, cutting through eras and genres.

This article makes two claims. The first is that Archimedes’ On Floating Bodies included a punning reference, in its key diagrammatic figure AΠΟΛ: the precise purpose of the pun may not be recovered by us, but even so it remains a powerful example of the playful in Archimedes’ writing. The second is that Apollonius could have been Archimedes’ younger contemporary. The outcome could be that we find Archimedes addressing a playful, hidden message to Apollonius, providing us with a unique insight into the communication of Greek mathematics.

Ancient Greek mathematics developed the original feature of being deductive mathematics. This article attempts to give a explanation f or this achievement. The focus is on the use of a fixed system of linguistic formulae in Greek mathematical texts. It is shown that the structure of this system was especially adapted for the easy computation of operations of substitution on such formulae, that is, of replacing one element in a fixed formula by another, and it is further argued that such operations of substitution were the main logical tool required by Greek mathematical deduction. The conclusion explains why, assuming the validity of the description above, this historical level is the best explanatory level for the phenomenon of Greek mathematical deduction.

This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor Netz argues that Hellenistic mathematical writings adopt a narrative strategy based on surprise, a compositional form based on a mosaic of apparently unrelated elements, and a carnivalesque profusion of detail. He further investigates how such stylistic preferences derive from, and throw light on, the style of Hellenistic poetry. This important book will be welcomed by all scholars of Hellenistic civilization as well as historians of ancient science and Western mathematics.