Classics in the History of Greek Mathematics

• 1. The Beginnings of Greek Mathematics.- Die Entdeckung der Möglichkeit von Wissenchaft.- Wie ist die Mathematik zu einer deduktiven Wissenschaft geworden?.- On the early history of axiomatics. The interaction of mathematics and philosophy in Greek antiquity..- 2. Studies on Greek Geometry.- Construction as Existence Proof in Ancient Geometry.- Book II of Euclid’s Elements in the Light of the Theory of Conic Sections.- The Meno and the Mysteries of Mathematics.- 3. Studies on Proportion Theory and Incommensurability.- Exdoxos-Studien I: Eine voreudoxische Proportionenlehre und ihre Spuren bei Aristoteles und Euklid.- The Discovery of Incommensurability by Hippasus of Metapontum.- Y avait-il une crise des fondements des mathématiques dans l’antiquité?.- The Impact of Modern Mathematics on Ancient Mathematics.- 4. Studies on Greek Algebra.- Zur Berechnung der quadratischen Gleichungen bei den Babyloniern.- Lost Greek mathematical works in Arabic translation.- Diophantus’ methods of solution.- 5. Did the Greeks Have the Notion of Common Fraction? Did They Use it?.- Techniques of fractions in Ancient Egypt and Greece..- Logistic and fractions in early Greek mathematics: a new interpretation..- 6. Methodological Issues in the Historiography of Greek Mathematics.- On the Need to Rewrite the History of Greek Mathematics..- Defence of a ‘Shocking’ Point of View..- Who Betrayed Euclid? (Extract from a letter to the Editor).- History of Ancient Mathematics: Some Reflections on the State of the Art.

From the reviews: In Classics in the History of Greek Mathematics, Christianidis has provided a very useful collection of papers that encompass many of these changes. Here one can find Unguru's original papers (and the angry responses they elicited), discussions of the supposed "crisis of foundations", papers on the origin of Greek axiomatics, on geometry and "algebra". The papers, alas, are in their original languages (German, French, and English), but anglophone readers can be reassured that most of the articles are in English, especially the more recent ones. In any case, this is an excellent place to go to learn what the historians have been up to, and the give-and-take of debate makes it fascinating. The book is probably too expensive for non-fanatic individual readers, but it is definitely a "must buy" for libraries [Fernando Q. GouvA*a; posted to MAA Reviews 1/11/2006] "This is a tool for working historian ... because it offers a cross-section of the main historiographical currents that represents well the evolution of the field in the last decades. ... Essays are reproduced that date back more than 40 years, and written in French or German. This is a very important feature of the book, especially because a large portion of contemporary scholarship appears to resort almost exclusively to the most recent secondary literature and to contributions written in English." (Fabio Acerbi, Aestimatio, Issue 3, 2006)