Piattaforma Kiro - Didattica Curriculare 3+2 e Lauree Magistrali Ciclo Unico

Program of the course

1) Introduction, the sources for the history of Ancient and Greek Mathematics.

2)Egyptian Mathematics

3)Babylonian Mathematics

4)The dawn of Greek speculation. Eupalinos, Hecateus, Thales and the Ionians

5)The Pythagoreans. Arithmetic, Music, Geometry and Application of Areas.

7)Hippokrates Theodorus, Theetetus and the problem of Irrationals

8) Parmenides, Zeno and Democritus, the problem of Motion and Infinitesimals

9) The Mathematics of Platos Academy

10) Eudoxus, Astronomy and Theory of Proportions. 

11) Mathematics and Metaphysics in Aristoteles

12)Alexandrinian Mathematics and Science. Euclids elements 

14)Archimedes

15) Apollonius and Diophantus

16) The transmission of Greek Mathematics to the Arabs. A sketch of Arabic Mathematics.

A short and incomplete bibliography

General texts.

The textbook will be:

Heath, Thomas Little. A history of Greek mathematics. Vol. 1-2. Clarendon, 1921.

The passages we will comment are found in:

Thomas, Ivor. Greek Mathematical Works: Volume I, Thales to Euclid.(Loeb Classical Library No. 335). 1939. Thomas, Ivor. "Selections illustrating the history of Greek mathematics. Vol. II. From Aristarchus to Pappus, volume2,Loeb Classical Library.

Other useful works are:

Becker, Oskar. Das mathematische Denken der Antike. No. 3. Vandenhoeck & Ruprecht, 1966.
Youschkevitch, Adolf-P. "Les Mathématiques Arabes: Viiie-Xve

Siècles." (1976).

Rashed, Roshdi. Encyclopedia of the history of Arabic science. Routledge, 2002.
Netz, Reviel. The shaping of deduction in Greek mathematics: A study in cognitive history. Vol. 51. Cambridge University Press, 2003.

Christianidis, Jean, ed. Classics in the history of Greek mathematics. Vol. 240. Springer Science & Business Media, 2004.

On special problems
( a star * denotes particularly recommended references)

Egyptian, Babylonian

* Neugebauer, Otto. "The exact sciences in antiquity."; Providence, Rhode Island: Brown University Press (1957)(1957).

*Neugebauer, Otto. Mathematische Keilschrift-Texte: mathematical cuneiform texts. Springer-Verlag, 2013.

Vogel, Kurt. Vorgriechische Mathematik. Vol. 2. H.

Schroedel, 1958.

*Høyrup, Jens. Lengths, widths, surfaces: A portrait of old Babylonian algebra and its kin. Springer Science & Business Media, 2013.

Pythagoreans

Burkert, Burkert, Walter. Lore and science in ancient Pythagoreanism. Harvard University Press, 1972.
Zhmud, Zhmud, Leonid J. "Wissenschaft, Philosophie Und Religion Im Frühen Pythagoreismus/Dc Leonid

Zhmud." (1997).

Huffman, Carl A., ed. A History of Pythagoreanism. Cambridge University Press, 2014.

Plato

Stenzel, Julius. "Zur Theorie des logos bei Aristoteles."Quellen und Studien zur Geschichte der Mathematik. Springer Berlin Heidelberg, 1926. 34-66.

Toeplitz, Otto. "Das Verhältnis von Mathematik und ideenlehre bei Plato." Quellen und Studien zur Geschichte der Mathematik. Springer Berlin Heidelberg, 1926. 3-33.

Brumbaugh, Robert Sherrick. "Plato's mathematical imagination." (1954).

Frajese, Attilio. Platone e la matematica nel mondo antico. Vol. 4. Editrice studium, 1963.
*Fowler, Fowler, The mathematics of Plató s academy: a new reconstruction. 1999.

Aristoteles

*Cattanei, Elisabetta. "Enti matematici e metafisica."

Platone, l'Accademia e Aristotele a confronto, Milano

(1996).

Annas, Julia. Aristotle's Metaphysics, books M and N. Vol. 18. Vita e Pensiero, 1992.

Heath, Thomas. Mathematics in Aristotle. Routledge, 2015.

Irrationals and infinitesimals

Fritz, Kurt V. "Platon, Theaetet und die antike Mathematik." Philologus 87.2 (1932): 136-178.

S. LURIA, Die Infinitesimaltheorie der antiken Atomisten (1932, Quelle und Studien)

*von Fritz, Kurt. "The discovery of incommensurability by Hippasus of Metapontum." Annals of mathematics (1945): 242-264

J. MAU, Zum Problem des Infinitesimalen bei den antiken Atomisten (1954). *von Fritz, Kurt. "Die APXAI in der griechischen Mathematik." Archiv für Begriffsgeschichte 1 (1955): 13-103.

*Burnyeat, Myles F. "The philosophical sense of Theaetetus' mathematics." Isis 69.4 (1978): 489-513.

*Høyrup, Jens. "Dýnamis, the Babylonians, and Theaetetus 147c7–148d7." Historia Mathematica 17.3 (1990): 201-222.

*Fowler, David H. "An invitation to read Book X of Euclid's Elements." Historia Mathematica 19.3 (1992): 233-264.

M. WHITE, The Continuous and the Discrete (1992),

Knorr, Wilbur Richard. The evolution of the Euclidean elements: a study of the theory of incommensurable magnitudes and its significance for early Greek geometry. Vol. 15. Springer Science & Business Media, 2012.

On Eudoxus

*Becker, Oskar. "Eudoxos—Studien I. Eine Voreudoxische Proportionenlehre und Ihre Spuren bei Aristoteles und Euklid." Classics in the History of Greek Mathematics. Springer Netherlands, 2004. 191-209.

*Becker, O. "Eudoxos-Studien II: Warum haben die Griechen die Existenz der 4." Proportionalen angenommen (1932): 369-87.

*Becker, O. "Spuren eines Stetigkeitsaxioms in der Art des Dedekindschen zur Zeit des Eudoxos." Eudoxos-Studien 5 (1936): 236-244.
*Becker, Oskar. "Eudoxos-Studien IV. Das Prinzip des Ausgeschlossenen Dritten in der Griechischen Mathematik." (1937).

*Becker, Oskar. "Eudoxos-Studien V: Die eudoxische Lehre von den Ideen und den Farben." Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik (1936): 389-410.

Waschkies, Hans-Joachim. Von Eudoxos zu Aristoteles:

das Fortwirken der Eudoxischen Proportionentheorie in der Aristotelischen Lehre vom Kontinuum. Vol. 8. John Benjamins Publishing, 1977.

Gardies, Jean-Louis. L'héritage épistémologique d'Eudoxe de Cnide: un essai de reconstitution. Vrin, 1988.

Special problems

Knorr, Wilbur Richard. The ancient tradition of geometric problems. Courier Corporation, 1986.

Apart from the authors quoted above, you can find very interesting recent work in the papers of Saito, Vitrac, Acerbi.