Sidoli, Nathan Camillo
Fall, 2018
Office hours: Thursday, 4th and 5th

SILS, 11, 1416
[email protected]


I will put announcements about the class in this space. Please check here periodically as the term progresses.

Seminar on Matter and Information:
History of Mathematics (Spherics)

Course Description

Science studies covers a broad range of topics in the history, philosophy and sociology of the sciences wherever and whenever they have been practiced. Because of this scope, there is great diversity in the styles of scholarship practiced and the views about science put forward by scholars in the field. For these reasons, this seminar will be based around a particular theme each term.

The theme for this term will be a special topic in the history of mathematics — namely, spherics, a field that used spherical geometry to investigate issues such as the length of daylight and night-time, and the rising times of stars or arcs of the ecliptic.

We will begin by reading papers on the philosophy of the history of mathematics, introductions to ancient mathematics, mathematics education in the Greco-Roman world, Euclid’s geometry, ancient spherics, and then read as much as possible of the text of the Spherics of Theodosius. We will meet each week to discuss the readings.

Required Texts

  • Texts will be made available for download from this website, and from the class Dropbox folder.
  • Grading:

    Participation 50%
    Final paper 50%

    General Format

    The class meets once a week for a seminar discussion. Attendance and participation in class are mandatory and graded. Each week, we will discuss the text, and other topics of interest. Students are expected to do all the readings, participate actively in the discussions and to submit a final paper.

    Final Paper

    Academic paper, around 3,000 words.

    This term the writing project will be a history or philosophy paper. You should start thinking about your topic early and do a lot of reading. You should come up with your own idea for a final project that is based on the work we are studying. The best kind of project will be on a subject in which you are personally interested.

    The project will be done in three phases: (1) a topic proposal and preliminary bibliography, (2) an annotated bibliography (3) a final paper.

  • (1) Start thinking about possible topics right away. Once you have selected a topic, you should write up a short description of the story you will tell, which should be followed by a short bibliography (two or three items).
  • (2) You should begin to read your sources and take notes on them. Make a bibliographic list of at least ten sources, with a short blurb on each one.
  • (3) Based on all this reading, write up your account of the historical events.
  • Please also read the general guidelines for written assignments.

    Discussion Topics, Readings and Assignments

    Week 1: Oct 2

    General Introduction

  • No reading.
  • Week 2: Oct 9


  • Reading: Crowe, M., Ten misconceptions about mathematics and its history.
  • Week 3: Oct 16

    Ancient mathematics

  • Reading: Lloyd, G.E.R., What was mathematics in the ancient world? Greek and Chinese perspectives; Asper, M., The two cultures of mathematics in ancient Greece.
  • Week 4: Oct 23

    Mathematics education in the Greco-Roman world

  • Reading: Bernard, A., Proust, C., Ross, M., Mathematics education in antiquity (just pages 38–51); Sidoli, N., Mathematics education.
  • Week 5: Oct 30

    Euclid’s plane geometry

  • Reading: Artmann, B., Euclid: The Creation of Mathematics, chaps. 4, 7, and 9.
  • Supplementary reading: Books I, II, and III from Euclid’s Elements.
  • Week 6: Nov 6

    Euclid’s solid geometry

  • Reading: Artmann, B., Euclid: The Creation of Mathematics, chaps. 25–27.
  • Supplementary reading: Books XI, XII, and XIII from Euclid’s Elements.
  • Week 7: Nov 13

    Ancient spherics

  • Reading: Evans, J., The History and Practice of Ancient Astronomy, extracts on the celestial sphere; Berggren, J.L., The relation of Greek spherics to early Greek astronomy.
  • Week 8: Nov 20

    Theodosus’ Spherics, Introduction

  • Reading: Thomas, R., The definitions and theorems of the Spherics of Theodosios; Sidoli, N., Saito, K., The role of geometrical construction in Theodosius’ Spherics.
  • Supplementary Reading: Malpangotto, M., Graphical choices and geometrical thought in the transmission of Theodosius’ Spherics from Antiquity to the Renaissance.
  • Week 9: Nov 27

    Theodosus’ Spherics, I

  • Reading: TBA.
  • Conference Trip: Dec 4

    No Class

  • No Reading.
  • Week 10: Dec 11

    Theodosus’ Spherics, II

  • Reading: TBA.
  • Week 11: Dec 18 (Paper phase 1 due)

    Theodosus’ Spherics, III

  • Reading: TBA.
  • Holiday: Dec 25

    No Class

  • No Reading.
  • Holiday: Jan 1

    No Class

  • No Reading.
  • Week 12: Jan 8

    Theodosus’ Spherics, IV

  • Reading: TBA.
  • Week 13: Jan 15 (Paper phase 2 due)

    Theodosus’ Spherics, V

  • Reading: TBA.
  • Week 14: Jan 22

    Theodosus’ Spherics, VI

  • Reading: TBA.
  • Week 15: Jan 29 (Paper due)

    Theodosus’ Spherics, VII

  • Reading: TBA.