Massachusetts Institute of Technology

Department of Mathematics

18.995 Cultural History of Mathematics

Fall 2009

Dr. Slava Gerovitch

Is mathematics a purely intellectual exercise isolated from social influences? Does the development of mathematics follow its inner logic, or is it subject to the pressures and biases of the time? Do mathematicians think differently if they live in different cultures? This discussion-based seminar will address these questions while exploring patterns of mathematical practice in different historical contexts: Greek antiquity, the Middle Ages, the Scientific Revolution, the Age of Enlightenment, the Romantic era, Victorian culture, and the tumultuous twentieth century. The students in the class will read and discuss short articles by professional historians. The readings link mathematical innovations with contemporary developments in politics, literature, philosophy, and theology. This seminar presents an opportunity to gain deep cultural understanding of some basic mathematical concepts and methods of reasoning.


Each week’s readings must be read prior to recitation section. Active participation in the discussions is expected.

Weekly Reading Response

A short reading response (1 page; roughly 300 words) must be submitted via the Stellar class site by 9 am every Monday. PDF format is preferred, but PS, DOC, and TXT are also allowed. A few tentative questions will be provided to stimulate your thoughts, but you are encouraged to raise your own questions.

Strategies for writing a good reading response:
* avoid generalities, be specific;
* define your personal stance towards issues raised in the readings;
* focus on the points where you disagree, or where you can push the argument further;
* cite examples from your personal experience or from other literature;
* ask provocative questions, even if you do not know the answers.

Your reading response will be made accessible online to other students in the class after the deadline. It may be part of discussion in class. Reading responses will be graded as Check+ / Check / Check–

All the responses must be submitted to complete the course.
By the instructor’s permission, graduate students may submit a 12-page final paper instead of the weekly responses.


Final grades will be based on:
Attendance (20%)
Participation in discussions (40%)
Weekly writing or Final paper (40%)


All required readings are available on the Stellar class site. The recommended readings are on reserve at MIT libraries. The main recommended textbook:

Ronald Calinger, A Contextual History of Mathematics to Euler (Upper Saddle River, NJ: Prentice Hall, 1999).

Primary sources (original writings by mathematicians) are not required, but if you wish to consult them, a collection of primary sources is also put on reserve:

Ronald Calinger, ed., Classics of Mathematics (Englewood Cliffs, NJ: Prentice Hall, 1994).

Topics and readings

09/14 (1) Introduction

09/21 (2) Greek Mathematics and the Idea of Proof

09/28 (3) Medieval Mathematics: Theology and Commerce

10/5 (4) Early Modern Mathematics as a Voyage of Exploration

10/13 Tues (5) Mathematics as Cultivation of Virtue in the Scientific Revolution

10/19 (6) The Scientific Revolution: The Mathematization of Nature?

10/26 (7) Mathematics as Rational Calculation in the Enlightenment

11/02 (8) Romantic Mathematics: Beauty, Rigor, and the Genius

11/09 (9) Oral and Written Cultures in Nineteenth-Century Mathematics

11/16 (10) Mathematics and the Arts: The Rise of Modernism

11/23 (11) Mathematics and Theology: Views of the Infinite

11/30 (12) Mathematics and Philosophy: Bourbaki and Structuralism

12/07 (13) Doing Mathematics on/with/by a Computer