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Impacts of a Unique Course on the History of Mathematics in the Islamic World - Initial Challenges and the Design of the Course

Author(s): 
Nuh Aydin (Kenyon College)

Kenyon College is a small liberal arts college, so the course I designed, History of Mathematics in the Islamic World, needed to appeal to a general liberal arts audience. General History of Mathematics courses at the undergraduate level are common across colleges and universities in the U.S., but I have not seen an introductory history of mathematics course that focuses on the Islamic world. Finding suitable textbook(s) was a real challenge. Fortunately, I came across J. Lennart Berggren’s Episodes in the Mathematics of Medieval Islam [2] (suggested by experts) for the mathematics content of the course. I also chose George Saliba’s Islamic Science and the Making of the European Renaissance [22] for the history and social science aspects of the course. I usually spend one day discussing Bradley Steffens’ book, Ibn al-Haytham: First Scientist [25], written for a general audience with useful information for the students in the course.

Figure 1. Left: Cover of the book, Ibn al-Haytham: First Scientist, by Bradley Steffens. Right: Title page of a Latin translation of Ibn al-Haytham's (Alhazen's) Optics, published in Basel, Switzerland, in 1572 (courtesy of History of Science Collections, University of Oklahoma Libraries). A complete copy of this book can be viewed online courtesy of ETH-Bibliothek Zürich via e-rara: http://dx.doi.org/10.3931/e-rara-9817.


Abu Ali al-Hasan ibn al-Haytham (965-1040), commonly known as Alhazen in the west, is one of the giants of Islamic science. He is known as the father of optics; however, his main contribution to science was introducing the experimental method into scientific inquiry in a systematic way. His work in optics is connected to a well-known geometry problem known as Alhazen’s problem in the literature, as well as to ideas of integral calculus ([10], [17]).

I have taught the course, History of Mathematics in the Islamic World, a few times since Spring 2011. The audience has been overwhelmingly general liberal arts students with very few majors in mathematics or natural sciences. It fulfills my college’s quantitative reasoning requirement, and it contributes to the Islamic Civilization and Cultures program which was recently established at Kenyon. About 60-65% of the course is devoted to mathematical content from Berggren’s text [2], and the rest is history and social science content, mainly from Saliba's book [22] with some additional supplementary materials. A weekly outline of the material discussed in the course is as follows.

Week 1   Overview and Introduction. Lives and works of selected Islamic scholars: Al-Khwārizmī, Al-Biruni, Omar al-Khayyám, Al-Kāshī, Ibn al-Haytham
Weeks 2-3   Islamic Arithmetic (Berggren Chapter 2)
Reading and Class Notes Guide: Sections 2.3 & 2.4
Reading and Class Notes Guide: Section 2.7
Weeks 4-5   Geometrical Constructions in the Islamic World (Berggren Chapter 3)
Reading and Class Notes Guide: Section 3.4
Week 6   Midterm Exam I, Saliba Chapters 1 & 2
Saliba Ch. 1: The Islamic Scientific Tradition: Question of Beginnings I
Saliba Ch. 2: The Islamic Scientific Tradition: Question of Beginnings II
Week 7   Saliba Chapters 2 & 3
Saliba Ch. 3: Encounter with the Greek Scientific Tradition
Weeks 8-9   Algebra in Islam (Berggren Chapter 4)
Reading and Class Notes Guide: Section 4.4
Weeks 10-11   Trigonometry in Islam (Berggren Chapter 5)
Week 12   Midterm Exam II, Saliba Chapter 4: Islamic Astronomy Defines Itself: The Critical Innovations
Week 13   Saliba Chapters 5-7, selected additional readings
Saliba Ch. 5: Science between Philosophy and Religion: The Case of Astronomy
Saliba Ch. 6: Islamic Science and Renaissance Europe: The Copernican Connection
Reading and Class Notes Guide: Chapter 6
Saliba Ch. 7: Age of Decline: The Fecundity of Astronomical Thought
Week 14   Presentations of final projects

Mathematical content constitutes the larger part of the course (about 60-65%) and it is challenging for this audience. As an additional resource for the students, I created several video lessons on selected topics from Berggren’s text [2]. They are publicly available on the course website: http://www2.kenyon.edu/Depts/Math/Aydin/Teach/Fall14/128/index.html. An innovative element I introduced to the course is a community service component, which is described later in this article.

I often use handouts for daily class activities (sometimes supplemented by PowerPoint presentations) to help students organize their notes and identify major points in each section. A sample of a few of these handouts are included for download in the schedule above.

In lieu of a final exam, students do a final project in this course on a topic of their choice. Many potential ideas and resources are suggested, but students are free to choose a different topic, subject to the approval of the instructor. The most popular topic has been mathematics – and geometry in particular – in Islamic art and architecture. There are many aspects of this topic for students to explore, including:

  • constructions of Islamic geometric patterns,
  • Islamic influence on European architecture,
  • mathematics of mosques,
  • geometry of muqarnas, and
  • geometry of Kufic calligraphy.

Some other examples of topics students have chosen for their final projects include:

  • contributions of particular Islamic scholars to mathematics and sciences, including Ibn al-Haytham, Jamshid al-Kāshī, Omar Khayyám, and Thābit ibn Qurra,
  • the Alhazen problem,
  • cryptology in the Islamic world,
  • the Qibla problem,
  • astronomy in the Islamic world,
  • number systems and numerical approximations, and
  • mathematical geography and cartography.

The list of potential topics and resources is very large and it continually grows. The final project gives students the chance to explore a topic they are interested in but we did not have time to discuss in class, or go deeper into a topic that was briefly discussed in class.

More details about the course, including the course syllabus, actual daily calendar, homework and reading assignments, exam dates, links to publicly available video lessons, information and resources for the final project, and links for additional resources can be found on the course web site from Fall 2014: http://www2.kenyon.edu/Depts/Math/Aydin/Teach/Fall14/128/index.html

Once again, the textbooks I have used in my History of Mathematics in the Islamic World course thus far are:

  • J. Lennart Berggren’s Episodes in the Mathematics of Medieval Islam [2];
  • George Saliba’s Islamic Science and the Making of the European Renaissance [22]; and
  • Bradley Steffens’ Ibn al-Haytham: First Scientist [25].

In addition to the second edition of Berggren’s Episodes in the Mathematics of Medieval Islam, published in 2016 [3], there are a few other textbooks that could be used for a course on the History of Mathematics in the Islamic World. For instance, one could use selections from:

  • Victor Katz’s A History of Mathematics: An Introduction [11];
  • Katz’s and Karen Parshall’s Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century [12];
  • Katz’s Sourcebook in the Mathematics of Egypt, Mesopotamia, China, India, and Islam [13a], especially the chapter contributed by Berggren, “Mathematics in Medieval Islam,” pp. 515-675; and/or
  • Katz’s Sourcebook in the Mathematics of Medieval Europe and North Africa [13b], especially the chapter contributed by Berggren, “Mathematics in the Islamic World in Medieval Spain and North Africa,” pp. 381-547.

The Convergence article, "Combining Strands of Many Colors: Episodes from Medieval Islam for the Mathematics Classroom" [24], presents several modules on Islamic mathematics that would be very useful for instructors interested in incorporating this material into their courses.

Nuh Aydin (Kenyon College), "Impacts of a Unique Course on the History of Mathematics in the Islamic World - Initial Challenges and the Design of the Course," Convergence (July 2017)

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