Combining Strands of Many Colors: Episodes from Medieval Islam for the Mathematics Classroom - Background

For the past 40 or more years, factories in southeastern Michigan have attracted immigrant workers from Middle Eastern and other countries. As a result, this area now has the largest population of people of Arab background in the Western hemisphere (approximately 300,000). In my own classes at a community college in metropolitan Detroit, students of Arab descent constitute the largest distinct ethnic and cultural minority (9%), followed by those of Indian and Chinese heritage (7% and 3%, respectively). Detroit proper is overwhelmingly African-American. Such rich diversity heightens both the necessity and the opportunity to explore the global history of science and other human endeavors, a history in which knowledge has been interwoven from many cultural strands.

Unfortunately, the cultural horizons of a classroom don’t automatically expand just because there are students from diverse backgrounds. Despite the fact that immigrants have played a key role in driving American industrial and scientific enterprise, the scientific contributions made by non-Western peoples are scarcely acknowledged in our classrooms (Joseph 1987).

The presence and interests of my culturally diverse students prompted me to find ways to learn and to teach about the mathematical contributions of Muslim, Indian, Chinese, and other peoples. Arab mathematicians, in particular, have been dismissed as mere copyists:

The Arabs made no significant advance in mathematics. What they did was absorb Greek and Hindu mathematics, preserve it, and […] transmit it to Europe. (Kline 1972: 197)

Although few writers nowadays would state views as extreme as Kline’s, the same underlying approach is often still at work, albeit more subtly. For instance, in David Burton’s widely used textbook on the history of mathematics, most recently issued in 2007, the discussion of medieval Islamic (as well as Chinese) contributions is relegated to the chapter, “The Twilight of Greek Mathematics: Diophantus.”

Far from simply preserving and transmitting ancient knowledge, the Arab people tremendously enriched mathematics and other sciences. Medieval scholars broke whole new ground, especially in these subfields of mathematics:

• algorithms of arithmetic
• algebra and the theory of polynomials
• number theory
• combinatorics
• plane and solid geometry
• plane and spherical trigonometry.

Some of these breakthroughs were incorporated into European mathematics centuries ago, while others can and should be resuscitated for classroom use today.