Impacts of a Unique Course on the History of Mathematics in the Islamic World - What I Learned and Impact on My Scholarship

I started learning about the material for my History of Mathematics in the Islamic World course from scratch. I was truly fascinated but also deeply disappointed by what I learned. I quickly realized that, despite new discoveries in recent decades, the research in the field is highly incomplete. This was stated by virtually every expert in the subject, most of whom are western researchers. (See the Note below for quotations on this topic from experts in the field of Islamic mathematics.) Worse still, there are many widespread misconceptions and exaggerations and much simply false information on the subject. This is the case not only in the west but also in the Islamic world as well. This unfortunate state of affairs can be largely attributed to what Saliba called “The Classical Narrative.” As a person who was born and raised in the Muslim majority country of Turkey and spent about half of his life in the U.S., Saliba’s description of the classical narrative resonated strongly with me as I witnessed it in so many different ways and places; from my home country to the local school district in rural Ohio, to textbooks on history of mathematics or science.

The details of the classical narrative can be found in Saliba’s Islamic Science and the Making of the European Renaissance [22], but in essence it is a certain way of describing the nature of scientific activities in the Islamic civilization which is based not so much on evidence or documentation, but rather on some preconceived ideological assumptions. It belittles the contributions to science from the medieval Islamic civilization, and views the preservation of the ancient Greek scientific heritage through translations as the main contribution of the Islamic civilization. Thus, according to this view, the role of the Islamic civilization was to serve essentially as a refrigerator for Greek ideas. It downplays or overlooks many fundamental and original contributions to mathematics and science from the Islamic civilization, and its influence on Renaissance Europe. For example, connections between Islamic scholars such as Nasir al-Din al-Tūsī (1201-1274) and ʿAlāʾ al‐Dīn ʿAlī ibn Ibrāhīm ibn al‐Shāṭir (c. 1305-1375) and Renaissance scholars such as Nicolaus Copernicus (1473-1543) are largely unknown ([20], [7]).

As a person who grew up in Turkey, I can attest that the classical narrative seems to be widespread in the Islamic world as well. As a result, the view that modern science is a western phenomenon [18] with ancient Greek origins and a revival in Renaissance Europe is common. Few people know about the significant and fundamental original contributions to science from the Islamic civilization. On the other extreme of the spectrum, there are people who have heard about some of the Islamic contributions to science, but they lack accurate knowledge and tend to exaggerate these contributions. One common misconception of this sort is the idea that Muslims first invented zero.  

To be fair to the general public, even the researchers missed some of the fundamental facts in the field. For example, the invention of decimal fractions had been incorrectly attributed to Simon Stevin for a long time [15], and the connections between Copernicus and earlier Islamic scholars were not known until the second half of the 20th century ([20], [7]). Research in more recent decades has provided a wealth of outcomes that challenge, contradict, or disprove the classical narrative, but it takes more than articles in specialized academic journals to remedy the damage caused by this narrative. For example, after studying the work of Copernicus and earlier Islamic scholars closely, Noel Swerdlow and Otto Neugebauer came to the conclusion in 1984 that “[i]n a very real sense, Copernicus can be looked upon as, if not the last, surely the most noted follower of the Maragha School” [27, p. 295]. This is a vastly different assessment than the one the classical narrative proposes.

To return to another example, although researchers realized in the mid 20th century that decimal fractions were invented and systematically treated many centuries before Stevin (1548-1620) in the Islamic world ([21], [15]), a popular book published in the 21st century still claims that Stevin was the first inventor [6]. A Nobel Laureate repeats this false claim in the foreword (page xiii):

The decimal system is so familiar to us that one might forget that it actually had to be invented by someone. This someone also had to find out how to add, subtract, multiply and divide such numbers. His name is Simon Stevin, ….

Therefore, there is a need to disseminate the results of established research to the general (educated) public. This is in addition to the great need to study the vast amount of original scientific material from the Islamic world that has not yet been examined by modern scholars. Expert after expert acknowledges that the research in this field is highly incomplete. (See the Note for details.) 

It is encouraging that a considerable amount of research has been done in the field of Islamic mathematics in recent decades. For example, survey articles by Berggren [4] and Glen Van Brummelen [29] give a summary of recent research through 2011. Still, much research remains to be done (again, see the testimonials in the Note below). Also, as noted above, there is still a large gap between what specialists know and what the (educated) general public knows that needs to be closed. The classical narrative is so widespread and has been around for so long that it will take time and effort to disseminate research findings in the field and change perceptions. This means it is important that contributions from the Islamic civilization be mentioned by those in the know when the history of certain topics in mathematics is discussed or taught. For example, a recent article in Convergence [5] that focuses on Stevin's work as a tool for helping future teachers understand multiplication of decimal fractions seems to me to have missed an opportunity to educate the larger community about the development of decimal fractions by Islamic mathematicians. One wishes the author had noted the highly relevant facts that Abu'l Hasan al-Uqlīdisī wrote about decimal fractions in around 952 in the city of Damascus [21] and Jamshīd al-Kāshī, a leading mathematician and astronomer at the observatory in Samarkand, presented a systematic treatment of decimal fractions in the year 1427 ([2], [3], [15]).

The History of Mathematics in the Islamic World course is an attempt to fill the gap between what academic researchers have discovered and what the educated public knows. The purpose of the course is not to promote the achievements of a particular culture. It is about understanding the history of mathematics better. It is true that we focus on the Islamic world; this is because it is an area that has been long neglected and misconceptions have caused a lot of damage to our understanding of the history of science. Moreover, there have been interesting and exciting discoveries by modern historians of science that are not yet widely known among the educated public. Without understanding what happened in the Islamic world, one really does not understand European history, or the history of mathematics more generally. As Saliba stated in Islamic Science and the Making of the European Renaissance ([22], p. ix), “I must quickly caution those readers [readers who feel a sense of kinship with the Islamic civilization] not to read this book as an expression of greatness of the Islamic scientific tradition ….” The goal instead is to understand global history of science better by studying history of Islamic science and disabuse ourselves of common misconceptions.

Given this state of affairs and my interest in the subject, I felt as if I needed to make a contribution. For this purpose, being able to read original documents, hence a reading knowledge of classical Arabic, was necessary. I spent a considerable amount of time studying Arabic, taking Arabic courses at Kenyon and attending a summer language program in Jordan. Then I started a major translation project in collaboration with a colleague from another institution in Ohio. We are translating from Arabic to English Al-Kāshī’s Miftāh Al-Hisāb, one of the most important mathematics books of the medieval Islamic civilization. Berggren described it as the “crowning achievement of Islamic arithmetic” ([3], p. 22). We have made significant progress in the translation project but there is still a long way to go. We published our first article related to the translation project in 2015 in Archive for History of Exact Sciences [1]. My work in studying Arabic and starting the translation project has been supported by two grants from the Great Lakes Colleges Association (GLCA) New Directions Initiative. As a result, a totally new area of research and teaching has been added to my professional life. Before talking to my colleague at Kenyon College who proposed the idea of the new course, I had no plans or intentions to start working in this field. I consider this experience to be a good example of the commitment to life-long learning and broad education that we would like to promote for our students, particularly at liberal arts colleges.

Note: Experts agree that much work remains to be done on the history of Islamic mathematics. Testimonials from some of these researchers follow.

I have not attempted to write "The History of Mathematics in Medieval Islam". Such a book could not be written yet, for so much material remains unstudied that we do not know enough of the whole story. – J. L. Berggren, in Episodes in the Mathematics of Medieval Islam ([2], page viii)

Clearly the field still offers an abundance of material for further investigation, and there is much work yet to be done. – J. L. Berggren ([4], page 91)

A complete history of mathematics of medieval Islam cannot yet be written, since so many of these Arabic manuscripts lie unstudied and even unread in libraries throughout the world. The situation has been improving recently as more and more texts are being edited and translated, but political difficulties continue to block access to many important collections. Still, the general outline of mathematics in Islam is known. In particular, Islamic mathematicians fully developed the decimal place value number system to include decimal fractions, systematized the study of algebra and began to consider the relationship between algebra and geometry, brought the rules of combinatorics from India and reworked them into an abstract system, studied and made advances on the major Greek geometrical treatises of Euclid, Archimedes, and Apollonius, and made significant improvements in plane and spherical trigonometry. – V. Katz, in A History of Mathematics: An Introduction ([11], page 267)

The historian of the Islamic exact sciences is frequently confronted with an embarras de richesse – hundreds of manuscript sources which have never been studied in modern times. – E. S. Kennedy, "Islamic Mathematical Geography," in Studies in the Islamic Exact Sciences (1983), page 18.

Today, even in the Islamic World, their activities and achievements have been completely forgotten …. Virtually all of the materials presented in this book have never been researched before in modern times. – David A. King, in In Synchrony with the Heavens: Studies in Astronomical Timekeeping and Instrumentation in Medieval Islamic Civilization (2004), page ix