The Role of Religion in the Development of Mathematical Sciences in Medieval Islamic Civilization

by Nuh Aydin Published on: 18th January 2021

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The rise of Islamic Civilization was one of the major events in world history. An important aspect of the medieval Islamic Civilization was the development of a remarkable scientific tradition in a relatively short period of time. It was home to most advanced scientific production of its time for several centuries. There were many factors behind this development and the religion of Islam was one of the key factors. In this article, we examine how the Islamic faith and practice led to the development of sciences in general and mathematical sciences in particular in the medieval Islamic World.

Introduction

Only about a century after its birth, Islam spread a large region from Spain to the borders of India and China and a remarkable civilization developed. One aspect of this civilization was it became the center of learning, scholarship and scientific research in a relatively short period of time.  There are some differences among historians of science in assessing the role of medieval Islamic science in terms of its duration (the period often referred to as  “the golden age of Islamic science”), its importance in the context of the development of the modern science, and its influence on other cultures and civilizations, particularly the European Renaissance (compare for example Arnold & Alfred 1931 and Saliba 2007). Still, there is a general agreement that the Islamic Civilization was home to the most advanced science for a few centuries (whether it was from 9th to 12th century or from 9th to the 16th  or 17th century). See (Saliba, 2007) for a detailed discussion of the two narratives on the history and importance of the Islamic science.

We would like to clarify the terms “Islamic science” and “Islamic Civilization”.  We will be using the terms “Islamic Civilization” and “medieval Islamic Civilization” in a very broad sense. We are particularly referring to the medieval Islamic civilization for which the time period extends approximately from the late 7th century to the 16th century (inclusive). Geographically, it spans a large region –from Spain in the west to China and India in the east. Therefore, it encompasses much diversity in terms of languages, ethnicity, and cultures. It also contains many different political powers and organizations (such as Umayyads, Abbasids, Fatimids, al-Andalus, Seljuks, Ottomans,  Safavids, and others).  It was ethnically and religiously highly diverse in which individuals from many different backgrounds contributed to scientific knowledge and progress, being a Muslim was not a prerequisite for this contribution. Arabic was the language of science during this time period, and it has been the language of religious studies. We use the term in a very broad sense and in no way do we imply a monolithic culture or civilization.

By the term “Islamic science” we refer to scientific works produced in the Islamic civilization as explained above. The persons who participated in the production of this science were not all Muslims, though most of them were, and certainly they were not all Arabs, though Arabic was the language used most of the time. In particular, this term does not refer to religious sciences in Islam such as tafsir, hadith, fiqh etc.

As explained in (Saliba 2007, Chapter 2) the rapid rise of scientific activities in the Islamic civilization was the consequence of many factors such as political, economical, social and religious. It cannot be explained by a single factor alone.  The purpose of this article is to examine one of these factors in the rise of sciences, particularly mathematical sciences, in the early Islamic civilization: the role of the religion of Islam. We can see that there are two main ways in which Islam made a direct impact on the scientific activities

  1. general encouragement of Islam on reasoning, acquiring knowledge, and studying nature
  2. fulfilling certain religious obligations requires mathematical calculations.

In the rest of the article, we will explain and expand these two points.

Encouragement of Islamic Faith for Scientific Inquiry

The religion of Islam places a great deal of emphasis on rational thinking, reasoning, learning, seeking knowledge, and studying nature as a sign of God’s creation and power. We can see an abundance of references to these points in the primary source of religion for Islam: The Quran. The Quran strongly encourages human beings to use their intellectual capacity and contemplate all sorts of phenomena in the natural world, everything from the movements of the sun and the moon to the benefits of honey. Similarly, sayings of the prophet Muhammed, called hadith the Islamic tradition which is the second source of religion in Islam, contain many examples that emphasize the value of seeking knowledge. We give a few examples from the verses of the Quran and hadith on the topic.

Verses from the Quran

The very first verses of the Quran that were revealed to the Prophet Muhammad had to do with learning and teaching.

Read! In the name of thy Lord who created the human from a clot. Read: And thy Lord is the Most Generous Who taught by the pen, taught human that which he knew not. (Quran, 96:1-5)

It is really interesting and significant to note that the Arabic word for the term verse (آية plural  آيا ت ) refers to both the verses of the Quran and the signs God placed in the universe for human beings to think about. Therefore, the command “read” can be understood as reading the verses of the Quran as well as reading the signs in the universe. Both of these types of reading require an intellectual effort. The following verse makes this point.

“Thus do We explain the signs for a people who use reason” (Quran, 30:28)

The Arabic language is based on the root system. Almost all Arabic words (with few exceptions) have a 3-letter root from which a large number of related words can be derived. The essential meaning from the root permeates all of the words derived from it. There are 49 verses in the Quran (corpus.quran.com) that contain words derived from the root  ع ق ل (a’- qa-la) which means to reason, to use one’s intellect, to understand, and to comprehend.  Below are three examples from these verses.

“Thus does Allah make clear to you His verses that you might use reason.”(Quran, 2:242)

 

It is He who created you from dust, then from a sperm-drop, then from a clinging clot; then He brings you out as a child; then [He develops you] that you reach your [time of] maturity, then [further] that you become elders. And among you is he who is taken in death before [that], so that you reach a specified term; and perhaps you will use reason.”(Quran, 40:67)

 

“Know that Allah gives life to the earth after its lifelessness. We have made clear to you the signs; perhaps you will understand. ” (Quran, 57:17)

The root ف ك ر  (fa-ka-ra)  contains the meaning of reflect, ponder and contemplate.  There are 18 verses in the Quran that contain words from this root. Below are a couple of examples:

“Say, [O Muhammad], “I do not tell you that I have the depositories [containing the provision] of Allah or that I know the unseen, nor do I tell you that I am an angel. I only follow what is revealed to me.” Say, “Is the blind equivalent to the seeing? Do you, then, not reflect?”(Quran, 6:50)

 

 “Then eat from all the fruits and follow the ways of your Lord laid down [for you].” There emerges from their bellies a drink, varying in colors, in which there is healing for people. Indeed in that is a sign for a people who ponder.” (Quran, 16:69)

In addition to the two examples above, there are many other words that contain the meaning of “knowing”, “understanding”, “informing”, “seeing”,  “observing”, “considering” “judging”, “deeming appropriate” “questioning”, “inquiring”, “proving”, “justifying”, “clarifying”, “explaining”, “making known”, “determining” and “measuring”  For example, words derived from the root  ع ل م (a’-li-ma:  know) appear in the Quran 854 times, from ر ا ي (ra-a-ya: see, perceive, notice, observe, discern, judge, to be of the opinion, deem appropriate) 328 times,  from س أ ل  (se-a-le: ask, inquire) 129 times, from ن ب ا  (na-ba-a: inform) 160 times, from  ح ك م(ha-ka-ma: judge) 210 times, from ح س ب  (ha-sa-be: think, take something into account) 109 times,from  ف ق ه (fa-qa-ha: understand, comprehend) 20 times, from ح ق ق (ha-qa-qa:  prove, justify, ascertain) 287 times, from ب ي ن  (ba-ya-na: clarify, explain, demonstrate) 257 times, from دري (da-ra-ya: make known) 29 times, from ف ص ل (fa-sa-la: to make clear, explain in detail) 43 times, from ق د ر  (qa-da-ra: determine, measure, assess) 132 times, from  ص ر ف  (sa-ra-fa: explain) 30 times.

Additionally, there are many verses in the Quran that encourage human beings to study nature as a creation of God and the manifestation of his power and attributes. These verses also draw attention to the fact that there is an order and balance in the universe and the movement of the heavenly bodies is by precise mathematical calculations. Here are a few examples

“Indeed, in the creation of the heavens and the earth and the alternation of the night and the day are signs for people of understanding.” (Quran, 3:190)

 

Then do they not look at the camels – how they are created? And the heaven- how it is raised? And at the Mountains, how they are fixed firm? And at the earth – how it is spread out? ” (Quran, 88:17-20)

 

“The sun and the moon [move] by precise calculation.”(Quran, 55:5)

 

 “And the heaven He raised and imposed the balance.” (Quran, 55:7)

 

It is He who made the sun a shining light and the moon a derived light and determined for it phases – that you may know the number of years and account [of time]. Allah has not created this except in truth. He details the signs for a people who reason.” (Quran, 10:5)

We end this section with a few verses that capture the general idea we try to highlight.

“Whoever has been given wisdom has certainly been given much good. And none will grasp [the message] except the people of understanding.”(Quran, 2:269)

 

“Are those who know equal to those who do not know? Only the people of understanding are mindful.”(Quran, 39:9)

 

“My Lord, increase me in knowledge.” (Quran, 20:114)

Sayings of the Prophet (Hadith) on Learning

The sayings of the Prophet Muhammed, called hadith in Islamic tradition, are a major source of religion in Islam, second after the Quran.  In fact, the science of hadith is one of the principle branches of the theological disciplines in Islam. There are a number of authentic hadiths of the prophet that encourage learning. Below is a selection of hadith on the subject. The first hadith in the list clearly states that it is compulsory for every Muslim, male or female, to seek knowledge.

  • Seeking of knowledge is a duty upon every Muslim, male or female (Sunan Ibn Majah, The Book of the Sunnah, 224)
  • Whoever goes out seeking knowledge, then he is in Allah’s cause until he returns (Jami at-Tirmidhi, The Book of Knowledge, 2647)
  • The word of wisdom is the lost property of the believer, so wherever he finds it he has a better right to it (Jami at-Tirmidhi, The Book of Knowledge, 2687)
  • God has revealed to me: Whoever walks in the pursuit of knowledge I facilitate for him the way to heaven. (Jami at-Tirmidhi, The Book of Knowledge, 2646; Riyad as-Salihin, The Book of Knowledge, 1381 )
  • Do not wish to be like anyone except in two cases. (The first is) A person, whom Allah has given wealth and he spends it righteously; (the second is) the one whom Allah has given wisdom and he acts according to it and teaches it to others (Sahih al-Bukhari, Book 3, Hadith 15)
  • The learned ones are the heirs of the prophets–they leave knowledge as their inheritance; he who inherits it inherits a great fortune (Riyad as-Salihin, The Book of Knowledge, 1388)
  • The superiority of the learned man over the devout worshipper is like that of the full moon to the rest of the stars (in brightness) (Riyad as-Salihin, The Book of Knowledge, 1388)
  • Contemplating deeply for one hour is better than a year of (mechanical/voluntary) worship (Suyutî, Camiu’s-sağir, 2/127; Aclûnî, I/310)
  • There is no disease that Allah has created, except that He also has created its treatment (Sunan Ibn Majah, The Book of Medicine, 3438)

Note that the last hadith listed above is a great encouragement for research in medicine. Perhaps, the most famous of all scientists from the Islamic civilization is Ibn Sina (980-1037), also known as Avicenna in the west. He is well-known for his research in medicine and philosophy. His authoritative medical book The Canon of Medicine ( القانون في الطب in Arabic)  was a standard textbook in European universities until the middle of the 17th century (al-Khalili, 2010). The importance and influence of Canon are acknowledged by so many historians of science. For example, “Probably no medical work was ever written has been so much studied” says Meyerhof in (Arnold & Alfred 1931).

Early Muslim scholars took this advice for seeking knowledge to heart and practiced it to the best of their ability. They sought knowledge wherever it was available. They travelled great distances to acquire wisdom and legacy of earlier civilizations that produced the most advanced sciences of the time. They did not hesitate to receive science all the way from ancient Greek, which was neglected and persecuted under the Byzantine rule, to India. An excellent example that shows a fruitful outcome of the synthesis of the knowledge Muslim scholars acquired from Greeks and Indians is the creation of the discipline of algebra that was started by al-Khwarizmi (780-850) in early part of the 9th century in Baghdad, at the house of wisdom under the patronage of caliph al-Ma’mun (reigned 813-833).  In his book Kitab al-jabr wa’l muqabala al-Khwarizmi combined the Greek approach to mathematics that was essentially geometrical with the Babylonian and Indian heritage of efficient numerical systems to create a new science of algebra. Many scholars in the Islamic civilization contributed to the development of algebra in the centuries after al-Khwarizmi. Today, algebra is one of the principle branches of modern mathematics. Not only is it an important discipline in its own right, but also it influenced virtually every branch of modern mathematics as evidenced by the fact that so many subfields of modern mathematics include the adjective “algebraic” in its title such as algebraic number theory, algebraic geometry, algebraic topology etc.

Mathematical Sciences Developed as a Response to the Requirements of Religious Practice

What we have discussed so far establishes a philosophical and theological basis in Islam for undertaking scientific activities. It turns out that Islam did not stop at the philosophical level to encourage people to learn. It also gave its followers practical challenges that could only be solved by producing new knowledge. There are many religious obligations in Islam whose practice requires mathematical calculations, sometimes very sophisticated ones. Many of these problems were brand new problems that earlier civilizations did not face. Hence, Muslim scholars needed to find novel solutions for them. This was one of the direct and concrete ways in which the religion played an important role in the rapid development of the sciences in the early Islamic civilization. Scholars strived to solve these problems using available knowledge of the time and in many cases creating new knowledge and mathematical tools. In his voluminous three volumes of In Synchrony with the Heavens, David King examines the relationship between religious requirements and creation of new science to meet those requirements based on original sources. He states “The material presented here makes nonsense of the popular modern notion that religion inevitably impedes scientific progress, for in this case, the requirements of the former actually inspired the latter for centuries” (King 2004, p. xvii).

We look at a few examples of such problems in this section:

Prayer Times One of the five pillars of Islam is five daily prayers (salat) that need to be performed during certain time periods of the day. These time periods are determined by the position of the sun and it changes by the location on earth and the seasons of the year. Therefore, they need to be calculated for each day of the year and for every location on earth. This is then an astronomical problem which also involves mathematical geography. Today, there are electronic devices and online calculators that compute daily prayer times for all locations on earth and for every day of the year for practicing Muslims (e.g. www.islamicfinder.org). Traditionally, this need has been met by prayer tables prepared for each location by competent astronomers. A large number of such tables are presented in (King 2004). The solution of this non-trivial problem led to the creation of a scientific discipline in Islam called ilm al-miqat (عِلم الْمِيقات ), the science of timekeeping. It also led to the rise of a professional class called muwaqqits (literally “timekeepers”) who were astronomers specialized in determination of daily prayer times. Born in Egypt and Syria in the 13th century (King 2004), muwaqqits were associated with a particular mosque. Perhaps the most famous of these muwaqqits is Ibn al-Shatir (1304-1375) who was associated with the Umayyad mosque in Damascus.  Aside from his official duty of timekeeping, he produced some of the most advanced work of theoretical astronomy of his time while working on the fixing cosmological problems in Ptolemy’s Almagest.  Researchers discovered in the middle of the 20th century that his work was directly influential on Copernicus’s astronomy (Roberts, 1957; Saliba 2007). This remarkable connection is still not widely known, not only among the educated public but among the historians of science either.

The definition of the intervals for the five Muslim prayers is based on the certain verses of the Quran and the hadith and the practice of the Prophet Muhammad. The prophet Muhammad lived in the cities of Mecca and Medina, which are close to the equator. As Islam spread much farther north in a short period after the prophet, some interesting issues appeared in determination of certain prayer times due to location. For example, the criterion for the determination of the afternoon prayer (asr) that was practiced in Mecca and Medina could not be used in places like Damascus in certain times of the year because the length of the shadow of an object is never as short as its length for many days of the year. The scholars responded by establishing new criteria for such cases. The problem was directly related to trigonometry. Muslim scholars defined the trigonometric functions of tangent and cotangent in terms of shadows, as the ratio of the length a gnomon to the length of its shadow (Berggen 1986). After the works of Muslim scholars, there was little left to be discovered in the field of trigonometry (Saliba 2007, p. 187).

The day starts with the sunset in the Islamic calendar. The sunset is the beginning of the period for the evening prayer, al-maghrib, which lasts until the nightfall when the interval for the next prayer al-isha begins. It lasts until the daybreak. The morning prayer, al-fajr, needs to be performed between the daybreak and the sunrise. The next prayer, al-zuhr,  starts shortly after the midday (when the sun crosses the meridian)  and lasts until the length of the shadow of an object equals the object’s length (or the shadow length at noon plus the length of the object). The final prayer of the day, al-asr, starts at the end of the period of the zuhr and ends when the length of the shadow is equal to twice the length of the object (or the length of the shadow at noon plus the twice the length of the object).

The following figure gives a general idea about the specific time periods for Muslim daily prayers. Keep in mind that there are significant variations in the length of each time period by the time of the year and location on earth.

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Figure 1: The approximate placement of the time periods for Muslim daily prayers. Diagram based on King, 2004

Figure 2: An illustration of the beginning and endpoints of the interval for the asr prayer. Diagram based on King, 2004

One of the medieval Islamic scholars who wrote on shadows, its utility in determination of daily prayer times and the definitions of trigonometric functions is the eleventh-century polymath from central Asia: Abu al-Rayhan Muhammad b. Ahmad al-Biruni (973-1048). His treatise of shadows is edited, translated and commented by E. S. Kennedy (Kennedy 1976).  Determination of prayer times was a brand new problem for the Muslim community that earlier civilizations did not encounter.

The Qibla Problem Another requirement for a practicing Muslim related to daily prayers is to face Ka’ba, located in Mecca. This is the most sacred mosque in the Islamic tradition. Initially, Muslims faced the Noble Sanctuary in Jerusalem for over 13 years in their prayers, then a verse revealed to the Prophet Muhammad during a prayer that instructed him to face Ka’ba instead from this point on (Quran, 2;144).  Qibla refers to the direction, relative to a given locality, one needs to face when performing Muslim prayers. For places close to Mecca, determination of qibla was a relatively straightforward problem. As Islam spread in many directions, determining qibla from faraway places became more difficult and the qibla problem turned out to be an interesting problem with religious, scientific and social aspects. As the knowledge of astronomy increased, scholars realized that spherical geometry was needed to solve the problem accurately for places far from Mecca.   They realized that some mosques built in earlier periods of Islam were misaligned, in some cases to a significant degree. What to do with such mosques and what method of determining qibla to use was the subject of a serious debate among Islamic scholars (Dallal, 2010). Some religious scholars argued that using sophisticated mathematical techniques for determining qibla should not be required because only a few people can attain such knowledge which is contrary to the spirit of  Islam (Dallal, 2010). However, this did not end the debate. Scholars with advanced astronomical knowledge continued to work on the problem and developed various mathematical techniques to solve it.

Ultimately, the solution of the qibla problem requires some non-trivial spherical trigonometry because the earth is a sphere (approximately). In a small scale, it is okay to assume that the earth is a flat surface but in greater distances one needs to use great circles to solve the problem (see Figure 3 below). The advanced spherical trigonometry knowledge that was needed was not available from earlier civilizations, therefore Muslim scholars developed this material. According to Berggren, there are three astronomers who were responsible for developing major results in spherical trigonometry: Habash al-Hasib (d. after 869), Abu’l-Wafa Al-Buzjani (940-998) and Abu Nasr Mansur ibn Ali ibn Iraq (970-1036) (Berggren, 2003). A key result that was useful in solving the qibla problem was the discovery of the law of sines for spherical triangles derived by Abu’l-Wafa.

One of the great Muslim scientists who worked on the qibla problem is Al-Biruni (973-1048), a true polymath who presented four methods to solve it (Berggren, 2003).  An outline of his solution can be found in (Berggren, 2003).  Another approach to the problem was the composition of tables showing qibla for a set of localities, similar to tables of prayer times. A great example of such a table was provided by Muhammad al-Khalili, a 14th-century muwaqqit, that contained 2880 entries, i.e., it showed the qibla for 2880 different locations (Berggren, 2003).

Figure 3: Map showing global qibla directions. Source http://muslimcalendar.files.wordpress.com/2010/07/world_qibla_map.jpg

Determination of Lunar Months and Visibility of the Crescent Moon Islamic calendar is a strictly lunar calendar, hence major religious days in Islam are determined on the cycles of the moon, such as beginning and end of the holy month of Ramadan, the two Eids and pilgrimage. A new month starts with a new crescent moon.  The average length of a lunar month is approximately 29.5 days, therefore some lunar months are 29 days others 30. Initially, the Muslim community determined the lunar months based on the observation by the naked eye. When the clouds made it impossible to observe the new moon, they completed the previous month to 30 days. As the science of astronomy progressed, Muslim scholars also paid attention to the calculations of lunar months. Since the visibility of the moon varies by location on earth, there are still disagreements among Muslim today despite the availability of the tools of modern science and technology. The following map is included to give the reader an idea about the complexity of the problem. The map is retrieved from http://moonsighting.com.

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Figure 4: The visibility curve of the moon for the month of Ramadan 1440 H (May 5, 2019).  Different levels of visibility are indicated by different colors. The map is obtained from http://moonsighting.com/1440rmd.html

Calculation of Zakat and Inheritance

One of the pillars of Islam is zakat, the community’s share of private wealth. It is paid on the accumulated wealth beyond basic necessities. The rate of zakat changes between 2.5% (1/40) to 20% (1/5) depending on the type of asset. It is 2.5% on the money and capital assets. Zakat is mentioned in more than thirty verses in the Quran. Clearly, a basic knowledge of arithmetic of fractions is needed for zakat calculations.

Another area of the Islamic law that requires basic arithmetic is calculations of the legal shares in inheritance and legacies. Depending on the situation, these problems can get complicated. The calculations of these shares emerged as a new science in Islam called ilm al-faraid, the science of obligations, which is both a religious science (jurisprudence) based on the verses of the Quan and the hadith, and mathematical science. This science of ilm al-faraid has an interesting connection to the beginning of algebra.

Al-Khwarizmi (780-850) wrote the first algebra book in history Kitab al-jabr wa-al-muqabala around the year 820 in Baghdad. The original text of his book together with English translation and commentary is available (Rasshed, 2009). At the beginning of the book Al-Khwarizmi explains his motivation for writing it. He says the caliph al-Ma’mun (813-833) encouraged him to write a concise book on the form of calculation in algebra and al-muqabala

…I wanted to include what is subtle in the calculation and what is most noble in it and what people have a real need in need of matters of their inheritances, their legacies, their judgments, their commercial transactions, and all they deal with in the matter of surveying parcels of land, digging water channels, mensuration and other things to do with calculation…

He clearly states that one of the motivations for the new science of algebra he introduces is to help people with their calculations of zakat and inheritance. In fact, about half of his book is Book of Wills (Kitab al-wasaya)  in which he discusses many examples of inheritance and legacy problems. It may be surprising that such a large portion of the first algebra book in history is devoted to the problems of inheritance and legacy.  A brief explanation of the historical context may shed some light on why that is the case, as explained in (Rasshed, 2009).

The eighth-century was the time when the foundations of the three of the four major schools of law of Sunni Islam were established: Hanefi, Maliki and Shafi. One element of the Islamic law was the rules of inheritance, wills and legacies. Therefore, jurists of the time wrote many books on the subject. Some of these jurists developed calculation methods (hisab) for these problems. Al-Khwarizmi states that some scholars of the Hanefi school made use of algebraic methods to solve problems of inheritance and legacies. Given this context, we can better appreciate  Al-Khwarizmi’s motivation quoted above.

One might think that the problems of these types should only involve arithmetic not algebra. It turns out that the legal scholars considered problems in such generality that the amount of inheritance is not a specific quantity, rather it is a general, unknown quantity. Therefore, it was necessary to apply the elementary operations of arithmetic to a general quantity. This is the essence of algebra: to treat an unknown quantity as if it is known and apply the basic operations of arithmetic for the known quantities on the unknown (and at the end find out the value of the unknown). Therefore, it was in the field of Islamic law that the problems that required arithmetical manipulations of unknown appeared in large numbers. When we examine the Book of Wills in Al-Khwarizmi’s work, we see that he approached the subject in a systematic way and reduced the problems into one of the types of algebraic equations he classified in the first part of the book.  Al-Khwarizmi’s work than can be seen as a theoretical justification and systematization for the jurist’s work that preceded him.

After commenting on the importance of the science of algebra, we would like to consider another discipline that was among the most important fields of research in Islamic Civilization: astronomy.

The Place of Astronomy in Islamic Civilization and Its Influence on Renaissance Europe

We see that most of the problems that arose from the practice of the religious obligations in Islam are related to astronomy. Therefore, it quickly became an important field of study in Islamic Civilization. Astronomy is a highly mathematical science and particularly connected to trigonometry. Before the contributions of the scholars in the Islamic civilization, trigonometry was not developed enough and not considered as a field in its own right. Medieval Islamic scholars contributed so much to the field of trigonometry that it reached its maturity in that period and was established as a discipline in its own right. Perhaps most of the credit in this regard should go to 13th-century polymath Nasir al-Din al-Tusi (Nasr, 1970).  According to Berggren, Tusi’s book The Complete Quadrilateral is the first systematic trigonometry text, independent of astronomy (Berggren, 2007). One aspect of astronomy in Islamic civilization was the separation of astrology from astronomy (Saliba 2007). Greek astronomy came to the Islamic World mixed with astrology. However, astrology was not approved as a legitimate discipline by the religious authorities. Hence, scholars working on the field separated astrology from astronomy, that is, they would calculate the positions of celestial bodies but they would refrain from commenting on their effects on human life or behaviour.

As a result of the importance of astronomy for Islam, the institution of the observatory was born and developed in the Islamic civilization (Berggren, 2003). It is one of the legacies of medieval Islamic science.  A particularly important observatory in the Islamic World was the celebrated Maragha observatory (Sayili 1960, chapter 6) which was established in 1259 under the patronage of Ilkhan Hulagu, a year after he invaded Baghdad. It was Nasir al-Din al-Tusi who convinced Hulagu to establish it. Tusi became the director of the observatory. It was considered as the best observatory of its time. Not only did it serve as a model for observatories established later (such as Ulugh Beg Observatory in Samarqand and Taqi al-Din observatory in Istanbul) but the work done in this institution and the tradition of astronomy program that was carried out there had some surprising effects on the Renaissance science.

Researchers discovered in 1950’s that some of Copernicus’s (d. 1543) astronomical models are identical to the astronomical models of earlier Islamic scholar Ibn Shatir (d. 1375) (Roberts 1957), who was a muwaqqit in the Umayyad mosque in Damascus. They also discovered a remarkable connection between Copernicus and Tusi when they realized that the statement and the proof of a geometry theorem given by Copernicus were nearly identical to the theorem first discovered by Tusi almost 3 centuries earlier (Hartner, 1973). Called Tusi Couple theorem in the literature, this theorem was instrumental in the works of Islamic astronomers and was also employed by Copernicus in his astronomical models. These discoveries generated many new questions in the history of science, particularly in the area of connections between medieval  Islamic science and the Renaissance science that were not noticed before. This opened the door for more research. After studying the Islamic astronomy and astronomy of Copernicus,  Swerdlow and Nunebaugher reached the conclusion that  “In a very real sense, Copernicus can be looked upon as, if not the last, surely the most noted follower of the Maragha School”  (Swerdlow & Neugebauer, page 295). Despite the fact that it has been decades since the researchers discovered these connections, when the scientific revolution in the Renaissance is discussed in school curricula the connections between Copernicus and earlier Islamic scholars is hardly ever mentioned. Consequently, most people never learn about the influence of medieval Islamic science on Renaissance.

Polymaths as Authorities in Religious Knowledge and Natural Sciences

Many of the medieval Islamic scholars were practicing religious people. In fact, some of them were also authorities in religious sciences. For example, Ibn al-Nafis (1213-1288) who was the first person to discover the pulmonary blood circulation (Akmal et al, 2010) was also a practicing Shafi lawyer (Saliba 2007, p.187). Nasir al-Din al-Tusi (1201-1274) was a well-known Ismaili scholar and an authority on Shia thought.  Ibn al-Shatir (1304-1375)  whose work shows up in Copernicus’ was a muwaqqit (timekeeper) at the Umayyad mosque in Damascus (Saliba 2007, p. 189). Even those scholars who were not necessarily religious authorities at the same time would usually start their books by praising God and the prophet Muhammad. We give two examples of this. The first one is the beginning of al-Khwarizmi’s algebra book (Rashed 2009, p. 92):

This book has been composed by Muhammad ibn Musa al-Khwarizmi. He began it by saying:

Praised be God for His blessings, of His praises He is worthy of. Rendering these praises – as a duty for anyone from among His creatures who adores Him – is given the name of gratefulness, which must be augmented, and preserved from deterioration: by recognizing His Divinity, by lowering oneself before His Almightiness, and by bowing down before His Majesty. He sent Muhammad – God bless him and grant him salvation – with prophecy as his mission, after an interval of time devoid of messengers, when truth was distorted and true religion was obliterated….

Al-Kashi who lived about six centuries after al-Khwarizmi starts his book Miftah al-Hisab as follows (Aydin & Hammoudi 2019, p. 19)

In the name of God, the Most Gracious Most Merciful. Lord make it easy, not hard.
Praise due to God who is the only one who created units and who is unique in forming the categories of numbers. Prayers on the best of His creation, Muhammad, the best of intercessors on the day of judgement. Prayers also on his family and offspring, the guiders to the path of salvation and righteous guidance. …

A Potential Conflict Between Religious Scholars and Science: Imam Ghazali

As we have demonstrated already, there was generally no real conflict between religious beliefs and scientific knowledge in Islamic civilization. Some propose that this was not the case referring to al-Ghazali’s (d. 1111) criticism of philosophers in Tahafut al-Falasifa (The Incoherence of the Philosophers). They even claim that this attack was the end of the golden age of Islamic science. It is possible that some people in the Muslim World may have misunderstood al-Ghazali’s attack on certain claims of a few philosophers by overgeneralizing his criticism to all-natural sciences. However, a close look at the purpose and the methodology of al-Ghazali in Tahafut shows that this claim is unfounded. Al-Ghazali clearly states that he will only be arguing, using the same logic as philosophers that the philosophers failed to prove their assertions, 20 in total, that are contrary to the Islamic belief. He clearly says (Al-Ghazali-Marmura 2000, p. 11) “Regarding mathematical sciences, there is no sense in denying them or disagreeing with them. For these reduced in the final analysis to arithmetic and geometry.  As regards to logical sciences, these are concerned with examining the instrument of thought in intelligible things.  There is no significant disagreement encountered in these.” Later, the Andalusian Polymath Ibn Rushd (Averroes)  clarified this issue by saying that many of Al-Ghazali’s views expressed in Tahafut apply only to the philosophy of Avicenna and not to that of Aristotle, which Averroes argues to be the true philosophy from which Avicenna deviated  He also argues that the Quran calls for Muslims to study philosophy because the study and reflection of nature would increase a person’s knowledge of “the Artisan” (God). He quotes Quranic passages calling on Muslims to reflect on nature and uses them to render a fatwa (legal opinion) that philosophy is allowed for Muslims and is probably an obligation, at least among those who have the talent for it (Adamson, Peter. Philosophy in the Islamic World: A History of Philosophy Without Any GapsOxford University Press. 2016, p181-182).

It is really interesting to note that the first two of the 20 doctrines of the philosophers that al-Ghazali refuted have been settled by modern science. Following their Greek ancestors, those Muslim philosophers claimed the pre-eternity and post-eternity of the world. Now, the modern cosmology gives us a definite time for the beginning of the universe and concludes that it will not be eternal.   Given the fact that there was original and advanced scientific production in the Muslim World well after al-Ghazali (see Saliba 2007, Chapters 1, 6 and 7), the popular idea that al-Ghazali caused a halt on scientific progress in the Islamic World does not hold up. This is not to say that some people may have misunderstood his position and purpose and opposed all secular sciences.

In summary, we can see a remarkably strong connection between the faith and practice of Islam and mathematical sciences. Even in the words of al-Ghazali, who is considered by some as the person who was responsible for ending the Islamic golden age, we see a great respect for mathematical sciences.

Bibliography

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by Prof. Nuh Aydin, Professor of Mathematics, Kenyon College

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