Lost History: Mathematics in the Muslim World

The history of mathematics, like any type of history, contains blind spots and lost information.  So much of history mirrors the movements and conquests of armies and their rulers, and armies usually destroy indiscriminately.  In 1258 Hulegu Khan, grandson of Genghis Khan and leader of the Mongols, sacked Baghdad, destroying perhaps the greatest city in existence. 

For over 500 years, the City of Baghdad was among the greatest cities in the world.  During what is sometimes known as the “dark ages” of medieval Europe, the Islamic Empire was among the most accomplished empires in the world, with Baghdad at its center.  In “Lost History” Michael Morgan quotes from a description found from a geographer’s account, the Kitab al-buldan:

“I begin with Iraq only because it is the center of this world, the navel of the earth, and I mention Baghdad first because it is the center of Iraq, the greatest city, which has no peer in the east or the west of the world in extent, size, prosperity, abundance of water or health of climate, and because it is inhabited by all kinds of people, town-dwellers and country-dwellers.  To it they come from all countries, far and near, and people from every side have preferred Baghdad to their own homeland.  There is none more learned than their scholars, better informed than their traditionalists, more cogent than their theologians”

The loss of such a great city is just one example of the “Lost History” outlined by Michael Morgan in his book.  Either through destruction, lost translations, or ignorance, there is a long history of Islamic scholarship that is unknown in much of the world.  Many advances that were later attributed to European thinkers found their origins in Muslim lands.  In particular, there are a number of mathematical ideas and tools that were either created or put into popular use by Islamic mathematicians. 

Today, the American image of the Muslim world is rife with anger, stereotypes and violence.  Years of war and terrorism have changed how Americans view countries like Iraq and cities like Baghdad.  There are limits to how much change we can make in math classrooms, but there are small steps that teachers can take to develop cultural understanding in our students.  After reading Lost History, I created a few ways in which I could incorporate some of the mathematical contributions of the Muslim world into a classroom.

Mohamed Al-Kwarizmi, the man for whom algorithms were named, did extensive work translating Indian mathematical texts into Arabic, which allowed the ideas to spread much more quickly.  One of the ground-breaking discoveries was the concept of the number zero.  Zero became the center of the numerical world and with its unique properties, made the world of mathematics much more complex and abstract.  It allowed math to move into more academic, less literal areas, like Algebra (whose root is an Arabic word, jabr describing the process of subtracting from both sides of an equation).  As an activity in an algebra class, students will be assigned to small groups, and each group will be responsible for evaluating a unit previously studied.  Students will make the determination, with proof, whether or not we could learn that unit without the concept of zero.  If it is impossible, students will gain insight into the power of zero, and if it is possible, this activity should foster creative thinking in devising new ways to solve math problems.

Al-Kwarizmi also introduced decimal numbers to the world.  Prior to the Indic-Arabic number system, there were three ways to represent numbers:  Counting on your fingers, writing the number in script, or using roman numerals.  As an activity, students will solve basic algebraic equations using either roman numerals, or script.  Students should grapple with the idea of variables.  What happens when X means 10?  How can we represent variables when we are writing out equations using words?  If students get stuck, or would like more information and inspiration, they can watch this video:

The Magic Square was also studied and popularized by a Muslim mathematician, Thabit ibn Qurra.  A magic square is one where, in a square grid, all the numbers in a row and column all add up to the same number (See below).  This is similar to what we now call Sudoku puzzles.  Rather than completing a Sudoku, students will receive extra credit for creating a magic square.  The extra credit will scale along with the dimensions of the square (3x3 is 3 points, 5x5 is 5 points, etc.)

 

Students in calculus could examine the chess board problem. Thabit ibn Qurra also worked on this type of problem, described here:

“The man who invented the game of chess asks his ruler for a favor, the receive one grain of wheat on the first square, then double that on the next, that is two on the second square, four on the third square, eight on the fourth square and so on until all 64 squares are filled”. 

This could serve as an introduction to exponential series, where students would require the new knowledge in order to solve.  Using this model, students will build the series representing the chess board problem:

1+2+4+8+16+… is the same as 2⁰+2¹+2²+2³+… which could be used as an introduction to series notation. 

As an FYI, the number of wheat grains, when calculated is a staggering 18,446,744,073,709,551,615.

If we were to generalize the contributions of Muslim mathematicians, we could say that they moved mathematics to a more abstract area of study.  Through their use of decimal numbers, they allowed math to be written more clearly.  Through the use of exponents, they evaluated numbers that were too complicated for ‘brute force’ calculation.  Moving from the literal and observable to the abstract is a big step for students.  Through studying the methods and techniques used by thinkers who were among the first to embrace abstract mathematics, students may gain insight into their own learning.  Beyond the mathematical insight, by studying the contributions of Muslim thinkers, students may also gain a more nuanced understanding of a religious and cultural force that is often misrepresented today.

Morgan, M. H. (2007). Lost History: The enduring legacy of Muslim scientists, thinkers, and artists. Washington, D.C.: National Geographic Society.