One thousand years ago, Mesopotamia, modern day Iraq, housed the world’s premier center of mathematics. During this period, scholars from many religions including Christians, Zoroastrians, and Jews joined Muslim scholars in the preservation and pursuit of knowledge. The scholars gathered and translated the works of many ancient civilizations ranging from, Greek and Roman to Indian and Persian, and created a comprehensive library in Arabic. The scholars also made major original contributions: the sum formula for the fourth power in calculus; tessellating tiles in geometry; the Law of Sines in trigonometry; and in mathematics, and life in general, the invention of algebra.
Mathematicians today celebrated the history of mathematics and its present and its future at the largest meeting of mathematics in the world with over 6,500 attendees: The Joint Math Meetings (JMM) in Baltimore, Maryland from January 15-18, 2014. Representing the 97th annual meeting of the Mathematical Association of America (MAA) and the 120th annual meeting of the American Mathematical Society (AMS), this annual joint meeting represents a reunion of mathematics, of ideas, of people, and of a shared calling to use numbers and letters and shapes to contribute to humanity.
Mathematics from the Islamic Golden Era was prominently featured at sessions devoted to the history of mathematics. Dr. Salar Alsardary from the University of the Sciences in Philadelphia gave a talk called “Contribution of Muslim scientists to science and mathematics.” Dr. Alsardary highlighted the fact that “Islam encourages its followers to seek all kinds of knowledge” and especially emphasizes “specific knowledge that can help them with daily life as well as their beliefs,” such as astronomy to calculate lunar months or arithmetic to calculate inheritance. Dr. Alsardary introduced Abu Ja’far Al-Khwarizmi, the 8th century Muslim scholar who wrote “Kitab Al-Jabr,” the first ever book on the subject from which we take the name “Algebra” today. This new construct allowed scholars to solve problems that other civilizations could not conceive. Dr. Alsardary explained, because Greek mathematicians lacked algebra, “they could not reach the more free attitude toward mathematical concepts necessary to invent Calculus.” Greek mathematicians were restricted to “things they readily saw with their eyes.” The new concept of Algebra enabled mathematical modeling at a level beyond simply what the eyes could see. In his book, Al-Khwarizmi provides applications and worked examples of using algebra to find volumes of solids, such as the sphere, cone, and pyramid. He also employed his techniques to calculate inheritance using Islamic Shari’a Law. These algebraic rules represent the same foundations that we rely on today.
While mathematics has contributed tremendously to society, the universe of what more mathematics can accomplish remains full of unknown potential. At the Joint Math Meetings, researchers shared their latest works and unanswered questions in the field. Professor Benson Farb, of the University of Chicago, delivered a joint invited address in which he introduced basic concepts in topology. He defined a configuration space in layman terms as a configuration of a space of points, such as satellites in outer space or robots on a factory floor. Before delving into the theories of topology, he prefaced, “I’m not working on satellites or robots, but if I can understand configuration spaces, then I can solve all these problems at the same time.” On this tantalizing note, he proceeded and left the audience with the basic building blocks to perform a standard calculation in topology and understand what types of questions this field can address. Consider, the space of polynomials, the points on a plane. Now, imagine that the dots are moving in a loop, such that at any given point, the dots return to their starting points. Follow the red dot in the diagram below, as if it were a motion picture:
How would you attach a number to the movement of the red dot? One method is to count how many times the red dot revolves around the other dots. In the case above, the red dot revolves around dot 6 one time, and then returns to its starting place. So you could describe the motion picture above with the number 1. Now imagine dots looping around one another more than once, and not just flat on a two-dimensional page, but on a sphere. This notion takes us one step closer to solving problems involving planets or satellites in outer space.
Consider another cutting edge math problem. Professor Jill Pipher, of Brown University, presented an MAA invited address on Cryptography in which she tackled a question about Fully Homomorphic Encryption (FHE), which was first posed as a faraway theory in 1978: “How can you compute on encrypted data withovut decrypting it?” Today, the Internet serves as an environment for data storage and computing, so we could all benefit from FHE. However this is an open problem. Dr. Pipher explained “There are no practical methods for FHE in public domains. This kind of capacity is just not there, but this is a fast moving field.”
Indeed, the branches within mathematics are moving rapidly and intersecting in new ways. Math is not just numbers or letters or shapes. Math is much more; it is like a machine that can answer questions in fields ranging from biology and astronomy to art history and psychiatry. The opportunities are endless, and we ought to study mathematics to determine what it can offer. Anisah Nu’man, a doctoral student specializing in geometric group theory at the University of Nebraska in Lincoln, put in a plug, “You should be advocating for advancements in math.”
Indeed, as Muslims, seeking knowledge is our duty. The first word of revelation, “Read!” commands us to do so. Like Algebra was to the Greeks, something not conceived, limiting the scope of their problems to what could be seen with two eyes, there are many problems today beyond our scope of imagination. Allah invites and challenges us in the Holy Qur’an:
“O company of jinn and mankind, if you are able to pass beyond the regions of the heavens and the earth, then pass. You will not pass except by authority [from Allah ].” (55:33).