Mathematics

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Mathematics

Numbers . Muslim scholars agreed with the ancient Greek notion that mathematics is the underlying foundation of all knowledge. They knew that studying mathematics gives one skill in logic and reasoning. Furthermore, one of the main foundations of Islam is the concept of Taiuhid (Oneness) of the whole interconnected world, and Muslims viewed mathematics as a way to make sense of the physical world and its union with the spiritual world. This link between the science of numbers and understanding of the divine reality was so critical to early Muslim scholars that they referred to mathematics as “the tongue which speaks of Unity and Transcendence.” Their affinity for mathematics as spiritual symbolism is apparent in Muslim art and architecture, which often includes the number 1, or a single, central design element, to remind the viewer that there is only one God. Hence, the number 1 is often called “The Source” because God is seen as the source of all creation. Similarly, a series of numbers is sometimes interpreted as symbolizing the steps Muslims must take to reach an understanding of Muslim beliefs. In a treatise written by the Ikhwan al-Safa (Brethren of Purity), a tenth-century brotherhood of mystical Muslim scholars, the primary position of mathematics among the sciences was clearly stated: “The science of numbers is the root of the sciences, the element of wisdom, the origin of the divine sciences, the pillar of meaning, the first elixir and the great alchemy.” These scholars had their strongest influence on

Western mathematics in the fields of algebra and trigonometry. In fact, the word algebra is a Latinized form of the Arabic term al-jabr, which stems from the word for “bone setting” and means restoration, putting together parts, or completion of a whole. Arab mathematicians drew mainly on ancient Greek and Indian mathematics, correcting the mistakes in these earlier sources and expanding on the work of the ancients. The “Arabic” numerals in use today get their name from the fact that Muslim mathematicians used them as symbols of quantities in their mathematical theories. These symbols—which revolutionized the field of mathematics—actually originated in India, where Indian mathematicians saw that the ancient numbering systems, including those devised by the Greeks and Romans, were adequate for expressing quantities but cumbersome and difficult to use in solving even the simplest mathematical equation. Once Indian scholars began to use symbols (such as 5 or 7) to express quantity and came up with the concept of place values (such as “thousandth,” “hundredth,” or “tenth” place), people were able to perform basic tasks such as adding and subtracting with relative ease (and without using stones, fingers, or an abacus). Finally, the Indians came up with the concept of a circular symbol to represent the concept of emptiness, or nothing —the origin of the universal mathematical symbol for zero. It is essential in writing a number like 608 without a zero, making it impossible to distinguish between 68 and 608, for example. Muslim scholars embraced these new Indian ideas with enthusiasm, applied them in new ways, and disseminated them widely, including to western Europe. The Muslim study of mathematics included the same four subjects as the Latin “Quadrivium,” the four parts of the liberal arts: arithmetic, geometry, astronomy, and music, which was considered a mathematical science. But Muslim scholars also included optics in the field of mathematics.

Algebra and Trigonometry . Scholars of the Muslim world developed both geometry and trigonometry as new scientific fields and first defined the sine, cosine, and cotangent mathematical functions. The best-known Muslim mathematician was al-Khawarizmi, whose name is the source of the English word algorithm. Working in the ninth century, he also developed tables of trigonometry that contained sine functions and theories of calculus, as well as studying the geometric qualities of cones. Though he spent most of his life in Baghdad, some historians think he may have traveled to India to study there. His work on the astronomical project in which Muslim scientists measured one degree of the meridian led him to write the first extensive Muslim treatise on mathematical geography, using tri-angulation to measure distances. During the twelfth century his Kitab al-mukhtasar fi hisab al-jabr wal-muqabalah (The Book of Summary Concerning the Process of Calculating Compulsion and Equation) was translated into Latin by Robert of Chester and led to the wide dissemination of algebra throughout European intellectual circles.

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Geometry . Other important ninth-century mathematical texts were written by the Banu Musa (Sons of Moses), three brothers working in Baghdad who wrote several works about geometry. Their Kitab ma'rifah misahat al-ashkal (The Book of Knowledge of the Area of Figures) created much interest in geometry among the scholars of Baghdad. After Gerard of Cremona translated the Banu Musa manuscripts into Latin in the twelfth century, these works brought to Europe a wealth of new information on mathematics, physics, and mechanical science.

Numerical Series . Another popular field of studies within mathematics was the area of numerical series. The geographer al-Biruni (973 - circa 1050) wrote several works on this subject, many of which offered mathematical puzzles to be solved. The best known of these is the fictitious story of the man who invented the game of chess. It was said that, when he presented his new invention to his ruler, the ruler absolutely insisted that he accept some sort of favor in return. The man asked for some grain, which would be measured according to the mathematics of the chessboard: there would be one grain for the first square, and then the number of kernels would double with each subsequent square. Thus, the second square would hold two grains, the third square four, the fourth square eight, and so on, up to the sixty-fourth square. The ruler accepted this proposal without doing the math first. Much to his dismay, he discovered that he owed his subject 18,446,774,073,709,551,615 pieces of grain—more than all the grain in the kingdom.

’Umar Khayyam . The development of algebra among the Muslims reached its peak with the studies of the Persian ‘Umar Khayyam (1048-1131), better known in the West as a poet than as a mathematical genius. In his best-known mathematical text, Maqalat fi al-Jabr wa al-Muqabalah, he classified algebraic equations according to their level of complexity. He was also the first scholar to develop the binomial theorem and determine binomial coefficients, and he did work on the multiplication of ratios and the mathematical theory of parallel lines. Also interested in physics and metaphysics, he did extensive research on how to determine specific gravity. When the Saljuk sultan Malik-Shah (ruled 1072-1092) asked Khayyam to update and make corrections to the Persian calendar, he undertook a massive project involving intense study of mathematics and astronomy and produced a solar calendar called the Jalali calendar, which is still in use today and is more accurate than the Gregorian calendar used in the West. Only about a dozen of Khayyam’s works on mathematics have survived. Most of them express his interest in philosophy and its relationship to science. One of the major goals of Muslim sages such as ‘Umar Khayyam was to show disciples how to see spiritual signs in the realm of numbers. This philosophy also influenced the study of geometry, a field that the Banu Musa called “one of the gates through which we move to the knowledge of the essence of the soul.”

Nasir al Din al-Tusi . Khayyam’s work in algebra and geometry was continued by Nasir al-Din al-Tusi (1201-1274), who is credited with much developmental work in geometry and trigonometry and also wrote about medicine, ethics, and religion. Tusi’s Kitab shikl al-qita ‘(Rook of the Figure of the Sector) is considered the first independent work on trigonometry. He also wrote an extensive commentary on Euclid’s Elements, an ancient Greek mathematical work on which several Muslim scholars expanded. Tusi also discovered many mistakes in the mathematics of the astronomical models put forth by Ptolemy.