Mathematicians and Scientists

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Mathematicians and Scientists


Born 476

Died c. 550

Indian mathematician and astronomer


Born c. 864

Died c. 925

Arab physician and philosopher


Born c. 780

Died c. 850

Arab mathematician, astronomer, and geographer


Born 965

Died 1039

Arab mathematician and physicist

Roger Bacon

Born 1213

Died 1292

English philosopher and scientist

"Praise God the creator who has bestowed upon man the power to discover the significance of numbers. Indeed, reflecting that all things which men need require computation, I discovered that all things involve number.… Moreover I discovered all numbers to be so arranged that they proceed from unity up to ten."

Al-Khwarizmi, Kitab al-jabr wa al-muquabalah

I n modern times, people are accustomed to thinking of the West—Western Europe and lands such as the United States that have been heavily influenced by Western Europe—as being at the forefront of mathematical and scientific knowledge. This was not always the case, however: during the Middle Ages, the focal point of learning in math and science lay far to the east, in India and the Arab world.

The five biographies that follow illustrate the process whereby knowledge seeped westward, from the Hindu mathematician Aryabhata in the 500s to the English scientist Roger Bacon seven centuries later. In between were many, many scientists, mathematicians, and philosophers in the region that produced perhaps the greatest intellectual achievements during the medieval period: the Middle East. Al-Khwarizmi, al-Razi, and Alhazen—along with Avicenna (see box in Moses Maimonides entry), Averroës (see entry), al-Mas'udi (see Historians entry), Omar Khayyám (see box in Dante Alighieri entry), al-Idrisi, and Yaqut—were far from the only notable Arab and Persian thinkers: just some of the greatest.

Two Great Byzantines

Much of the driving force behind advances in science during the Middle Ages came from the rediscovery of ancient Greek texts by Arab scientists. During the early part of the medieval era, the writings of Aristotle and others were lost to Western Europe, where learning in general came to a virtual standstill. By contrast, knowledge of the Greek writers remained alive in the Greek-controlled lands of the Byzantine Empire.

One of the greatest Byzantine commentators on science was not even a scientist but a philosopher and theologian who also wrote about grammar—as his name, John the Grammarian or Johannes Philoponus (yoh-HAHN-uhs ful-AHP-uh-nus; c. 490–570), suggests. Johannes challenged the assertion by Aristotle that a physical body will only move as long as something is pushing it. On the contrary, Johannes maintained, a body will keep moving in the absence of friction or opposition. Five centuries later, Avicenna would uphold Johannes's idea; and many centuries after that, the concept would be embodied in one of the laws of motion established by Sir Isaac Newton (1642–1727).

Also important was the surgeon Paul of Aegina (i-JY-nuh; c. 625–c. 690). He was the first to practice obstetrics, the branch of medical science dealing with birth, as a specialty. His writings summed up virtually all that was known about medicine up to his time, and greatly influenced the work of later Arab scientists.


During the 500s, at a time when Europe was descending into darkness and Arabia had not yet awakened, India had a thriving scientific community at the city of Ujjain (ü-JYN) in the central part of the subcontinent. Yet Aryabhata (ar-yah-BAH-tuh), one of India's greatest mathematicians, came from Pataliputra (pah-tuh-lee-POO-trah) in eastern India. The city, which had served as the capital of the Mauryan Empire centuries before, had long since fallen into ruins. Symbolic of its state of disrepair was the fact that Pataliputra was a center of superstition where priests taught that Earth was flat and that space was filled with invisible and demonic planet-like forms. The persistence of these ideas made the achievements of Aryabhata all the more impressive.

As was typical of Hindu scientists, Aryabhata considered mathematics of secondary importance to astronomy, and most of his achievements in math were in service to his study of the planets. His greatest work, the Aryabhatiya, brought together teachings from ancient Greek and Indian astronomers, and contained a number of cutting-edge ideas: for instance, Aryabhata suggested that the reason why the stars and planets seem to move around Earth is that Earth is in fact rotating on its axis, and moving around the Sun. It would be nearly a thousand years before a Western astronomer, Nicolaus Copernicus, recognized the same fact.

Among Aryabhata's mathematical achievements were great advances in trigonometry (the study of triangles and their properties), as well as the principle of inversion. The latter involves starting with a solution and working backward, developing the steps whereby one reached that solution. Perhaps most notable was Aryabhata's use of two vital concepts, the numeral zero and the idea of number position, or decimal place-value (i.e., tens, hundreds, thousands, etc.). These would have enormous impact as they moved westward. Finally, Aryabhata calculated the most accurate number for pi—a figure equal to approximately 3.14, used for finding the area of a circle—up to that point in history.


The word algebra is just one of the legacies given to the world of mathematics by al-Khwarizmi (KWAR-iz-mee), a mathematician in the city of Baghdad (now capital of Iraq) who wrote Kitab al-jabr wa al-muquabalah. The English name for algebra, a branch of mathematics used for determining unknown quantities, is taken from the second word of the book's title.

Al-Khwarizmi was not only interested in mathematics as an abstract study, but for its practical application; thus one of the principal uses for algebra, as described in his book, was for helping men divide up their inheritances proportionately. In assessing business transactions from a mathematical standpoint, al-Khwarizmi maintained that these transactions involved "two ideas," quantity and cost, and "four numbers"—unit of measure, price per unit, the quantity the buyer wants to purchase, and the total cost.

As with Aryabhata, al-Khwarizmi and his readers considered mathematics merely as a tool in service to other things, including astronomy. The latter was particularly important to Muslims, who needed to know the exact location of the holy city of Mecca, toward which they prayed five times a day. He offered tables and techniques for computing the direction to Mecca and the five times for prayer, which were based on the Sun's position.

Al-Khwarizmi's ideas would prove perhaps even more influential in the West than in the Middle East. A testament to his impact is the word algorithm, a term derived from his name and referring to any kind of regularly recurring mathematical operation such as those routinely performed by a computer. One modern scholar maintained that al-Khwarizmi was the single most important mathematician in a fifteen-hundred-year period between about 100 b.c.. and the mid-1400s.


Like al-Khwarizmi, the physician and philosopher al-Razi (RAH-zee), better known in the West as Rhazes (RAHZ-ez), spent much of his career in the great Islamic cultural center of Baghdad. There he wrote a number of important works and established the medieval world's most advanced hospital. In selecting the location for the hospital, it was said that al-Razi had pieces of meat hung in various parts of the city, and picked the place where the meat was slowest to decompose, reasoning that the air was most healthful there. As a doctor he was noted for his compassion, caring for his patient's emotional wellbeing in addition to their physical bodies, and even helping to support them financially while they recovered at home.

Al-Razi's written works include a ten-volume encyclopedia of medicine as well as a book translated as Upon the Circumstances Which Turn the Head of Most Men from the Reputable Physician (c. 919). In it he addressed questions as vital to the medical practice today as they were eleven hundred years ago, warning doctors that patients think they know everything, and encouraging the physicians themselves not to fall under the sway of this mistaken belief. His most important work was The Comprehensive Book (c. 930), an encyclopedia in twenty-four volumes that summed up the medical knowledge of his time.

Like many doctors in the pre-modern period, al-Razi accepted the ancient Greeks' idea that drawing blood would help a patient recover. He did, however, urge caution in doing so, and warned physicians not to apply the technique on the very old, the very young, or the very sick. He applied a variety of herbs and medicines, the uses of which he said he had learned primarily from female healers around the Muslim world.

As both a doctor and a philosopher, al-Razi was interested in alchemy, which was based on the idea that ordinary metals can be turned into precious metals such as gold. Although alchemy was not a real science, it influenced the development of chemistry. Al-Razi's experiments in alchemy may have contributed to his later blindness, and when he died he was in poverty, having given all his wealth to the care of his patients. But he is remembered with great honor: in its School of Medicine, the University of Paris—one of the first institutions of higher education established in the Middle Ages—included the portraits of just two Muslim physicians, al-Razi and Avicenna.


Born in the city of Basra in what is now Iraq, Alhazen (al-HAHZ-un) achieved fame as a scholar and was invited to undertake a special project in Egypt. The caliph or leader of the Fatimids, an Islamic sect that controlled Egypt in his time, asked him to develop a means for controlling the flooding of the Nile River. Eager for advancement, Alhazen had insisted that he could do so. As he sailed southward on a barge toward the city of Aswan (AHS-wahn), however, he observed the magnificent structures built by the ancient Egyptians, and realized that if the river's flooding could be controlled at all, the people of that great civilization would have managed it thousands of years before. (Only in the 1960s was the Egyptian government, using modern technology, able to construct a dam to deal with this problem.) As for Alhazen, he got out of the job by pretending to be insane, then laid low until the caliph who had hired him died in 1021.

During the remaining eighteen years of his life, Alhazen wrote about a wide array of subjects, most notably optics, or the science of vision. In his day, a number of beliefs about vision prevailed, all of them inherited from ancient times, and all extremely fanciful from the standpoint of modern knowledge. Some theorists promoted the idea of extramission, which maintained that the eye sent out rays that made it possible to see objects. Others claimed intromission, which took a variety of forms but basically came down to the idea that the object sent out rays to the eye. Alhazen was the first to realize that in fact light comes from self-luminous bodies such as the Sun or a lamp, then is reflected off of objects to the eye, which "catches" the reflected rays.

In addition to this and other theories put forth in his most famous work, Optics, Alhazen wrote about a number of related subjects such as rainbows, shadows, and the camera obscura, an early ancestor of the camera. He also wrote about astronomy, and like a number of Arab thinkers, helped chip away at mistaken beliefs inherited from the Greek astronomer Ptolemy (TAHL-uh-mee; c. a.d.. 100–170)—including the idea that other planets revolve around Earth as part of imaginary circles. His greatest achievement, however, was the Optics, which influenced Roger Bacon and a number of scientists through Johannes Kepler (1571–1630), the first to add significantly to Alhazen's ideas.

Roger Bacon

Though he wrote widely about a number of scientific disciplines, the greatest contribution of Roger Bacon was in the philosophy of science. Like many Europeans of his day, Bacon, a Franciscan monk from England, was heavily influenced by the scientific knowledge of the Middle East, to which Westerners had first been exposed during the Crusades (1095–1291). Starting in 1247, when he was about thirty-six years old, he became interested in alchemy and other "secret" forms of learning, which he believed would contribute to religious belief.

Many within the Catholic Church, on the other hand, feared that the increase of knowledge in science would damage people's belief in God, and this—combined with the fact that Bacon had a rather disagreeable personality—often got him into trouble. Nonetheless, in 1266 Pope Clement IV took an interest in Bacon's work, and asked for a full report. The result of this request was Bacon's writing of several important works, which unfortunately arrived after the pope's death in November 1266.

Nonetheless, these books have proven highly valuable to scientific knowledge, though not so much for the information they contained as for the principles they outlined. In particular, Bacon helped shape the idea of experimental science, or the gathering and testing of new information.

For More Information


Bruno, Leonard C. Math and Mathematicians: The History of Math Discoveries around the World. Lawrence W. Baker, editor. Detroit: U•X•L, 1999.

Bruno, Leonard C. Science and Technology Breakthroughs: From the Wheel to the World Wide Web. Detroit: U•X•L, 1998.

Hoyt, Edwin Palmer. Arab Science: Discoveries and Contributions. Nashville, TN: Thomas Nelson, 1975.

The New Book of Popular Science. Danbury, CT: Grolier, 2000.

Stewart, Melissa. Science in Ancient India. New York: Franklin Watts, 1999.

Web Sites

"Index of Biographies" (Mathematicians). [Online] Available (last accessed July 26, 2000).

Medieval Technology Pages [Online] Available (last accessed July 26, 2000).

Muslim Scientists and Islamic Civilization. [Online] Available (last accessed July 26, 2000).

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Mathematicians and Scientists