Mathematics of Central and Northern Asia

Summary: The contributions of central Asia have included algebra and its great houses of wisdom.

Throughout history, countries in Asia have had shifting sociopolitical boundaries. The names of some countries have changed, influenced by the Arab and Islamic empires as well as European colonialism in the eighteenth and nineteenth centuries. Though not widely used, Northern Asia sometimes refers to the part of the Asia occupied by the transcontinental country of Russia, which is commonly included in eastern Europe. Central Asia includes the former Soviet satellites of Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, and Uzbekistan. Mongolia, typically considered part of central Asia by historians, is in the modern world classified as part of Eastern Asia by the United Nations. “Northern Asia” is a term that is not commonly used, thus the transcontinental country of Russia is usually thought of as part of Eastern Europe. Knowledge of the contributions of mathematicians around the world is constantly changing as historians discover and translate written materials in many languages. Further, the breakup of the Soviet Union and shifting alliances have given researchers access to documents from decades in which many Eastern Bloc nations kept themselves in isolation, as well as even older works contained in the libraries and educational institutions of these nations. For example, medieval Islamic texts in Uzbekistan have helped shed light on the rich mathematics culture of central Asia. However, the mathematics contributions and achievements of some people from central Asia may be included in the histories of other areas, countries, or cultures.

In the seventh century, the great Library of Alexandria in Egypt was captured by a Muslim army, and there are some historians who believe some contents of the library were taken into Muslim lands. Many cities in central Asia became famous in the medieval period for their own libraries, which contained original works and translations of texts from Greek and Sanskrit, some of which became the only surviving copies of these earlier works. Houses of wisdom provided places for scholars to gather, as well as scientific centers such as the fifteenth-century Samarkand Observatory in what is now Uzbekistan, which was founded by astronomer Muhammad Taragay Ulughbek. This observatory reputedly served as a model for later observatories in India. Astronomer and mathematician Ala al-Din Ali ibn Muhammed, also known as Ali Kushji, later preserved and disseminated some of the knowledge gathered by the observatory when it was destroyed. This catalogue of stars, containing the most accurate mathematical measurements of location known prior to the invention of the telescope, is still studied.

Significant Central Asian Mathematicians

In the same way that mathematicians in central Asia studied and developed many concepts that were first introduced by other cultures, other concepts and techniques in twenty-first-century mathematics were first brought to Europe by mathematicians who worked in or came from central Asia. The word “algorithm” derives from a Latin transliteration of the name of eighth- and ninth-century mathematician Abu Abdallah Muhammad ibn Musa al-Khwarizmi (sometimes written as Al-Khoresmi). The Khwarizm (or Koresm) region included portions of what are now Turkmenistan and Uzbekistan. The word “algebra” comes from the term al-jabr, which was found in al-Khwarizmi’s treatise on that subject. Another of his mathematical writings, the Book of Addition and Subtraction by the Indian Method, helped promote the Hindu base-10 decimal system within the Arabic world. This system spread to Europe and revolutionized mathematics around the world in subsequent centuries.

Historical evidence suggests that tenth-century astronomer and mathematician Abu Mahmud Hamid ibn al-Khidr Al-Khujandi was born in the city of Khudzhand, in what is now Tajikistan. His mural sextant produced some of the most accurate astronomical observations of the day, and he may have contributed to trigonometry. The tenth- and eleventh-century mathematicians Abu Rayhan al-Biruni and Abu Nasr Mansur are also cited as being natives of Khwarizm. Al-Biruni studied a diversity of topics in mathematics and science, including cartography and map projections, trigonometry, combinatorial analysis, ratio theory, algebraic problem solving, geometry, Archimedes of Syracuse’s theorems, conic sections, and spherical triangles. Along with his own prolific body of writings, he was also a translator of Sanskrit texts. Abu Nasr Mansur taught and collaborated with al-Biruni—the two frequently cited one another’s contributions to their own work.

Many consider Mansur’s primary mathematical contributions to be his commentary on Menelaus of Alexandria’sSphaerica, his development of trigonometry, and his tables for numerical solutions to problems in spherical astronomy. In the same time period, Abu Ali al-Husain ibn Abdallah ibn Sina, also known by the Latin name Avicenna, wrote on many topics, including medicine and mathematics. Some of his investigations included ruler and compass constructions, areas of circles, and geometric algebra. He also considered music to be a subdiscipline of mathematics, and some believe that his studies led to musical tuning by the method of just intonation, where the note frequencies are related by ratios of small whole numbers, rather than Pythagorean tuning, named for Pythagoras of Samos.

Beginning in about the twelfth century, central Asia underwent a great deal of social and political disruption, and there is often little surviving evidence regarding mathematics and science during those eras. During the Soviet period, mathematicians from Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, and Uzbekistan may have been drawn to some of the central academic centers in Russia and other parts of the Soviet Union. Since the fall of the Soviet Union, these countries are reestablishing themselves as independent nations, and achievement in mathematics continues. For example, students from central Asia have participated in and won numerous medals in the International Mathematical Olympiad, an annual competition for high school students in which individual medals are awarded based on each student’s success in solving a set of mathematics problems. Countries send six-member teams.

Kazakhstan, Kyrgyzstan, and Turkmenistan first participated in 1993, Uzbekistan in 1997, and Tajikistan in 2005. In 2010, Kazakhstan hosted the 51st Olympiad in its capital of Astana. Students from 98 countries around the world participated. Professor Askar Dzhumadildayev noted, “Mathematics is one of the most important indexes of the education level in the country. Gathering the best young mathematicians in Astana is a great honor for us.” A news report regarding the Olympiad acknowledged the rich history of central Asia: “. . . we should not forget that our country is an heiress of the mathematical school founded by great scientists of the Middle Ages.… who greatly contributed to development of mathematics long before the modern countries of the West appeared.”

Bibliography

Bobojan, Gafurov. “Al-Biruni: A Universal Genius Who Lived in Central Asia 1000 Years Ago.” UNESCO Courier (June 1974). http://unesdoc.unesco.org/images/0007/000748/074875eo.pdf.

“The 51st International Mathematical Olympiad.” http://www.imo2010org.kz.

Matvievskaya, G. P. “History of Medieval Islamic Mathematics: Research in Uzbekistan.” Historia Mathematica 20 (1993).