Mathematics of Southern Asia

Summary: Southern Asia’s history of mathematics reaches back thousands of years and mathematics continues to be a priority.

Southern Asia has a rich tradition in mathematics. Persian, Hindu, and Vedic scholars, among others in this area, contributed to the body of mathematics knowledge. Some of the achievements that have been historically credited to Arabic or Islamic mathematicians may have been influenced by pre-Islamic Persia. From ancient times, the rise and fall of various empires, wars, migration, and colonial influences have resulted in shifting cultural and geographical boundaries. As a result, many countries and regions in southern Asia have changed over time. The United Nations statistical classification for southern Asia contains Afghanistan, Bangladesh, Bhutan, India, Iran (Islamic Republic of), the Maldives, Nepal, Pakistan, and Sri Lanka. In the twenty-first century, these Asian nations continue to make advances in mathematics and mathematics education.

History

Construction of many ancient temples or monuments in southern Asia clearly involved mathematical knowledge, and mathematicians from this time period made various contributions to mathematics. One example is Indian scholar Baudhayana, who lived around 800 b.c.e. and is credited by some with developing the Pythagorean theorem, although others feel he was reflecting Babylonian work. The Vedic priest Katyayana, who lived approximately six centuries later, appears to have been interested in mathematics for religious purposes. Panini (520–460 b.c.e.), born in Shalatula, now part of Pakistan, wrote a scientific theory of Sanskrit. Some historians have theorized that development of algebraic structures and number systems in this region may be tied to the linguistic structure of Sanskrit. Panini’s work also influenced computer languages. Aryabhata (476–550) wrote a mathematical text known as the Aryabhatiya. It is composed of 123 metrical stanzas, whose organization has been studied by mathematicians because it differs from later mathematical works in many traditions. Some historians believe that it was influenced by Mesopotamia, while others suggest that it might be an anthology of works by earlier mathematicians. Another text, the Bakhshali manuscript, discovered in 1881 near Peshawar in present-day Pakistan, is believed to date from the seventh century, although some experts have dated it to up to eight centuries earlier or five centuries later.

By medieval times, Indian mathematicians had developed the notion of zero as a number, the use of negative numbers, and the definitions of sine and cosine. Some early Indian poetry also shows evidence of the binary number system and the use of decimal numbers. Mathematician Abd Al-Hamid ibn Wasi ibn Turk Al-Jili (c. ninth century) is believed to have been born in Iran, Afghanistan, or Syria. He wrote an algebra book. Persian mathematician, poet, and astronomer Omar Khayyam (1048–1141) wrote books on arithmetic and algebra by the age of 25 and contributed to many mathematical areas. Mathematician Nasir al-Din al-Tusi (1201–1274) was born in the city of Tus, now in Iran. He wrote Arabic translations of several Greek mathematical texts and is also credited with developing planar and spherical trigonometry from what many considered an astronomical tool into a separate mathematical discipline. Ghiyath al-Din Jamshid Mas’ud al-Kashi (1380–1429) was born and worked in Kashan, now in Iran. His Treatise on the Circumference included a calculation of π, which exceeded any known precision at the time. He also authored a teaching text called The Key to Arithmetic.

Education

Mathematics education has long been a focus in southern Asia. Mathematics was a part of garakula residential schools in ancient Nepal and India. From the fourteenth century, what became known as the “Kerala school of astronomy and mathematics” emerged in southern India. There was a flourishing of new discoveries, including the use of calculus long before it was developed by Isaac Newton and Gottfried Leibniz. These developments continued under mathematicians such as Citrabhanu (c. 1530) and Jyesthadeva (c. 1500–1575). English scholar Charles Whish (1794–1833) publicized many of the Kerala achievements to the rest of the world. Even then, the work of Whish—primarily a collector of Sanskrit manuscripts—was largely unknown beyond the scholarly community until the Indian mathematicians K. M. Marar and C. T. Rajagopal were able to demonstrate the advances made in Kerala just prior to the establishment of the European colonial empires in India.

British colonialism brought some European teaching styles into areas of southern Asia, and many universities were founded in the nineteenth century. Also in the nineteenth century, some Nepalese students traveled to India to study, where they were exposed to texts like Bhaskaracharya II’s (1114–1185) Siddhanta Siromani. French mathematics traditions were introduced to southern Asia by Father Racine (1897–1976), a Jesuit missionary who had previously earned a doctorate in mathematics. With Indian colleagues such as Ramaswamy Vaidyanathaswamy (1894–1960), he promoted “modern” or contemporary mathematics teaching versus solely classical mathematics in the twentieth century. Indo-French collaborations continue to flourish into the twenty-first century and have been cited as contributing to development of areas like algebraic geometry and theoretical partial differential equations in southern Asia. There were other well-known collaborations, such as that between Indian mathematician Srinivasa Ramanujan and British mathematician Godfrey (G. H.) Hardy. In the 1980s, the Maldives introduced a new school curriculum that increasingly emphasized the importance of a variety of subjects, including mathematics.

Researchers in southern Asia have investigated a wide variety of different curricular issues such as gender differences in mathematics in Pakistan. King of Bhutan Jigme Khesar Namgyel Wangchuck noted in 2009:

In all the countries where progress has been strong in the areas we strive to develop, the strength of the education system has been in Math and Science. In fact in India, the favourite subject for most students is Mathematics. In Bhutan, Mathematics is one of our main weaknesses.

Students from Bangladesh, India, Iran, Pakistan, and Sri Lanka have competed in the International Mathematics Olympiad: Iran since 1985, India since 1989, Sri Lanka since 1995, and Bangladesh and Pakistan since 2005. Mumbai, India, hosted the Olympiad in 1996.

Bibliography

Dauben, Joseph W., and Rohit Parikh. “Beginnings of Modern Mathematics in India.” Current Science 99, no. 3 (August 10, 2010). http://www.ias.ac.in/currsci/10aug2010/suppl/15.pdf.

Jha, K., P. R. Adhikary, and S.R. Pant. “A History of Mathematical Sciences in Nepal.” Kathmandu University Journal of Science, Engineering and Technology II, no. 1 (2006). http://www.ku.edu.np/kuset/second‗issue/e2/KANAIYA%20JHa-pdf.pdf.

Joseph, George. The Crest of the Peacock: Non-European Roots of Mathematics. 3rd ed. Princeton, NJ: Princeton University Press, 2011.

Katz, Victor. The Mathematics of Egypt, Mesopotamia, China, India, and Islam. Princeton, NJ: Princeton University Press, 2007.

Waldschmidt, Michel. “Indo–French Cooperation in Mathematics.” Mathematics Newsletter of the Ramanujan Mathematical Society 19, Special Issue 1 (2010) http://www.math.jussieu.fr/~miw/articles/pdf/IndoFrenchCooperationMaths.pdf.