Bharatiya Mathematics

The history of mathematics in India goes back over 3000 years. The ancient Indian mathematical works were composed in sūtras in Sanskrit language in verse form to aid memorization. These were followed by prose commentary that explained the problem in more details and provided justification for the solution. All mathematical works were orally transmitted until 500 BCE and thereafter, they were transmitted both orally and in manuscript form. There are about 30 million manuscripts in India today – the largest body of handwritten material anywhere in the world.

In the classical period of Indian mathematics (400 BCE to 1200 CE), important contributions were made by many scholars including: Aryabhata, Pingala, Brahmagupta, Bhaskara I, Bhaskara II, Hemachandra, Katyana, Shridhara, Virahanka, Varahamihira, Apastamba, Baudhayana, manava, Yativrsabha, Pavulur, Mallana, and Panini. The Indian scholars made seminal contribution in developing the decimal number system, concept of zero as a number, negative numbers, arithmetic, algebra, geometry and trigonometry. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics.

Mathematics is the backbone of science. Recognizing the seminal contributions by India, the famous scientist, Albert Einstein had this to say: “We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.” _ Albert Einstein

The earliest mathematical prose commentary was written by Aryabhata in 499 CE, known as Āryabhaṭīya, a work on astronomy and mathematics. It included Ganita (Mathematics), Kala-kriya (Time calculations), and Gola (Sphere- dealing with astronomy). In Ganita Aryabhata names the first 10 decimal places and provides algorithms for obtaining square-roots and cube-roots. He treats geometric measurements, using the value of Pi π (62,832/20,000 = 3.1416). In Kala-kriya Aryabhata defined various units of time, eccentric and epicyclic models of planetary motion. He ends with spherical astronomy in Gola, where he applied plane trigonometry to spherical geometry by projecting points and lines on the surface of a sphere onto appropriate planes. It included prediction of solar and lunar eclipses.

Brahmagupta (598 – 668 CE) in his book Brahmasphutasiddanta provides rules for arithmetic manipulations that apply to zero and negative numbers. He is the first person to treat zero as a number in its own right not just as a place holder. He also made important contributions in Algebra, Geometry and Trigonometry. He also contributed in astronomy. His mathematical advances were carried further by Bhaskara II (1114 – 1184 CE) who filled the gaps like division by zero equals infinity.

Important contributions have been made by all the mathematicians whose names have been mentioned above. One of the names that is not mentioned above is that of Srinivasa Ramanujan (1887 – 1920). Though he had no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. In 1913 he began to write to British mathematician G. H. Hardy at the University of Cambridge, in UK. Professor Hardy, recognizing the research of Ramanujan, brought him over to England and published joint papers with him. Ramanujan became one of the youngest Fellow of the Royal Society and was elected a Fellow of Trinity College, Cambridge. He was a deeply religious man, a staunch Hindu. He said that Goddess Managiri Thayar reveals to him the mathematical knowledge. He died very young at the age of 32 only. A movie was made in 2014 on his life biography.

Recent developments

Vedic mathematics – is the rediscovery of the ancient Indian mathematics based on Vedas by Sri Bharati Krsna Tirthaji (1884 – 1960), who was the Shankaracharya of the Govardhana Math in Puri, Odisha from 1925 to 1960. He composed 16 sūtras for performing various mathematical calculations in very simple form. This allows the calculations to be done mentally. To get a good idea about Vedic mathematics please go to their website: https://www.vedicmaths.org/. On this website you can find the online tutorials and courses available. In fact, there is wealth of material available there. I would urge you to please have a look at the website. There are schools teaching Vedic math worldwide. In Australia, please look at the Vedic Maths Forum Australia website: http://www.vedicmaths.com.au/. You can help school going children to learn mathematics more easily. In India, the book on Vedic maths has been included in the school syllabus of Madhya Pradesh and Uttar Pradesh.

Podometic Project – Jonathan J. Crabtree, an Australian mathematician has started this project to bring back the Indian Maths. He has found some shortcomings in the treatment of zero and negative numbers in basic mathematical calculations, ignoring how Brahmagupta defined them and gave his rules for calculations. This leads to difficulties for the young students. He is proposing to modify the current system introduced by the British, who were not aware of Brahmgupta’s postulations in this regards. You can look at his website: www.podometic.in , where he has posted his papers on the subject. He is petitioning the Indian government to trial Bharatiya Maths as a part of India’s new National Education Policy.

I propose that Indian government should also consider including Vedic Mathematics also in the new National Education policy.

– Vijai Singhal