A rare Tamil translation of Aryabhata

Ganita or mathematics is one of the three chapters of 'Aryabhateeyam'. The book 'Aryabhatarin Ganitam' by Badri Seshadri focuses on this part. The author has treated each stanza as a chapter, explaining the method and nuances, and pointed out errors.

ByR Gopu

Published Jan 20, 2023 | 11:03 AM Updated Jan 20, 2023 | 11:16 AM

'Aryabhatarin Ganitam', a Tamil translation of Aryabhatta's mathematics by Badri Seshadri

Aryabhata was translated into Arabic in the eighth century by ibn Fazari. His ideas, algorithms, algebra (bija-ganita in Sanskrit), and subsequent developments by Arabs were translated into Latin by Leonardo Fibonacci in the 12th century.

This spread across Europe after their Renaissance and Enlightenment. These returned to India during British rule, with Europeanised names.

Aryabhata’s work in Tamil

There are English, French, German, and perhaps several other translations of his work. But I think Badri Seshadri’s book Aryabhatarin Ganitam is the first Tamil translation of Aryabhata in 1,500 years. A historic achievement!

Ganita or mathematics is one of the three chapters of the book Aryabhateeyam, the other two being Kaalakriyaa (Time) and Gola (Celestial Sphere). The author has focused on only Aryabhata’s mathematics in this Tamil translation.

Each sloka or verse gives a formula (e.g. areas of triangles, circles), an axiom, a table (e.g. a series of sines), or a procedure (e.g. calculating square roots, cube roots).

Here is a link to an article by the author in Tamil on calculating square roots as taught in schools and the method used by Aryabhata. The video version of the latter is below:

Each stanza as a chapter

Most readers will be shocked to find out how much of the mathematics they learnt in school is Indian, but is taught anonymously, while all European theorems and formulae are presented with the names of their inventors.

Aryabhata uses these for astronomy, but they are applicable in general mathematics. What Aryabhata explained, in a stanza or two, was explained in whole chapters by later Indian mathematicians like Brahmagupta and Bhaskara, often with their own additional discoveries and alternative methods.

The author Badri has also treated each stanza as a chapter in his Tamil work on Aryabhata, explaining the method and nuances, and pointed out errors in very simple language. He has also mentioned later developments where appropriate. In some chapters, he has included the original stanzas and word-by-word meaning too.

Aryabhata’s Ganitam is historically important because most of the mathematics we learn is Indian, developed in the few centuries after the invention of zero and the place value system, around his era.

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Kuttaka, an ingenious yet simple algorithm

The kuttaka segment will be of great interest to algebraists. It is not taught in any school, but was a fundamental algorithm of Indian astronomy for centuries. It solves a class of problems called simultaneous linear indeterminate equations.

Most schools teach determinate equations, but none deal with indeterminate equations. Kuttaka is ingenious yet simple, a brilliant recursive algorithm, to solve a tricky problem.

There are not many books in Tamil that explain mathematics, especially any maths discovered by Indians. Let us hope that this remarkable book becomes popular.

(The book is available in the ongoing Chennai Book Fair 2023 at Kizhakku Pathippagam and several other stalls. Cost: ₹110)

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(R Gopu is part of the Tamil Heritage Trust (THT), and is interested in history and heritage. He is also one of the co-founders of the Varahamihira Science Forum

He is also one of the speakers in the 4th edition of India Science Festival (ISF 2023) that is being held from 20–22 January in Hyderabad)