Aryabhata: the Aryabhatiya · Chapter 1 of 8

#Aryabhata and his book

#A book of 121 verses

The Aryabhatiya is one of the most important books in the history of science. It is very short — 121 verses, which fit on a few pages — and it sets out, in compressed verse, a complete system of mathematical astronomy: the numbers that govern the motions of the planets, the mathematics needed to use them, the reckoning of time, and the geometry of the heavens.

This book takes you through everything Aryabhata taught, section by section and verse by verse, in plain English. It keeps Aryabhata's teachings together, apart from those of the astrologers who came later. You do not need to have read anything else on this site first.

#Who he was

Aryabhata tells us almost nothing about himself — but he tells us his age at one exact moment:

When three yugapadas and sixty times sixty years had elapsed [from the beginning of the yuga], then twenty-three years of my life had passed (Kalakriya 10).

In his system, the present age (the Kali yuga) began in 3102 BCE. Three thousand six hundred years later is 499 CE, when he was twenty-three; so he was born in 476 CE. Some old commentators read the verse instead as fixing the date for which his tables were set; either way, the book belongs to about 499.

He wrote at Kusumapura, the ancient name of Pataliputra, near modern Patna in Bihar. In the opening verse of his mathematics he says he "sets forth here the science which is honoured at Kusumapura" (Ganita 1).

That is all we know for certain. Later writers attached many stories to him; this book keeps to what the text says.

#How the book is built

The Aryabhatiya has four sections (padas):

Aryabhata announces the plan in his opening verse: "Having paid reverence to Brahman ... Aryabhata sets forth three things: mathematics, the reckoning of time, and the sphere" (Dasagitika A).

The first section is called "the ten verses" although it has thirteen: an invocation, a verse explaining his number code, the ten verses of numbers, and a closing verse (Clark's note to Dasagitika A).

#The translation used here

This book follows the English translation of Walter Eugene Clark, Professor of Sanskrit at Harvard, published in 1930 as The Aryabhatiya of Aryabhata. Clark's notes are careful and honest: he often says plainly when the meaning of a verse is uncertain or when the commentators disagree. Verse references in this book follow his numbering: "Ganita 10" means the tenth verse of the mathematics section. Where Clark marks a reading as doubtful, this book says so too.

#A style built for memory

The verses are extremely compressed. Aryabhata expected a teacher to explain them, and a student to memorise them. A single verse may give a rule that takes a paragraph to explain in prose. He also invented a special code for writing large numbers in syllables (Chapter 2), so that a number of eight digits could be fitted into half a line of verse.

The traditional way to study the Aryabhatiya was with a commentary. Several survive. The greatest is that of Bhaskara I (7th century); later ones include those of Parameshvara (15th century) and Nilakantha Somayaji (around 1500) in Kerala. Clark used them, and this book mentions them where they help.

#How Aryabhata was received

The Aryabhatiya was admired and attacked. The astronomer Brahmagupta (628 CE) criticised Aryabhata repeatedly; Clark quotes his remark that what Aryabhata said about the setting of the planets "is false" (note to Gola 37, quoting Brahmasphutasiddhanta XI.9). Later astronomers rejected his rotating Earth (Chapter 7). But his school of astronomy lasted for over a thousand years, especially in Kerala, where it grew into the great mathematical tradition of Madhava and his followers.

Aryabhata himself was not modest about his achievement. He closes the book:

By the grace of God the precious sunken jewel of true knowledge has been rescued by me, by means of the boat of my own knowledge, from the ocean which consists of true and false knowledge (Gola 49).

#How to read this book

Each chapter gives Aryabhata's teaching in his own order, explains it in plain words, works examples where they help, and ends with a short summary and exercises.

#Summary

• The Aryabhatiya is a 121-verse book of mathematical astronomy, in four sections: Dasagitika, Ganita, Kalakriya, Gola.
• Aryabhata was born in 476 CE and wrote at Kusumapura (near Patna) about 499 (Kalakriya 10; Ganita 1).
• This book follows W. E. Clark's translation (1930) and his verse numbering.
• The work was studied with commentaries (Bhaskara I, Parameshvara, Nilakantha), criticised by Brahmagupta, and continued in Kerala for a thousand years.

#Exercises

1. How do we know when Aryabhata was born?
2. Name the four sections of the Aryabhatiya and their subjects.
3. Why is the first section called "the ten verses" when it has thirteen?
4. Why was the Aryabhatiya studied with a commentary?

Answers: 1. He says he was 23 when 3,600 years of the Kali yuga had passed (Kalakriya 10); with the Kali yuga starting in 3102 BCE that is 499 CE, so he was born in 476. 2. Dasagitika (the basic numbers), Ganita (mathematics), Kalakriya (time), Gola (the sphere). 3. Because ten verses give the numbers of the system; the invocation, the number-code verse and the closing verse are not counted. 4. Because its verses are extremely compressed and need explanation.