Aryabhatta, also called Aryabhatta I was born possibly around 476 C.E. around the regions of the Godavari river. Aryabhatta was one of the earliest Indian mathematicians and astronomers whose pioneering work in these fields is still referenced by many modern scholars.
Aryabhatta’s magnum opus is his treatise in mathematical and astronomical observation, named Aryabhatiya.
The work in Aryabhatiya is so extensive and detailed that it was years ahead of any work of the time. With so much wisdom compiled in one single book, let’s have an insight into the book and how its composer created it.
- Aryabhatta was only 23 when he composed the Aryabhatiya. Before the book, there were Vedic scriptures which detailed mathematical relationships in geometrical shapes for the construction of altars and temples.
There were also other Jain mathematicians whose work also contributed to mathematics. But what makes Aryabhatiya so different is the way it was written.
The entire script was written in Sanskrit and hence reads like a poetic verse rather than a practical manual. There are exactly 123 stanzas in the book and without a tutor, the book would seem ambiguous.
- The book is divided into four sections– Gitikapada, Ganitapada, Kalakriyapada and the Golapada, each covering various fields.
Gitikapada dealt with time, especially large units of time. Ganitapada covered mathematics of measurement, arithmetic and geometric progressions.
Kalakriyapada told how one could determine the positions of the planet for any given day and finally, Golapada dealt with the earth’s shape and its celestial presence.
- At the time, word numerals were only used to denote numbers. These are like the Roman numerals with words to describe the number. But Aryabhatiya is the oldest book ever to use alphabetic numerals.
That means Aryabhatta used letters of the alphabet to form number-words, with consonants giving digits and vowels denoting place value of those digits. This allowed him to do complex calculations of large numbers and even execute divisions.
- Talking about numerals, Aryabhatta was known to develop the zero. But in this book, he never uses the digit. In fact, Aryabhatta did not invent the zero but came up with the concept of zero.
Zero, meaning nil, is both a number and a concept. Although Aryabhatta never used zero numerically, he did use a placeholder for the power of tens. This is implicit that zero was a concept that Aryabhatta was well aware of.
- In Aryabhatta’s time, the common notion was that the earth was the centre of the universe and everything revolved around it. This is called the geocentric model.
But in Aryabhatiya, the astronomical observations by the mathematician is ingenious. He describes the heliocentric model, where the earth revolves around the sun, 1,000 years before Copernicus proposed his theory in 1543.
This proposal by Aryabhatta was so controversial at the time that there were books by other mathematicians trying to rebuke his theory. All in vain, we suppose.
- Along with this, Aryabhatta deduced the approximate value for Pi. Again, a feat no one at the time had even come close to. His approximation was close to five digits whereas Archimedes’ approximation was only to four digits.
Though these seem way too ordinary for us in the age of computers, do remember that this was when metal horseshoes were becoming common.
- In his book, Aryabhatta formulated the sine table which is believed to be the first ever sine table constructed in the history of mathematics.
The sine table consisted of 24 values which were derived from the computation of half chords of a circle. To derive the values, Aryabhatta had to use alphanumeric words in his formulation. What looks simple to us, was ingenious for that time.
How Aryabhatta derived the table still leaves mathematicians dumbfounded for he doesn’t explain his derivation in detail.
- In the book, Aryabhatta derives the revolutions of the sun, the moon and of the earth as well. He also derives square and cube roots with precision. He also directly correlated the area of a geometric shape to its volume. A correlation that Greek mathematicians were yet to make.
Aryabhatta also explained why the moon shone and said it was because of the sunlight bouncing from it and that it had no illuminating property to it.
Aryabhatta derived the size of the earth by studying shadows cast onto its surface. He also explained how eclipses occurred with a proper computation of shadows with his angle-measuring device.
The book is one the earliest mathematical scripts that explain various mathematical topics at length. The book, if used in the technical studies of that time, would have helped in the advancement of humankind. Aryabhatta was truly a mathematical pioneer.
(Edited by Shruti Singhal)