Mathematics is often one of the most dreaded and hated subjects in school. However, the people of ancient India absolutely loved the subject, and made great discoveries and inventions in it that have stood the test of time.

Stories of any genre catch my attention. Recently, I found an interesting piece revolving around mathematics. A little bit of research led to the complete story of Bhaskaracharya penning down the legendary *Lilavati*.

Those familiar with Bhaskaracharya would know that he was a distinguished mathematician and astronomer of Ancient India. *Lilavati* is the first volume of his principal work, the *Siddhant Shiromani. *It contains numerous word problems on arithmetic and geometry.

Lilavati, the daughter of Bhaskaracharya, was destined to die a spinster. To avoid this fate, Bhaskaracharya predicted an auspicious moment for her wedding. To alert her at the right time, he nailed a small hole in a cup and allowed it to float in a vessel filled with water.

## Lilavati was told not to go near it, lest it sink at the wrong time.

Curious as she was, she made her way up to the cup. As luck would have it, a pearl from her trousseau fell into the cup and upset its arrangement. The propitious moment thus passed, leaving Lilavati teary-eyed for the rest of her life. To help her come out of her grief, Bhaskaracharya granted her a second life in the form of a book in her name. Little did Lilavati know that the book would inspire generations of mathematicians to carve a niche for themselves in the world of numbers.

Ancient India was dotted with excellent mathematicians. There were no clear and distinct water tight compartments as far as knowledge was concerned. Mathematics for the Indians then was part-and-parcel of their everyday curriculum.

Here is a list of 17 riveting stories that remind us about the mathematical acumen of our ancestors:

## 1. It is said that the inhabitants of the land near the Saptah-Sindhu led a highly organized life. The drainage system, granaries, dockyards, and houses of the Harappan Civilization continue to astound archaeologists who find these constructions a geometrical marvel.

2. It has now been ascertained that geometry was first studied by ancient Indians – the synthetic approach to geometry can be traced back to the *Sulbasutras*.

3. *Ganita –* or mathematics – has been placed at the crest of all sciences as per the *Vedanga Jyotisha* that even goes to the extent of comparing it to the hood of snakes.

*4*. It goes without saying that it was Aryabhatta who calculated the value of pi to 3.1416 and the length of a solar year to 365.3586805.

5. Indians gifted the world with the zero, indispensable for our survival today.

6. An inscription from Allahabad is a testimony to the fact that the decimal system was in vogue in India as far ago as the 5th century AD.

7. Sridharacharya, a mathematician, used a rule to accurately determine the value of x from the equation ax^{2}+bx+c=0 – eventually recognized as the quadratic formula – around 1025 A.D.

## 8. Trigonometry originated in ancient India. Travelling from India to the Middle East, it reached Europe and people everywhere immediately adopted it.

10. We revere the *siddantas* (Sanskrit astronomical works) for their contribution towards the introduction of the sine function. Historians consider Aryabhatta, Brahmagupta, Bhaskara-I, and Bhaskara-II the chief exponents of trigonometry. Bhaskara-I gave the formulae to find values of sine functions for angles more than 90^{o} (obtuse angles). On the other hand, Bhaskara-II gave accurate expressions to calculate trigonometric ratios of acute angles such as 18^{o}, 36^{o}, 54^{o}, and 72^{o}.

11. The 24th *Tirthanakara* of the Jains, Vardhaman Mahavir, was a great mathematician. In his work, the *Ganitasara* *Sangarah*, he notes that a negative quantity has no square root. Bhaskara, author of the *Bijaganita*, seconded this view.

12. Mahavir and other Jain scholars considered the concept of permutations and combinations a distinct branch of mathematics, under the name of *Vikalpa*. We can also find the subject of permutations and combinations under the name of *Anka Pasha* in *Lilavati*, Bhaskaracharya’s scholarly work.

## 13. Sushruta, the renowned surgeon of ancient India, in his medicinal work, the *Sushruta Samhita,* gives 63 different combinations of the six primary tastes, namely *Amla* (sour), *Tikta* (bitter), *Kashay* (astringent), *Katu *(pungent), *Lavan* (salty), and *Madhur *(sweet).

14. Pascal’s Triangle, studied under the concept of the Binomial Theorem today, is similar to the *Meru-Prastara*, a diagram provided by Pingla in his book, the *Chhanda Shastra.*

15. Historians also credit Aryabhatta, Brahmagupta, Mahavir, and Bhaskara with formulating the sum of squares and cubes of numbers.

16. Aryabhatta discovered the formula to find sum of *n* terms of an arithmetic progression starting with the *pth* term.

17. As noted by the Greek scholar Megasthanese, Chandragupta Maurya ran an efficient system for administrative statistics about births and deaths. Kautilya’s masterpiece – also identified with Chanakya – *Arthashastra* also supported this view.

Ancient India has always been the subject of great speculation. However, there is no doubt that its people were brilliant mathematicians, and deserve every bit of admiration possible.

**You can read more about mathematics in Ancient India here, here, and here.**