Mathematics, History and worms eating manuscripts…

इन्द्र: वायुर्यमश्चैव नैरृतो मध्यमस्तथा ।
ईशानश्च कुबेरश्च अग्निर्वरुण एव च ॥

The one given above is one such, composed by Leelavati. When one learns Sanskrit, there is a problem. Words spill over into one another, following the rules of grammar. Because one doesn’t know how to break them up, one can’t understand. Once you learn how to break things up, it becomes simpler. Let me break up the one given above.

इन्द्रो वायु: यम: च एव नैरृतः मध्यम: तथा ।
ईशान: च कुबेर: च अग्नि: वरुण: एव च ॥

So far, so good. But I couldn’t figure this one out. Why was this important enough to be written down in the form of a shloka? It is just the names of various gods. Actually, not just any gods. This gives the names of lokapalas. Lokapalas are protectors or guardians of the world. There are 10 directions. If you leave out above and below, there are 8. These are north, north-east, east, south-east, south, south-west, west and north-west. North, south, east and west have specific Sanskrit names as directions. But we will place that on hold. Look at the matrix below. Vayu is the guardian of the north-west, Kubera of the north, Ishana of the north-east, Indra of the east, Agni of the south-east, Yama of the south, Nairrita of the south-west and Varuna of the west. You get the idea. It is because Yama, the lord of the death, is the guardian of the south that there is a belief that you should not sleep with your feet pointing towards the south. You will offend Yama.

Vayu Kubera Ishana
Varuna Indra
Nairrtta Yama Agni
But what’s the point of the shloka? Why write out a shloka that only lists the names of the lokapalas? We know their names. Wait. Now follow the order listed by Leelavati, Indra is the first, Vayu is the second, Yama is the third and so on. Madhyama means middle, there is no guardian there. Fill in the matrix below in the order in which Leelavati has listed the names.

2 7 6
9 5 1
4 3 8

At the end of this painstaking research, the first kosa or dictionary of Sanskrit to English mathematical terms is ready and there are four more to follow. This central government project is being touted as the first of its kind in the world as never before have the Indian etymology of so many modern technical terms been so radically established.

The project was given to these scholars by the Rashtriya Sanskrit Sansthan, a wing of the ministry of human resources development, through the city-based Sanskrit Sahitya Parishat. The chief investigators of the project are retired faculty members of Jadavpur and Calcutta universities, Manabendu Banerjee and Pradip Kumar Majumdar, respectively.

While the world gives credit to India for invention of the concept of ‘zero’, not much else in modern maths is attributed to this country. “Also, while it is generally believed that it was the fifth century AD mathematician Aryabhatta who invented zero, we have been able to establish in our project that zero or ananta was a concept as old as the Rig Veda. Similarly, eka or number one also has roots in this Veda,” explained Majumdar.

All branches of mathematics are well represented in the Vedas, Aranyakas, Brahminical literature, Upanishads, Panini’s Ashtadhyayi and Yaska’s Nirukto, the dictionary explains. It goes on to prove that most solutions that can be arrived through algebra, geometry and trigonometry have Sanskrit roots. Thus, what the world knows as Pythagoras’ theorem existed in the Sulbasutras provided in the manuscripts of Boudhayan, Apostombo, Manaba and Katyayan. A large number of formulae developed thousands of years ago, which lead to the same assumption as modern theorems, have been provided in the dictionary, with their places of occurrence in Indian punthis.

“Take the case of Euclid’s concepts, on which modern geometry is based. You will find that all of today’s geometric shapes and angles were present in the way the yajnabedis or the holy sacrificial fires were erected. Each design had a typical astronomical or cosmic meaning to it and a specific purpose for which the yajna was to be conducted,” explained Banerjee, who is also the former vice-president of Asiatic Society. The dictionary is replete with the designs of these yajnabedis and go on to explain their modern geometrical equivalents. The additional benefit is that the ancient custom and belief system surrounding these bedis have also been explained in the dictionary. It says that the origin of most of these designs can be found in Vedanga Jyotish of 12th century BC.