In ancient India, Mathematics was considered to be the mother of all sciences. It helped in understanding astronomical phenomena and thus aided in the development of calendars and determining the timing of festivals and determining auspicious times for rituals and events. Ritual altars and building construction (to be built according to vastu shaastra) had to be built to stringent specifications for them to have the properties desired. Mathematics and geometry enabled the construction to these specifications.
Unlike today, we have not been able to determine how detailed professions were separated in Ancient India. As a result, most mathematicians are considered to be priest-mathematicians or rishis who also focused on mathematics, etc.
Religion and mathematics
According to the Vedic world view, one can also come to understand the intricacies of the phenomenal world while culturing transcendental knowledge. By the process of knowing the absolute truth, all relative truths also become known. In modern society today, it is often contended that never the twain shall meet: science and religion are at odds. This erroneous conclusion is based on understanding of Abrahamic faiths which are constantly at odds with science. In Sanatana Dharma, science is a small circle within the larger circle of spirituality.
Mathematics served as a bridge between understanding material reality and the spiritual conception. Vedic mathematics differs profoundly from Greek mathematics in that knowledge for its own sake (for its aesthetic satisfaction) did not appeal to the Hindu mind. Vedic mathematicians strongly felt that every discipline must have a purpose, and believed that the ultimate goal of life was to achieve self-realization and self-perfection-as a result, mathematics were often presented in a very different format. Most mathematics was presented using the Sutra method where there would be a list of laws and each law would borrow data/authority from a super-ceding law. These lists were compressed into small poems - with the first and last word and the length of the rule-similar to how hashing based indexing works in Computer Science today. Those practices which furthered this end either directly or indirectly were practiced most rigorously .
In order to illustrate how secular and spiritual life was intertwined in Vedic India, Bharati Krishna Tirtha Maharaja has demonstrated that mathematical formulas and laws were often taught within the context of mantra. Thus while learning spiritual lessons; one could also learn mathematical rules.
Numbers in Sanskrit
Bharati Krishna Tirtha Maharaja has pointed out that Vedic mathematicians preferred to use the devanâgarî letters of Sanskrit to represent the various numbers in their numerical notations rather than the numbers themselves, especially where large numbers were concerned. This made it much easier for the students of this math in their recording of the arguments and the appropriate conclusions. Maharaja wrote,
“In order to help the pupil to memorize the material studied and assimilated, they made it a general rule of practice to write even the most technical and abstruse textbooks in sutra or in verse (which is so much easier-even for the children to memorize). And this is why we find not only theological, philosophical, medical, astronomical, and other such treatises, but even huge dictionaries in Sanskrit verse! So from this standpoint, they used verse, sutra and codes for lightening the burden and facilitating the work (by versifying scientific and even mathematical material in a readily assailable form)!”
|Sanskrit Consonant||Denotes Number|
|ka, ta, pa, ya|
|kha, tha, pha, ra|
|ga, da, ba, la|
|Gha, dha, bha, va|
|jña, na, ma|
|ca, ta, sa|
|cha, tha, and sa|
|ja, da, and ha|
|jha and dha|
Vowels make no difference and it is left to the author to select a particular consonant or vowel at each step. This great latitude allows one to bring about additional meanings. For example kapa, tapa, papa, yapa all mean 11. By a particular choice of consonants and vowels one can compose a poetic hymn with double or triple meanings.
Value of Pi
Here is an actual sûtra of spiritual content, as well as secular mathematical significance:
gopi bhagya madhuvrata sringiso dadhi sandhiga khala jivita khatava gala hala rasandara
While this verse is a type of petition to Krishna, when learning it one can also learn the value of pi/10 (i.e. the ratio of the circumference of a circle to its diameter divided by 10) to 32 decimal places. It has a self-contained master-key for extending the evaluation to any number of decimal places.
The translation is as follows:
O Lord anointed with the yogurt of the milkmaids' worship (Krishna), O savior of the fallen, O master, please protect me
At the same time, by application of the consonant code given above, this verse directly yields the decimal equivalent of pi divided by 10:
pi/10 = 0.31415926535897932384626433832792
Thus one can memorize significant mathematical facts while offering praise to God in devotion.
Representation of Large Numbers
The place value system is built into the Sanskrit language, whereas in English we only use thousand, million, billion etc. In Sanskrit, there are specific nomenclature for the powers of 10, the most used in modern times are dasa (10), sata (100=10^2), sahasra (1,000 = 10^3), ayuta (10,000 = 10^4), laksha (100,000 = 10^5), niyuta (1 million = 10^6), koti (10 million = 10^7), vyarbuda (100 million = 10^8), paraardha (1 trillian = 10^12) etc.
Results of such a practice were two-folds.
- The removal of special importance of numbers - Instead of naming numbers in groups of three, four or eight orders of units, one could use the necessary name for the power of 10.
- The notion of the term "of the order of" - To express the order of a particular number, one simply needs to use the nearest two powers of 10 to express its enormity (ie: koti koti (10^7 * 10^7 = 10^14)).
- Mathematics of the Vedas
- Mathematics of the Indus-Saraswati Civilization
- Mathematics in the classical era (500 - 1200 CE)
- Mathematics in the post-classical era (900 - 1800 CE)
- Mathematics in the modern era
- Computing Science in Ancient India, edited by TRN Rao, Subash Kak, Center for Advanced Computer Studies, University of Southwestern Louisiana, 1998
- Jagadguru Swami Shri Bharati Krishna Tirthaji Maharaja, "Vedic Mathematics", Motilal Banarsidass, Delhi, 1988