**THE INDUS VALLEY CIVILIZATION**

**WAS A PART OF THE ADVANCED VEDIC CULTURE**

Besides what we have already discussed, more light is shed on the advanced civilization of the Indus Valley and how it influenced areas beyond its region when we consider the subject of Vedic mathematics. E. J. H. Mackay explains in his book, *Further Excavations at Mohenjo‑Daro*, that the whole basis of Vedic mathematics is geometry, and geometrical instruments have been found in the Indus Valley which date back to at least 2800 B.C. The Vedic form of mathematics was much more advanced than that found in early Greek and Egyptian societies. This can be seen in the *Shulbasutras*, supplements of the *Kalpasutras*, which also show the earliest forms of algebra which were used by the Vedic priests in their geometry for the construction of altars and arenas for religious purposes. In fact, the geometrical formula known as the Pythagorean theorem can be traced to the *Baudhayans*, the earliest forms of the *Shulbasutras* dated prior to the eighth century B.C.

The *Shulbasutras* are the earliest forms of mathematical knowledge, and certainly the earliest for any religious purpose. They basically appear as a supplement to the ritual (*Shrauta*) aspect of the *Kalpasutras*. They essentially contain the mathematical formulas for the design of various altars for the Vedic rituals of worship, which are evident in the Indus Valley sites.

The date of the *Shulbasutras*, after comparing the Baudhayana, Apastamba and Katyayana *Shulbas** *with the early mathematics of ancient Egypt and Babylonia, as described by N. S. Rajaram in *Vedic Aryans and The Origins of Civilization* (p.139), is near 2000 B.C. However, after including astronomical data from the *Ashvalayana** Grihyasutra*, *Shatapantha** Brahmana*, etc., the date can be brought farther back to near 3000 B.C., near the time of the *Mahabharata* War and the compilation of the other Vedic texts by Srila Vyasadeva.

With this view in mind, Vedic mathematics can no longer be considered as a derivative from ancient Babylon, which dates to 1700 B.C., but must be the source of it as well as the Greek or Pythagorean mathematics. Therefore, the advanced nature of the geometry found in the *Shulbasutras* indicates that it provided the knowledge that had to have been known during the construction of the Indus sites, such as Harappa and Mohenjo-Daro, as well as that used in ancient Greece and Babylon.

It is Vedic mathematics that originated the decimal system of tens, hundreds, thousands, and so on, and in which the remainder of one column of numbers is carried over to the next column. The Indian number system was used in Arabia after 700 A.D. and was called Al‑Arqan‑Al‑Hindu. This spread into Europe and became known as the Arabic numerals. This, of course, has developed into the number system we use today, which is significantly easier than the Egyptian, Roman, or Chinese symbols for numbers that made mathematics much more difficult. It was the Indians who devised the methods of dividing fractions and the use of equations and letters to signify unknown factors. They also made discoveries in calculus and other systems of math several hundred years before these same principles were understood in Europe. Thus, it becomes obvious that if the Europeans had not changed from the Roman numeral system to the form of mathematics that originated in India, many of the developments that took place in Europe would not have been possible. In this way, all evidence indicates that it was not any northern invaders into India who brought or originated this advanced form of mathematics, but it was from the Vedic Aryan civilization that had already been existing in India and the Indus Valley region. Thus, we can see that such intellectual influence did not descend from the north into India, but rather traveled from India up into Europe.

Additional evidence that it was not any invaders who originated the highly advanced Vedic culture in the Indus Valley is the fact that various seals that Waddell calls Sumerian and dates back to 2800 B.C. have been found bearing the image of the water buffalo or Brahma bull. Modern zoologists believe that the water buffalo was known only to the Ganges and Brahmaputra valleys and did not exist in Western India or the Indus Valley. This would suggest a few possibilities. One is that the Sumerians had traveled to Central and Eastern India for reasons of trade and for finding precious stones since Harappa was a trading center connected by way of the Indus River with the gold and turquoise industry of Tibet. Thus, they learned about the water buffalo and used images of them on their seals. The second and most likely possibility is that the Aryan civilization at the time extended from Eastern India to the Indus region and farther west to Mesopotamia and beyond, and included the Sumerians as a branch. So, trade and its Vedic connections with India naturally brought the image of the water buffalo to the Indus Valley region and beyond.

Further evidence showing the Vedic influence on the region of Mohenjo-Daro is a tablet dating back to 2600 B.C. It depicts an image of Lord Krishna as a child. This positively shows that the Indus Valley culture was connected with the ancient Vedic system, which was prevalent along the banks of the Rivers Sarasvati and Sindhu thousands of years ago.

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