Creation of Place Value System of Enumeration

In our twenty first century mathematics found themselves at a crossroads. While new rules of number arrangements, logic and calculation are invented and studied; one significant front remains unchanged, new numbers. One of the most important inventions in mathematics was the creation of place value system of enumeration, in other words the base ten system of calculation that uses nine numerals and zero to represent the set of numbers from the lowest to the highest value. The Greeks did not develop this system, because the largest number value was the myriad for them neither did Chinese since those had the largest unit of enumeration equal ten thousand.  It wasn’t also developed by the Arabs, though the system is often called Arabic numerals in Europe, where base ten system of calculation was first introduced in 13th century.

This system was developed in India, where, according to historians, it was of rather ancient origin. Yajurveda Samhitaa, one of the Vedic texts predating Euclid and the Greek mathematicians by at least a millennium tells us about the names for each unit number up to 10 to the twelve power. Later Buddhist and Jain increased the list up to 10 in fifty-third power.

The base ten system is actually built into Sanskrit language, where each power of ten received a different, original name. Not only are the units ten, hundred and thousand (daza, zata, sahasra) named as in English, but also ten thousand, hundred thousand, ten million, hundred million (ayuta, lakSa, koti, vyarbuda), and so forth up to the fifty-third power, providing distinct names where English makes use of auxiliary bases such as thousand, million, etc.

The purpose of giving al those names was to give no special significance to any number. Therefore the Sanskrit way is evidently more objective to that of the Arabs, or Chinese and Greeks and even to the contemporary system that we use every day. Indians did not name numbers in certain groups of three of four; instead they from a very early time expressed numbers taking the power of ten and names of first nine numbers. To put it simply, to express a certain number, one could just place the name indicating the order of units between the name of the order of units immediately below it and the one immediately above. This all that is needed to gain an exact idea of the base ten system, the rule goes in natural way and so is easy to understand. In other words, Sanskrit numeration had the key to the invention of base ten system.

As you can see, there is much evidence proving that the base ten system has originated in India, this system is embedded in the Sanskrit language, several aspects of which make it a very logical language, well suited to scientific and mathematical reasoning. This system is not everything that Indians produced as far as mathematics goes: Pingala, who lived circa the first century BCE, developed a system of binary enumeration convertible to decimal numerals. His system is very similar to Lebniz system that has lived hundred years later.

Another huge invention by Indians in mathematics is the invention of numeral zero. The most ancient text that contained zero is found in Jain text called the Lokavibhaaga, which has been definitely dated to Monday 25 August 458 CE. This invention together with the base ten system has given the start for classical era renaissance in Indian mathematics.

The Indian numeral system and its place value, decimal system of enumeration came to the attention of the Arabs in the seventh or eighth century, and served as the basis for the well known advancement in Arab mathematics, represented by figures such as al-Khwarizmi. It reached Europe in the twelfth century when Adelard of Bath translated al-Khwarizmi’s works into Latin. But the Europeans were at first resistant to this system, being attached to the far less logical roman numeral system, but their eventual adoption of this system led to the scientific revolution that began to sweep Europe beginning in the thirteenth century.


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