Zero - Used before Aryabhatta

By Mitul Trivedi | Jan 09, 2019 | in Ancient Mathematics | Share

Zero vs. concept of zero. Who used it? How was it used? Read on to get a perspective on the history of zero.

I have always heard that zero was invented by the great Indian mathematics scholar, Aryabhatta. But is it true? 

Let us for a time being forget about who invented it. Let me provide 2 examples from Ramayana and Mahabharata.

 

  • Ramayana: Ravana had 10 heads.
  • Mahabharata: There were 100 Kauravas.

 

Aryabhatta was in the era of Kalyug. Ramayana took place in Treta Yuga. And Mahabharata took place in Dwapar Yuga.

 

If 0 / zero was invented in Kaliyug, how was it used and referenced so widely in treta and dwapar yugas?

 

The answer depends on how you define the word "invention". Aryabhatta utilized the concept of zero in his mathematical work, but he did not ascribe a symbol for it. The oldest documentation of the actual symbol "0" and the origin of the word zero comes from the Persian al-Khwarizmi about 450 years later.

 

Zero was invented independently by the Babylonians, Mayans and Indians (although some researchers say the Indian number system was influenced by the Babylonians). The Babylonians got their number system from the Sumerians, the first people in the world to develop a counting system. Developed 4,000 to 5,000 years ago, the Sumerian system was positional — the value of a symbol depended on its position relative to other symbols. Robert Kaplan, author of "The Nothing That Is: A Natural History of Zero," suggests that an ancestor to the place holder zero may have been a pair of angled wedges used to represent an empty number column. The Babylonians had symbols for one through to nine as vertical stylus marks. Ten was a horizontal mark. They then continued to add vertical marks to the right of the ten symbol, which got them up to nineteen. They then added another vertical symbol. There was room for about five horizontal marks, and then for sixty, they had to do something else. So, they had a space as a place holder for the 'ones' column, and one in the 'sixties' column. This was in about 3100 BC. However, Charles Seife, author of "Zero: The Biography of a Dangerous Idea," disagrees that the wedges represented a place holders. The Sumerians’ system passed through the Akkadian Empire to the Babylonians around 300 B.C. There, scholars agree, a symbol appeared that was clearly a placeholder — a way to tell 10 from 100 or to signify that in the number 2,025, there is no number in the hundreds column. Initially, the Babylonians left an empty space in their cuneiform number system, but when that became confusing, they added a symbol — double angled wedges — to represent the empty column. However, they never developed the idea of zero as a number.

 

Some scholars assert that the Babylonian concept wove its way down to India, but others give the Indians credit for developing zero independently. The concept of zero first appeared in India around A.D. 458. Mathematical equations were spelled out or spoken in poetry or chants rather than symbols. Different words symbolized zero, or nothing, such as "void," "sky" or "space." In 628, a Hindu astronomer and mathematician named Brahmagupta developed a symbol for zero — a dot underneath numbers. He also developed mathematical operations using zero, wrote rules for reaching zero through addition and subtraction, and the results of using zero in equations. This was the first time in the world that zero was recognized as a number of its own, as both an idea and a symbol. Perhaps the most fundamental contribution of ancient India to the progress of civilisation is the decimal system of numeration including the invention of the number zero. This system uses 9 digits and a symbol for zero to denote all integral numbers, by assigning a place value to the digits. This system was used in Vedas and Valmiki Ramayana.

 

Mohanjodaro and Harappa civilisations (3000 B.C.) also used this system. The ancient Egyptians (5000 B.C.) had a system based on 10, but they didn't use positional notation. Thus to represent 673, they would draw six snares, seven heel bones and three vertical strokes. Babylonians in Mesopotamia (3000 B.C.) had a sexagesimal system using base 60. Greeks and Romans had a cumbersome system (try to write 2376 in Roman numerals). Many civilisations had some concept of "zero" as nothing - for example, if you have two cows and they both die, you are left with nothing. However, the Indians were the first to see that zero can be used for something beyond nothing - at different places in a number, it adds different values. For example, 76 is different from 706, 7006, 760 etc. Brahmgupta (598 AD - 660 AD) was the first to give the rules of operation of zero.

 

A + 0 = A, where A is any quantity. 
A - 0 = A, 
A * 0 = 0, 
A / 0 = Not Defined

 

He was wrong regarding the last formula. This mistake was corrected by Bhaskara(1114 AD - 1185 AD), who in his famous book Leelavati, claimed that division of a quantity by zero is an infinite quantity or immutable God.

 

The ancient Indians represented zero as a circle with a dot inside. In Sanskrit, it was called "soonya". This and the decimal number system fascinated Arab scholars who came to India. Arab mathematician Al-Khowarizmi (790 AD - 850 AD) wrote Hisab-al- Jabr wa- al-Muqabala (Calculation of Integration and Equation) which made Indian numbers popular. "Soonya" became "al-sifr" or "sifr". The impact of this book can be judged by the fact that "al-jabr" became "Algebra" of today. An Italian Leonardo Fibonacci (1170 AD - 1230 AD) took this number system to Europe. The Arabic "sifr" was called "zephirum" in Latin, and acquired many local names in Europe including "cypher". In the beginning, the merchants used to Roman numbers found the decimal system a new idea, and referred to these numbers as "infidel numbers", as the Arabs were called infidels because they had invaded the holy land of Palestine. However, nowadays this system is called Hindu-Arabic System. This positional system of representing integers revolutionised the mathematical calculations and also helped in Astronomy and accurate navigation. The use of positional system to indicate fractions was introduced around 1579 AD by Francois Viete. The dot for a decimal point came to be used a few years later, but did not become popular until its use by Napier.

 

(From wikipedia:) The Mesoamerican Long Count calendar developed in south-central Mexico and Central America required the use of zero as a place-holder within its vigesimal (base-20) positional numeral system. Many different glyphs, including this partial quatrefoil——were used as a zero symbol for these Long Count dates, the earliest of which (on Stela 2 at Chiapa de Corzo, Chiapas) has a date of 36 BC. Since the eight earliest Long Count dates appear outside the Maya homeland, it is generally believed that the use of zero in the Americas predated the Maya and was possibly the invention of the Olmecs. Many of the earliest Long Count dates were found within the Olmec heartland, although the Olmec civilization ended by the 4th century BC, several centuries before the earliest known Long Count dates. Although zero became an integral part of Maya numerals, with a different, empty tortoise- like "shell shape" used for many depictions of the "zero" numeral, it is assumed to have not influenced Old World numeral systems. (upto here from wikipedia)

 

By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (a small circle with a long overbar) in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest. The way in which it is used can be seen in his table of chords in that book. Ptolemy's zero was used within a sexagesimal numeral system otherwise using alphabetic Greek numerals. Because it was used alone, not just as a placeholder, this Hellenistic zero was perhaps the first documented use of a number zero in the Old World.

 

Another zero was used in tables alongside Roman numerals by 525 (first known use by Dionysius Exiguus), but as a word, nulla meaning "nothing", not as a symbol. When division produced zero as a remainder, nihil, also meaning "nothing", was used. These medieval zeros were used by all future medieval computists (calculators of Easter). The initial "N" was used as a zero symbol in a table of Roman numerals by Bede or his colleague around 725.

 

If we really want to give credit for the concept, we need to go back a hundred years before Aryabhatta to the Mayans or 700 years back to the Babylonians. Although, it is fair to say that our use of the concept comes from Aryabhatta.