Evolution of Zero: From Ancient Origins to Modern Mathematics

Evolution of Zero: From Ancient Origins to Modern Mathematics

The number 0 (zero) that we use every day was a number that people in the past could not even imagine. The concept of zero is a numerical digit that represents the absence of value or a placeholder. It is a fundamental concept in mathematics. The Indian subcontinent played a significant role in the development of zero as a numerical digit. It was invented by Brahmagupta, a renowned Indian mathematician and astronomer who lived in the 7th century CE.

The concept of zero is known as “shunya” in Sanskrit, which first appeared in ancient Indian texts such as the Bakhshali Manuscript, which dates back to the 3rd to 4th century CE. Aryabhata and Brahmagupta, two Indian mathematicians are the reason behind investing in the digit zero. They understand the concept of 0 and use zero in mathematical calculations.

History of Zero

Aryabhata was a renowned Indian mathematician and astronomer who belonged to the 5th century CE. He describes the zero as a numeral and its use in the mathematical concept. He used the zero as a value in his decimal numeral system for more efficient mathematical operation. Where Brahmagupta, another prominent Indian mathematician developed the concept of zero and provided rules to use in the mathematical concept of operation. He involved zero in his treatise “Brahmasphutasiddhanta.” He also discussed the properties of zero, such as its role in multiplication and division.

Brahmagupta’s Treatise – “Brahmasphutasiddhanta”, which means  “The Corrected Treatise on Brahma’s Doctrine,” is the most famous work by Brahmagupta who served as a comprehensive treatise on mathematics and astronomy. It is written in Sanskrit and contains 25 chapters covering various mathematical topics, including arithmetic, algebra, geometry, and astronomy.  In this treatise, he describes the concept of zero as a numerical digit and its significance in mathematical calculations. He also describes its use in the decimal numeral system.

Babylonians, Mayans

The origins of zero are also traced back to ancient civilizations such as the Babylonians, and Mayans. To determine the origin of the number zero, we must refer to the ‘positional zero’: 2019 is not the same as 219. The first to devise the ‘counting’ zero were the Babylonians and the Mayans. From both civilizations, the system reached India, where it underwent great evolution by the Brahmagupta. 

  • According to Babylonians, he developed one of the earliest known positional numeral systems based on the number 60. He lived in Mesopotamia (modern-day Iraq) around 300 BCE. In his number system, he used a placeholder symbol to represent an empty place in a number like we use zero today to fill the empty placeholder. However, their placeholder symbol was more than just a space. There is no zero or numeric number in his system, he just uses a symbol.
  • According to Mayans, he used a shell-like symbol to represent zero in his system. He lived in Mesoamerica (present-day Mexico and Central America) and also developed a sophisticated numeral system around the same period. His shell-like symbol represents zero and allows him to perform complex mathematical calculations and create calendars with remarkable precision.

After the Babylonians and Mayans, zero or their symbol reached India where it played a significant role in the numerical digit. Aryabhata and Brahmagupta give it a name- zero and its rules. Brahmagupta explains to the world about it, how to use it and where to use it.

Zero In Other Country

After zero emerged in ancient India, it spread to China, Europe and the Middle East in about a millennium later. The decimal system was introduced to Europe by the Italian mathematician Fibonacci around 1200. He wrote about India that “The method of the Indians surpasses any known method of calculation.” It’s an excellent technique. They use the zero symbol and nine digits in their calculations.”

Mathematicians were liberated from basic yet laborious tasks by this superior method of calculation. This allowed them to explore the general properties of numbers and take on much more complex problems. For instance, it made possible the contributions of Brahmagupta, the Indian mathematician and astronomer who is regarded as the founder of modern algebra.

It’s powerful to utilise 0 since it makes it possible to create straightforward calculation rules. Consider attempting to demonstrate long addition without utilising the zero sign. There would be just too many exceptions to any rule you could come up with. The first person to carefully document and use these mathematical instructions was the Persian mathematician Al-Khwarizmi in the ninth century. This would eventually make abacuses unnecessary. These mechanical instructions demonstrated that a portion of mathematics could be automated, which paved the way for the creation of contemporary computers. The term Al-Khwarizmi is also the source of the word “algorithm,” which is used to characterise a collection of fundamental guidelines.

Day by day, the use of zero was spread around the world. Now, zero in modern mathematics plays a significant role. The widespread acceptance and adoption of zero as a numerical digit revolutionised mathematics and created calculus, algebra, and various branches of mathematics. Zero serves as the cornerstone of the modern numeral system, enabling complex mathematical operations, equations, and concepts to be expressed and understood.

Origin of Fractions

The invention of zero also created a new, more accurate way to describe fractions. A number’s magnitude increases when zeros are added to the end, it reduces when zeros are added to the beginning of the number. Infinite precision is equivalent to an infinite number of places to the right of the decimal. The brilliant geniuses Gottfried Leibniz and Isaac Newton of the 17th century needed precisely this kind of precision to advance their work on infinitesimal calculus.

Thus, algebra, algorithms, infinitesimal calculus, and the three pillars of modern mathematics are the result of the notation of nothing. The study of mathematics is the study of invisible things that are only explicable through writing. By including zero in the number system, India unlocked the full potential of numbers, advancing mathematics from its primitive state into adolescence and beyond.


How To Divide By Zero

Mathematicians highlight that one of the most complex operations that exist is dividing by zero. The first person to use this number for multiplication, subtraction, and addition was Brahmagupta. However, what about dividing? He did not specify how to divide a number other than zero by zero; he merely stated that the outcome of dividing zero by zero is zero.

Several years later Mahavira pointed out that dividing a number by zero leaves it the same, which is not entirely correct.

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