Indians and zero, popular stories
“Well! The Indians, you know? They invented zero. It was the only thing missing in modern maths, and they had it. It changed everything.”, “You know? Aryabhatta, the Vedic mathematician, who invented zero……”, “Srinivasan Ramanujan’s works on zero, you know? It influenced Western mathematics a lot. In fact, modern technologies such as cryptocurrency is inspired by the number zero”. If you are hearing this around everywhere, or if you are one of the people who use these statements, please read further.
There are three things common between these statements: they have reference to Indian mathematicians, there is the number zero involved, and they all are wrong.
Let’s start with the first statement. It is popularly used by everyone in the world when they wanna show off that they are knowledgeable about the history of mathematics. It is a common misconception that conveys that only zero was missing in the world of mathematics, which Indians apparently created out of nowhere. However, the truth is zero was not in common practice in the Indian number system during the early days. There have been mathematicians such as Brahmagupta, who have understood the need for representing “nothingness” in terms of mathematics, but the representation was not widely used.
If you could refer to any of India’s original numerical symbols, it has one to ten instead of zero to nine as the fundamental numbers. To clarify that statement, any whole number can be represented using the fundamental numbers of zero to nine in the modern (Indo-Arabic) system. For example, the number eight hundred and sixty can be expressed with 8, 6 and 0. In the ancient Indian system, the same eight hundred and sixty would have the numbers 8, 5 and a symbol for ten. In other words, a decade of numbers is given as 1 to 10 in the Indo-Arabic system. Note that there is no separate symbol for the number 10. Ten is represented as a combination of one and zero. In the old system, India had a symbol for the number ten, so a decade will have all one-digit numbers.
Does that mean India did not really contribute anything to the numbers? No. The representation of numbers using the place-value system is the best contribution of India to the world. In the place-value system, a symbol used in different places (ones, tens, hundreds) will have different values. This simplifies the large number representation by eliminating the need for additional symbols and reducing the length of numbers. If you do not understand this, please try to write six hundred and thirty-five million, four hundred and eighty-five thousand, and nine hundred and seventy-four using Roman numerals and Indo-Arabic numerals. If you don’t find the difference, try to multiply the number by fifty-six using both systems.
The place-value system has revolutionised mathematics and extended the scope of performing complicated arithmetic. Without that, we would be lagging far behind in technologies. We should probably appreciate the traders, who shared the mathematical knowledge from different countries to standardise the system and allow everyone to expand further. More than the Vedic literature and innate spirituality of Indians, the place value system would have given a better intuition about the value zero. When people wanted to standardise the number of digits to represent all numbers, they might have wanted to invent a symbol to show that there is nothing in that position. For example, if you’re going to write nine as a 2-digit number using Indian systems, you would need to fill the tens digit with a null (a dummy symbol or a zero). That is how Indians might have arrived into common practice. Intuitively Indians might have migrated to a set of fundamental numbers from zero to nine instead of one to ten. A system of this sort would have been of great help to the traders. That is why this system is spread across the world instead of the original system.
There is still a faith in India to relate everything to the religious texts. India still wants to be known as a religious country. That is why people have been fighting a lot to find mathematical meanings in religious texts. Yes. Indian religious texts have valuable information beyond their time. That doesn’t mean that they should be the origin of every knowledge in the country. There could have been other types of knowledge and literature as well.
The same applies to Aryabhatta. His mathematical works were centuries ahead compared to Western works. But still, he did not invent zero. In fact, no one could invent a number. Now, the “Grant Sanderson” fans will argue that Mathematics is more of an invention than a discovery. That is completely true. The representation of nothingness, designing a symbol, developing laws to define the symbol are all inventions. However, the number as an abstract idea is merely a discovery. You could quote the Vedic literature of how a story in Upanishad explains everything in the universe comes out of nothing. That is a high-level imagination, and it gives an intuition about mathematical concepts such as integration. The mathematicians might have even been inspired by them. However, they are so abstract to be considered an origin of mathematical theories.
You can’t say apple is the origin of gravity just because falling of an apple made Newton think about its science.
Coming to Ramanujan, I don’t understand why he is associated with zero’s invention. Zero had been existing for centuries during his time. He has worked on mathematical theorems based on his intuition. He has nothing to do with the so-called “invention of zero”. Just because his theorems were used in cryptography and other modern technologies, it does not mean that they have anything to do with the invention of zero. Indian mathematicians have played an essential part in the development of modern mathematics. To give them a tribute, let us at least try to understand what they have actually done.
