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The extraordinary concept of the thing that led to the invention of zero |  Sciences

The extraordinary concept of the thing that led to the invention of zero | Sciences

Medieval illustration of Alexander the Great meeting gymnasts (circa 1420) – Image: BBC

It is said that once upon a time, after conquering Persia nearly 2,300 years ago, Alexander the Great reached the banks of the Indus River and found a gymnast – a naked sage – sitting on a rock, looking up at the sky.

Alexander asked, “What are you doing?”

The gym replied, “You suffer from nothingness.”

“and what are you doing?”

Alexander replied: “Conquer the world.”

The two laughed, each thinking the other was a fool wasting his life.

The famous Indian mythologist Devdutt Pattanaik recalls this story to illustrate the differences between Indian and Western cultures—and also to show how philosophically open India was to the concept of nothingness long before the number zero was written.


The three great religions of ancient India – Buddhism, Hinduism and Jainism – retained an exceptional focus on numbers.

The history of Indian mathematics dates back to the Vedic period (c. 800 BC), when religious practice required very complex calculations.

At that time, rituals were an important part of people’s lives. The construction of fire altars was governed by precise specifications detailed in the Śulbasūtras, India’s oldest scholarly texts.

Written between 800 BC and 200 BC, the Śulbasūtras contain, among other things:

– Transforms geometric shapes, such as square to circle or rectangle to square, keeping the same areas. For this, it was necessary to calculate the value of the number pi (π);

– calculating the square root of 2 (2), the irrational number that would threaten Pythagorean philosophy;

– And speaking of Pythagoras, Indian writings already included the theorem that bears his name, 200 years before the Greek philosopher and mathematician was even born.


In addition to advances in engineering, the Indians developed a unique old-world obsession for sheer numbers.

“Very large numbers are part of the talk,” says Indian mathematician Shrikrishna G. Dani.

“For example, if you say ‘badartha’ without explanation, almost everyone understands.”

It’s 10¹⁷ – 1 followed by 17 zeros [, ou 100 quatrilhões] – It literally means “halfway to heaven,” explains the professor.

“And in the Buddhist tradition, numbers have gone much further: 10⁵³ is one of them.”

But why these numbers? Are they used for something?

“There is no obvious practical reason,” says Danny.

“I think there’s a certain kind of satisfaction that people feel when they think about those kind of numbers.”

In the ‘Śulbasūtra’, Baudhayana (c. 800-700 B.C.) writes down the values ​​of f and 2, as well as a theorem very similar to the Pythagorean theorem – Image: BBC

What better reason than satisfaction!

The Jains were not far behind either. Raju, for example, is the distance covered by God in six months, after covering 100,000 yojanas in each blink of an eye.

This explanation probably doesn’t tell you anything, but when you do a rough math, if God blinks 10 times a second, he’s traveling about 15 light years.

No Western religious text mentions anything close to this.

And as if this were not enough, the Indians thought of and classified many types of infinity, which were fundamental to the development of abstract mathematical thinking two thousand years later.

From nothing to zero

Of course, to imagine that many zeros, you had to invent them first.

The concept of emptiness was already present in many cultures. For example, the Mayans and Babylonians used signs of absence of quantity. But it was the Indians who converted this absence into a zero, calling it shunya (“emptiness” in Sanskrit).

Giving a symbol for nothing, and saying, in other words, that nothing was a thing, was perhaps the greatest conceptual leap in the history of mathematics.

But when did this jump happen?

As of 2017, the first recorded mention of zero is in an ancient Indian scroll known as the Bhakshali Codex. It has been carbon-dated to the third or fourth century – but some experts do not accept this dating.

In any case, as far as we know, the Indian astronomers and mathematicians Aryabhata, born in 476, and Brahmagupta, born in 598, were the first to formally describe the decimal places and the current rules governing the use of the number zero, attesting to their amazing usefulness.

The Indian numerical system outdid others in the way it facilitated calculations, and spread first through the Middle East, and later reached Europe and the rest of the world, until it became the dominant system.

But why did zero originate in India? Was it just a matter of writing large numbers, or were there other spiritual forces at play?

In Indian architectural manuals, the empty space of buildings was more important than the walls – Image: GETTY IMAGES


The circle, a symbol of heaven and emptiness, was chosen to denote zero – Image: GETTY IMAGES

“The interesting thing is that there’s a lot of shunya popping up all over the place. They’ve been around since about 300 BC,” according to historian of mathematics George Gewerghese Joseph.

He notes that the shunya was present in “architectural manuals, saying that the important thing was not the walls, but the space between them”, and even “in the belief that is found in Buddhism, Jainism and the primordial and fundamental religion that you need to achieve a certain state called nirvana, in which everything is erased”.

“It was a very fertile environment for someone whose name we do not know, to realize that this philosophical and cultural concept would also be useful in a mathematical sense,” says the historian.

“Zero does not denote anything, but it is derived in India from the concept of shonia, a kind of salvation, a qualitative pinnacle of humanity, in a sense,” he explains.

“When all our desires are fulfilled, we have no desires and then we go to Nirvana or Shunya.”

In other words, nothing is all.

In fact, the very use of the circle to denote zero may have religious origins.

“The circle also symbolizes the sky,” notes Indian mathematics historian Kim Plovker.

“Many of the words used to symbolize zero verbally in Sanskrit mean heaven or emptiness. So, since heaven is represented by the circle of heavens, this is a very appropriate symbol for zero,” he explains.

Said the mathematician Marcus du Sautoy in the episode The Genius of the East (“The Genius of the East”) of the TV series Story of Maths (“History of Mathematics”), BBC.

“So perhaps it is not surprising that a culture that has so enthusiastically embraced a vacuum can easily internalize the idea of ​​zero,” he says.

We can never say with complete certainty, but according to the opinions of various experts, it is likely that something in the spiritual wisdom of India led to the invention of zero.

Oldest mathematical zero ever found – Image: BBC

Another idea related to zero and emptiness has had a profound impact on the modern world.

Computers operate on the principle of two possible states: on and off. When connected, the value is set to 1; And when it’s off, it’s 0.

“Perhaps not surprisingly, the binary number system was also invented in India in the second or third century BC by a musicologist named Pingala, despite his use of the metre,” historian of science and astronomy Subhash Kak told BBC Travel journalist Marilyn. Ward.

And the belief that everything was born in India… out of nowhere!