14/03/2019

How India revolutionized mathematics before the West.

Um pequeno templo dentro da fortaleza de Gwalior abriga o mais antigo registro conhecido do uso do número zero / Foto: Getty Images

Reproduction of the BBC article.

Like China, India discovered the benefits of a decimal system a long time ago.

They were, in fact, already using it in the 3rd century.

It's the same system we use today, where the numerical position indicates units, tens, hundreds, thousands, and so on.

We don't know exactly how they arrived at the decimal system, but the Indians certainly perfected it, laying the foundation for the numbers one through nine that are used throughout the world.

They also invented a new number: zero.

Nothing but an empty space.

Its earliest known use dates back to the 9th century, but it was likely used hundreds of years before that.

This strange number is engraved on the walls of a small temple inside the Gwalior fortress in Central India.

It has become a place revered by mathematicians because it houses the "beginning" of the number zero.

In ancient Egypt, Mesopotamia, and China, there was a zero, but as a marker, an empty space.

It was the Indians who transformed it into an actual number, a conceptual leap that revolutionized mathematics.

Since then, it has become possible to form numbers of astronomical sizes in a very efficient way.

O zero mais antigo do mundo, em Gwalior

How did we arrive at zero?

We'll never know for sure, but it's possible that the idea and symbol used for zero originated from calculations done on the ground with stones.

When the stones were removed, a round indentation remained in place, representing the movement from something to nothing.

But there may also have been a cultural reason for the invention of that number.

The concepts of nothingness and eternity were part of the belief system of the ancient Native Americans.

Both Buddhism and Hinduism adopt the concept of nothingness as part of their teachings.

Therefore, it shouldn't have been all that surprising that a culture that enthusiastically embraced nothingness could accommodate the notion of zero.

The Indians even used the word shunya , which represents the philosophical idea of emptiness, to represent the new mathematical term.

Cálculos feitos no chão deixavam um círculo vazio após subtração

From zero to infinity

Brahmagupta, a famous 7th-century Indian mathematician, demonstrated some of the essential properties of zero.

His basic rules for calculations involving zero are still taught in schools around the world.

1 + 0 = 1

1 – 0 = 1

1 x 0 = 0

But Brahmagupta found more when he tried dividing 1 by 0.

What number multiplied by zero equals one?

The solution required a new mathematical concept: infinity.

But the calculations using zero went even further.

Although it was accepted that 3 minus 3 equals zero, what would be the result of 3 minus 4?

It may seem like you have nothing, but the Indians realized that this was a new kind of nothing: negative numbers.

The Indians were able to arrive at negative numbers and zero because they conceived of them as abstract entities.

Numbers were not merely something used for counting or measuring; they had a life of their own, floating freely in the real world.

This line of thinking generated an explosion of mathematical ideas.

X and Y

The abstract Indian approach to mathematics revealed new ways to solve quadratic equations – those that include square numbers.

Brahmagupta, born in 598, understood negative numbers and saw that quadratic equations always had two solutions, and that one of them could be negative.

He went even further by solving equations with two variables (X and Y).

This movement would only happen in the West in 1657, when the French mathematician Pierre de Fermat presented his solution, unaware of what his Indian colleague had discovered a thousand years earlier.

Pierre de Fermat ‘resolveu’, por sua vez, o problema da equação quadrática em 1657 / Foto: Getty Images

Brahmagupta also developed a new language for expressing the solution to these equations.

While experimenting with ways to present his calculations, he used the initial letters of two color names to represent variables.

The decision resulted in the adoption of X and Y, which we still use today.

It didn't end there.

Indian mathematicians were also responsible for further discoveries in trigonometry.

It is true that the Greeks were the first to develop what we might call a "dictionary" that translated geometry into numbers and vice versa.

But the Indians went further.

They used trigonometry to study the world around them, which included navigating the seas and calculating spatial distances.

Indian mathematicians, for example, have managed to calculate the distance between the Earth and the Moon and between the Earth and the Sun.

Mathematicians in India have also solved the mystery of one of the most important numbers in mathematics: Pi.

Foto: Steemit

Pi is the numerical value of the ratio between the circumference of a circle and its diameter.

It's a number that appears in all kinds of calculations, but it's especially useful for engineers and architects, since any measurement involving curves requires Pi.

For centuries, mathematicians have sought the precise value of Pi.

But it was in the 6th century that the Indian mathematician Aryabhata gave a fairly accurate approximation: 3.1416.

He also used Pi to measure the circumference of the Earth, arriving at a value of 39,968 km – a number very close to the one we know today (40,075 km).

Madhava realized that by adding and subtracting different fractions, it was possible to determine an exact formula for Pi.

This formula is still taught in many universities around the world as if it had been discovered by the German Gottfried Wilhelm Leibniz in the 17th century.