09/10/2019

The origins and advancements of Indian mathematics.

Foto: Alex Pylypenko/Flickr

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

I just spent two weeks in India on business, participating in a conference co-organized by IMPA (Institute of Pure and Applied Mathematics) in Bangalore. I took the opportunity to visit the renowned Tata Institute for Fundamental Research in Mumbai and to explore Goa, the former capital of the Portuguese empire in the East.

Indian mathematics dates back to 1200 BC, and its achievements are remarkable. The Hindus discovered zero (independently of the Babylonians and the Mayans), and the symbol 0, which we use to represent this number, also comes from them: its first known use was in the Bakhshali manuscript, written on fragments of birch bark around the 3rd century.

This important advance allowed them to create the decimal positional system to represent numbers. The central principle ("from place to place, each one is ten times the previous one") already appears in the Aryabhatiya, written in Sanskrit at the end of the 5th century by the mathematician and astronomer Aryabhata (476 – 550). Transmitted to the West by the Arabs, and popularized by Fibonacci, the Hindu decimal system freed Europeans from the awkward Roman numeral system, becoming the standard throughout the planet.

Meanwhile, mathematics in India continued to advance. By the 7th century, they were already working with negative numbers, having correctly identified the respective rules of operation, such as "negative times negative equals positive".

What they didn't do was discover the quadratic formula… My colleague in Bombay was surprised when I told him that in Brazil it's called "Bhaskara's formula": there were two important mathematicians with that name, in the 7th and 12th centuries, but nobody in India associates either of them with the formula (which was already known to the Babylonians around 1800 BC). As far as we know, this nonsense is a Brazilian invention.

Today, India remains one of the most developed countries in mathematical research, occupying a place in Group 4 of the International Mathematical Union, the second most important group. This is partly due to the prestige of the Tata Institute in Mumbai, historically the first center of excellence in mathematics in the developing world.

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