Indian Mathematics

Count to 10. That’s what anyone studying math needs to know to get started. But think about this: numbers have always existed, but the written symbols, called numerals, haven’t. Someone needed to invent them! Historians don’t know who created Brahmi numerals, the first numeral system discovered, but they do know that these written numbers started appearing in what is now India around 300 BC. These earliest numerals don’t look very much like the numerals that we used today, but they were only the beginning of modern mathematics.

The next big step for numerals can be found on a scrap of old birch bark written around 600 years after the appearance of the Brahmi numerals. The bark, called the Bakhshali manuscript, shows two dramatic mathematical leaps forward. In the Bakhshali manuscript, there aren’t just single numbers like two, five, or eight. Instead, there are much bigger numbers, like 30,984. This tells us that people were using what we now call the decimal place value system. This system helps mathematicians all over the world express numbers big enough to launch astronauts into space!

The second leap is a small black dot. It doesn’t look like much, but this dot is how the Indians represented zero. A numeral for zero did not exist in Brahmi numerals, but it is now considered one of the most important ideas in all of mathematics.

Three hundred years after the Bakhshali manuscript was written, an astronomer and mathematician named Brahmagupta finally gave the numeral zero a definition. He described zero as the number that you get when you subtract a number from itself. This idea is common today, but it was revolutionary in Brahmagupta’s time. He then began to ponder the existence of numbers that were even smaller than zero. This led to the idea of negative numbers. Although negative numbers appeared in China before this, Brahmagupta was the first to create rules about how they worked. His studies were eventually translated. In 1494, Luca Pacioli—a friend of Leonardo da Vinci’s—included Brahmagupta’s negative numbers in a book that summarized all of the world’s most important math.

After Brahmagupta, another astronomer-mathematician called Bhāskara II took the idea of zero and wondered what would happen if someone divided a positive number by it. In his writings, he guessed that the result would be infinity, a guess that modern mathematics confirms. Bhāskara II did more than just study zero, however. He also used letters to indicate unknown quantities, like we do in modern-day algebra, and estimated the value of pi (π). A later group of Indian mathematicians called the Kerala School estimated pi even more precisely as they explored trigonometry and calculus. Today, mathematicians use these kinds of maths to build skyscrapers and create medicine.

From infinity to zero and from basic numbers to algebra and calculus, ancient Indian mathematicians paved the way for the math of the modern world.