# India’s Unknown Change to the World

Modern day society benefits from mathematics in unimaginable ways. The internet has enabled people on every side of the earth to have a voice, regardless of their background. Space exploration has made living on other planets feasible in the near future. None of this would be possible without ancient advancements, such as the concept of zero, a notion that originated hundreds of years ago in India. However, the people of this civilization went far beyond zero. They can be accredited with some of the most critical aspects of our modern mathematical system. For example, place value, which has had a profound impact on the daily lives of nearly every person on earth. Trigonometric principles that have served as the foundation for abstract mathematics and engineering originated in ancient India as well. The ancient Indians contributed to global society on a scale unparalleled by any civilization throughout history.

In each area of math, from subtraction to calculus, there are concepts that wouldn’t be taught if it weren’t for the brilliant thinkers of ancient India. The most well known of these concepts is zero. In the early sixth century C.E., a Guptan mathematician named Aryabhatta wrote a book titled *Aryabhatiya* containing his findings in the field of Mathematics (Stewart 31). One of these was Zero. This reason this notion was conceived in India was the prominence of Hinduism during the Guptan empire (Prasoon 185). One of the most fundamental themes of this religion is the idea of nothingness. If everything around a person was gone, there would still be that person (Prasoon 34). For this reason, Hindus place high value on being a good person, and having good morals. Without the influence of Hinduism, the concept of Zero may never have been created. Because Hinduism is almost exclusively practiced in the Indian subcontinent, nobody anywhere else on Earth would likely have been able to discover such a pivotal concept during this time period. Without this contribution to global society, the world might still be dark, and lacking in the technology and math that makes it go round. The idea of zero was originally depicted with a dot (Ushakov 186). The smallest thing that can be written is a dot. Anything less would be blank space, nothing. This explains why he chose such a mundane symbol to represent an idea so revolutionary. Far more important than it’s symbol, the number zero has become the backbone of all Mathematics since. Zero opened the gateway for mathematicians to explore negative numbers, and for scientists to understand forces like gravity (Khilnani 52).

The very first of such applications was a system of place value. Being such an extraordinary scholar, it comes as no surprise that Aryabhata devised this concept as well. In fact, he wrote about this along with the concept of zero, in the very same book, the Aryabhatiya (Stewart 33). When computers were first invented, only a select few understood them or why they were of any use. However, computers have gone on to change the world, allowing people to constantly be connected and running calculations unimaginably fast. In modern day, a common person is more likely to be scrolling through Instagram or snapchat than holding a conversation with another human being. Unlike people, regardless of how difficult a problem is or how many problems one is given, a computer will solve for an answer in practically no time. Thus, computers can be used for virtually any variety of calculation. Similarly, when place value was invented, many knew nothing of it. While most counting systems of the day relied on fingers or symbols to represent arbitrary numbers, place value is comprised of just 10 symbols, which when put in certain combinations, can represent any number (Stewart 32). Furthermore, only a few digits have to be written out to represent a desired number. This invention directly changed the way people did financial transactions and led life on a daily basis. This is because keeping track of money is very easy with place value, as opposed to noting every golden nugget or trading item. For example: present-day stock traders and businessmen don’t need to tally down every transaction made, which allows unimaginable amounts of money to change hands every second. This investment system allows for average people to invest, which makes the makes the world very civilized.

In addition to fundamental concepts such as zero and place value, Indian scholars of this time period made several praiseworthy advances in more abstract mathematics. One of the subjects ancient Indians contributed to was trigonometry. The earliest known advances in this field were written in the *Siddhantas* by various mathematicians. These books defined the sine, arcsine, cosine and arccosine functions (Yadav 155). These functions alone are applied every day by modern architects and engineers, enabling the calculation of figures such as how high to build bridges or towers. Metropolises like New York and Tokyo which play a big part in modern society would not exist had it not been for these substantial contributions to mathematics. Not long after, Aryabhata calculated the values of sine and cosine from 0° to 90°. Without a calculator or even an abacus, Aryabhata did so on a 3.75° interval and calculated each value to the ten-thousandths place (Khilnani 52). Furthermore, a man named Varāhamihira calculated the relationship between sine and cosine.

Regardless of where one is, the field of mathematics known as algebra can be seen everywhere. Cash registers, spacecrafts and zoologists all use algebra, the area of mathematics that deals with relating quantities and equations. Algebra is comprised of copious formulae. Foundational formulas such as the quadratic formula are built upon radicals, which are commonly referred to “roots”. Radicals determine the number that can be multiplied by itself a certain number of times to result in a given number (Maddocks). For instance, the fourth root of sixteen is two. Scholars of ancient India introduced the world to the square and cube roots (Monaghan 103). Books from this time period show knowledge of radicals and exponents being applied to solving systems of equations (Murthy 93). This is a skill taught to all students in public schools, because it is so helpful. Algebra is used in all forms of advanced mathematics and science such as calculus and physics. Without algebra, society would not be centered around technologies like the computer, airplane and car. The extent of advanced mathematics and science is so vast that many present-day institutions are entirely dedicated to math and computer science. These institutions would not be the same if it weren’t for the groundbreaking developments in algebra made in ancient India.

Modern day society would by vastly different if it weren’t for the ancient Indians. This civilization developed much of the mathematical system in use today, for tasks ranging from farming to landing people on the moon. A notion so simple as zero laid the foundation for higher level thinking and the advanced modern world. These people also invented place value, which has played a big role in improving the way all people, ranging from kindergarteners to astrophysicists think about mathematics. The advanced mathematics of trigonometry, which make much the advanced engineering in present-day society possible, originated in India as well. Algebra would not be taught to eleven and twelve year olds if it was not so useful and engrained in daily life. The scholars of ancient India made this possible, forming early algebra. If it weren’t for ancient Indian advancements in mathematics, the world would not be the same place it is today.