Brahmagupta Essay, Research Paper

Brahmagupta was born c. 598, in Bhillamala, which was located in Northwestern India. The suffix -gupta probably indicated that the family belonged to the Vaisya caste (made up of mostly farmers and merchants).

He likely lived the majority of his life in Ujjain, India, which at the time was the center of Hindu astronomy and mathematics. There he had access to the best observatory in India as well as the writings of many great scientists and mathematicians who came before him, such as Hero of Alexandria, Ptomely, Diophantus and Aryabhata. In his own work he drew heavily from these sources and often corrected their mistakes.

At the age of 30, Brahmagupta wrote his first book, Brahma Sphuta Siddhanta. In 25 chapters this work explains much of his work in astronomy and mathematics. One of his greatest contributions that was revealed with the Brahma Sphuta Siddhanta was the defining of zero. He defined it as the result of subtracting a number from itself. Some of the properties he listed follow:

When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero.

He also gave rules for zero in terms of fortunes, which represent positive numbers, and debts, the negative numbers, as well as fortunes related to debts:

A debt minus zero is a debt.

A fortune minus zero is a fortune.

Zero minus zero is a zero.

A debt subtracted from zero is a fortune.

A fortune subtracted from zero is a debt.

The product of zero multiplied by a debt of fortune is zero.

The product of zero multiplied zero is zero.

The product or quotient of two fortunes is one fortune.

The product or quotient of two debts is one debt.

The product or quotient of a debt and a fortune is a debt.

The product or quotient of a fortune and a debt is a debt.

In a failed attempt to extend these statements to include division by zero Brahmagupta stated that zero divided by zero is zero, which is now known to be wrong today (0/0 is 1). He also suggested that n divided by zero is n/0, which stated very little. However, he is still praised for these attempts to further advance mathematical thinking.

Brahmagupta also made great contributions with his work on negative numbers and intermediate equations. Another of his major accomplishments was a formula he created now called Brahmagupta s formula. He also completed a second book near the end of his life called Khandakhadyaka.

His mathematics was widely used by merchant society during his time and by 700, his work was introduced to the Arabs, who where involved in heavy trade with the Hindu s during that time. It was several centuries before European mathematics became aware of Brahmagupta s work, but his influence became great and still exists today. His death came at approximately 70 years old, c. 660.

Brahmagupta s influence on modern mathematics is easily visible and undeniable.

Without his work there would be no concept of zero. We nee the concept of zero when setting certain algebraic equations to zero. Without zero the act of multiplying a number by zero would not exist, therefore we could not represent that there are zero sets of a given number in an equation.

The ideas on negative numbers that he presented are also greatly appreciated in modern mathematics, for without his work on negative numbers we would not be able to use the four quadrants, because negative representations exist in them. He also created rules on how negative numbers relate to positive numbers with multiplication. Today we use these relations a lot.

Not to mention we would not have Brahmagupta s Formula, and countless other equations that he worked on or fixed existing mistakes.

Those preceding reasons are why Brahmagupta is a great influence on modern mathematics, and why we need his works today.