Brahmagupta: Biography, Inventions & Discoveries

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Brahmagupta was a famous mathematician and astronomer who lived in seventh century India. His ideas were so profound that they still influence mathematics today! In this lesson, learn all about his life and his discoveries.

Brahmagupta and Brahmasphutasiddhanta

About 1500 years ago, in 628 A.D., a book called the Brahmasphutasiddhanta was published in India. Over the next few hundred years, it would cause a revolution within the world of mathematics that slowly spread across the entire world. Sixth and seventh century India was a hotbed for scientific and mathematical innovation, and the basic numerical system that we use today developed in this time and place.

However, even in that exciting and progressive environment, this book stood out among the rest. It was written by a brilliant mathematician and astronomer named Brahmagupta, and in it, he developed most of the rules that we still use to work with the numeral zero.

The Infamous Zero

While most of us take the numeral zero for granted today, its usefulness was certainly not apparent throughout most of history. There is evidence that Babylonian people were using zero as a placeholder digit as early as 400 BC, but even then, they did not understand how it could exist as a number or concept on its own. In Ancient Greece, great thinkers were revered, and we still rely on much of the knowledge they discovered and passed down to us. However, even these renowned philosophers and mathematicians did not use zero!

Finally, in India, mathematicians like Brahmagupta began to first think about how zero could be used as a number by itself. The evidence suggests that Brahamagupta was the first person to really explain how to use zero in mathematics, and without his remarkable achievement, our world would be very different today.

Even more impressive, this was not the only significant contribution that Brahmagupta would make to the world of mathematics and science. He developed several more mathematical theorems, calculated the length of the solar year more precisely than anyone had done before, and calculated the circumference of the Earth. He was truly one of the greatest thinkers who have ever lived.

Early Life and Work

The remarkable life of Brahmagupta began in 598 AD in northwestern India. He spent most of his life living near the modern Indian city of Bhinmal, which was then known as Bhillamala. It is sometimes referred to as Bhillamalacharya, which means the teacher from Bhillamala.

He began to study astronomy when he was a young man. At this time, Indian astronomy was quite advanced compared to the work being done in the rest of the world. When he was only 30 years old, he published his most famous book, the Brahmasphutasiddhanta. In this book, he mainly focused on issues related to astronomy. He asserted that the Earth was round and not flat, as many people still believed, and even calculated that the circumference of the Earth was approximately 36,000 km. Today, we know that the Earth's circumference is actually about 40,000 km, so Brahmagupta's calculations were pretty accurate!

He was also able to predict the motion of the planets and the timing of solar and lunar eclipses. He calculated the solar year very accurately, writing that one solar year was 365 days, 5 minutes, and 19 seconds. Down to the minute, this is what scientists have now measured the solar year to actually be!

His book also contained chapters on mathematics, and it was in these chapters that he explained the rules for using zero in mathematical calculations. He also explained how to work with negative numbers, which he referred to as debts. In his writing, positive numbers were called fortunes, and among other things, he was the first person to explain why the product of a positive and a negative number (fortune and debt) would also be negative. No one had ever done this before either!

He also made contributions to geometry, including accurately calculating the constant pi, and developing a way to calculate the area of a cyclic quadrilateral that is still known as Brahmagupta's Formula.

Brahmagupta developed a formula that could be used to calculate the area of a cyclic quadrilateral like this one.
Diagram for Brahamagupta Formula

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