Brahmagupta: The Pioneer of Zero and Ancient Indian Mathematics

Brahmagupta was a prominent Indian mathematician and astronomer in the 7^th century CE. From arithmetic to algebra and geometry to positions of heavenly bodies—Brahmagupta’s contributions placed him as one of the greatest mathematicians of his time. He influenced international scholars and is still remembered as the mathematician who introduced clear arithmetic rules involving zero and negative numbers.

Origin Story of Brahmagupta

Brahmagupta’s life began in 598 CE in Bhillamala, now known as Bhinmal, in Rajasthan. His father, Jishnugupta, was a scholar, and Brahmagupta grew up learning astronomy and mathematics.

Scholarly Contributions of Brahmagupta

In 628 CE, at 30 years of age, Brahmagupta wrote his first great work, the Brahmasphutasiddhanta (“Correctly Established Doctrine of Brahma”). A few decades later, in 665 CE, he wrote a second treatise called Khandakhadyaka (a Sanskrit title meaning “edible morsel of food”). Soon after these works, Brahmagupta moved to Ujjain – the leading centre of mathematical astronomy in India – and became head of the observatory there.

1. The magical number Zero

Brahmagupta’s books are filled with many mathematical rules and formulas. He clearly explained the number zero and how it works. He defined zero as what you get by subtracting a number from itself, and he gave rules such as “adding or subtracting zero does nothing to the number” and “any number multiplied by zero is zero”.

Brahmagupta the pioneer of zero

2. Algebra

Algebra is a branch of maths which is like solving puzzles where letters stand for numbers we don't know yet. Brahmagupta made major advances in algebra. He solved complex equations that other mathematicians had not solved. He liked to work on complex arithmetic problems, such as finding unknowns in interest and loan puzzles, showing how to create and solve the required equations for such problems.

3. Numbers and shapes

Acharya Brahmagupta used everyday terms in explaining maths: he called positive numbers “fortunes” and negative numbers “debts,” and he showed rules for combining them (for example, a debt minus zero stays a debt, but subtracting a debt from zero gives a fortune). He discovered remarkable formulas in geometry as well. Perhaps his most famous formula is for finding the area of a cyclic quadrilateral (a four-sided shape with all corners on a circle). Brahmagupta also gave a way to compute values of advanced mathematical concepts called sine functions and wrote formulas for adding up squares and cubes of consecutive numbers.

4. Contributions in astronomy

In astronomy, Brahmagupta believed the Earth was stationary (not moving) and the cosmos moved around the Earth. He calculated the length of the solar year as about 365 days and 6 hours, which is very close to the true value. His books explain the motions of the planets, the timings of lunar and solar eclipses, and the rising and setting of stars. He also described that all objects fall to Earth: he wrote that “heavy things fall down to the earth by a law of nature, for it is the nature of the earth to attract and to keep things”. Though this principle is different from the modern concept of Newtonian gravity, Brahmagupta had made an important observation. His insight reflects an early understanding of how objects tend to fall toward the Earth—what later scholars would describe as gurutvaakarshan (gravitational attraction) in Sanskrit.

Legacy and Recognition

Brahmagupta’s work had a far-reaching legacy. About a century after his death, his work was translated into Arabic (around 771 CE). In the Islamic world it was called Sindhind, and these translations helped spread the Hindu–Arabic numeral system (including zero) to Arab and later European mathematicians. The Persian scholar al-Khwarizmi drew on these ideas when he wrote his own arithmetic and astronomy books.

Historians honour Brahmagupta as a great scientist. For example, historian George Sarton called him “one of the greatest scientists of his race and the greatest of his time”. Bhaskaracharya or Bhaskara II, an illustrious 12th century mathematician, acknowledged Brahmagupta's significant contributions to mathematics by calling him "Ganita Chakra Chudamani"—translating to "The Gem of the Circle of Mathematicians". 

Brahmagupta’s respect has not diminished with time. A modern metal sculpture of Brahmagupta (made from recycled materials) stands in Shaheedi Park, Delhi, to celebrate his contributions. Students still learn Brahmagupta’s rules for zero and his famous formulas in school. Brahmagupta is remembered for laying important foundations in arithmetic, algebra, and astronomy that influenced scientists for centuries.

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Contentious - Brahmagupta did not mention gravitational force per se, rather that everything falls towards the Earth. 

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Brahmagupta

Brahmagupta was born in 598 AD into an orthodox Sahivite Hindu family. His father name was Jishnugupta. He is believed to have lived and worked in Bhinmal in present day Rajasthan, India. The city was center of learning mathematics and astronomy. King Vyaghramukh was the ruler of Bhinmal and made Brahmagupta the head of the astronomical observatory in Ujjain, in these days, Ujjain was the destination of all mathematician and astronomers.

Brahmagupta’s text “Brahmagupta Siddhanta” discussed the loopholes of his contemporary mathematician’s theories. This book has 24 chapters and 1008 Sanskrit verses. In this book he discussed the mathematical chapters of geometry, trigonometry, algebra and algorithmic. At the age of 67, he wrote another book “Khanda Khadyaka”, discussing astronomy.

He studied the works of great mathematician’s and astronomers like, Aryhatta, Varahmihira, Srisena, Vijainandin, Latadeva, Pradyumna, Simha and Vishnuchandra.

He wrote “Brahmagupta Siddhanta” at the age of 30 One of the most significant input of Brahmagupta to mathematics was the introduction of ‘Zero’ to the number system which stood for nothing in this book he states many rules for arthmatic:

·       A positive number multiplied by negative number is negative.

·       A positive number multiplied by positive number is positive.

·       A negative number multiplied by positive number is negative.

·       A negative number multiplied by negative number is positive.

Brahmgupta calculated the length of a year is 365 days 6 hours 12 minutes 9 seconds which is very close to today’s calculation. Brahmgupta talked about “Gravity” to quote him, “Bodies fall towards the earth as it is in the nature of the earth to attract bodies, just as it is in the nature of water to flow.”  He also proved that earth is sphere and calculated its circumstance to be around 36000 km Modern (40.075 Km)

In his “Khandkhadyaka” he explores to longitude of the planets, diurnal rotation, lunar an solar eclipses, rising and settings, the moon’s crescents, conjunctions of the planets. He explains that since moon is closer to earth than the sun, the degree of the illuminated part of the moon depends on the relative position of the Sun and Moon and this can be computed from the size of the angle between the two bodies.

His death is supposed to be 668 A.D. in Ujjain. After his death, his books were translated into Arabic and transported to Baghdad where they helped Islamic revolution in science and Mathematics overall Brahmgupta’s ideas spread throughout the world and influenced mathematical thought for hundred of years.

He was given the title of “Ganita Chakra Chudawani” by a fellow scientist, which is translated as “the gem of the circle of mathematician.