Brahmagupta was a renowned Indian mathematician and astronomer who lived during the 7th century CE.
He made significant contributions to many areas of mathematics, including number theory, algebra, geometry, and trigonometry.
One of his most important achievements was giving a clear understanding of zero as a number.
He explained how zero behaves in calculations and described rules for working with it.
Brahmagupta introduced a multiplication technique known as “gomutrika,” which resembles the lattice method used today.
He developed practical methods to find square roots and cube roots, and he provided solutions for linear and quadratic equations.
He also worked on more complex equations, such as what is now called Pell’s equation (x² − ny² = 1), and gave systematic ways to solve them.
In addition, he found integer solutions for equations of the form ax by = c.
In geometry and trigonometry, he discovered important results, including a formula to find the area of a cyclic quadrilateral, an identity related to sums of squares, and properties connected to cyclic figures.
He also calculated approximate values of pi and worked with trigonometric functions like sine.
He wrote two major works, the Brāhmasphuṭasiddhānta and the Khandakhadyaka. These texts contain many original ideas that influenced later scholars in India and other parts of the world.
Brahmagupta is considered one of the greatest mathematicians of ancient India, and his ideas continue to play an important role in modern mathematics.