Posted on October 16, 2024
We Indians take pride in boasting an archaically long mathematical tradition. From sages laying down the foundation stones of modern mathematics to the contemporary mathematicians advancing their knowledge and achievements in various fields, it is a history worth mentioning. This blog takes you through the lives and achievements of some of India’s most renowned mathematicians and depicts their contributions as well as how their work has influenced global mathematics.
Aryabhata (476–550 CE)
Aryabhata was one of the earliest and most influential mathematicians and astronomers in ancient India. Born in 476 CE, Aryabhata was a great contributor to algebra, arithmetic, and trigonometry. His most famous work, the Aryabhatiya, written when he was just 23, covers a wide range of mathematical topics. He introduced the concept of zero in a positional number system which changed the world of mathematics.
One of his notable contributions was that he was able to calculate pi correctly to four decimal places (3.1416) and even suggested that the Earth rotated on its own axis. His manner of solving quadratic equations provided much impetus to the development of the sine function, wherein was recognized the fundamentals of trigonometry.
Brahmagupta (598–668 CE)
There was another influential Indian mathematician and astronomer Brahma Gupta, who made incredible breakthroughs into algebra and number theories. He was born in the year 598 CE. Brahmagupta is more famously known for his work: Brahmasphutasiddhanta, which contains detailed explanations on how arithmetic operations are performed using zero. He was the first to develop rules about doing calculations with zero, including both addition and subtraction, making him a pioneer in understanding how important zero was in mathematical calculations.
He also solved quadratic equations, introduced negative numbers and made significant contributions to geometry: computing the area of a cyclic quadrilateral. His work was later passed on to the Islamic world and then to Europe, influencing mathematical development worldwide.
Bhaskara II (1114–1185 CE)
Bhaskara II, or more famously known as Bhaskaracharya, was an illustrious mathematician and astronomer of medieval India. His most celebrated work Siddhanta Shiromani he divided into four sections that include; Lilavati (Arithmetic), Bijaganita (Algebra), Grahaganita (planetary mathematics), and Goladhyaya (Spherical Astronomy).
In Lilavati, Bhaskara provided solutions to problems that are complex arithmetic today, including permutations and combinations, which is now basic to probability theory. Bhaskara’s Bijaganita ran through solutions to quadratic, cubic, and quartic equations many centuries before European mathematicians made similar advances. He further calculated the time the Earth would take to orbit the sun, basing his answer on a close approximation of the modern value.
His work on calculus was revolutionary. He introduced the differential coefficient, which later evolved into the theory of differential calculus. Bhaskara’s notions on infinitesimals and derivatives were indeed precursors to the discovery made many centuries later and made him one of the driving forces for calculus.
Srinivasa Ramanujan (1887–1920)
Perhaps the most famous Indian mathematician of modern times, Srinivasa Ramanujan is often considered to be a genius who shook the world number theory. Born in 1887 into a Brahmin family from Madras, India, who were so poor that they could hardly provide formal education in mathematics, Ramanujan had gained an incredible amount of insight into this subject by the age of five.
Ramanujan’s output fell into three streams: infinite series, continued fractions, and modular forms. Contributions to partition theory by Ramanujan were also notable, including multiple new formulas for pi (π). Many new mathematical theorems were discovered during joint work with British mathematician G.H. Hardy in Cambridge University, the most famous of them is Ramanujan-Hardy number, which is now known as the smallest number that can be expressed as a sum of two cubes in two different ways.
Although he died at the age of 32, he left behind an enormous legacy of mathematical discoveries most of which still lie to be explored. Modern mathematics in number theory and modular functions in particular still continue to be graced by his intuitive methods and insights.
C.R. Rao (1920–2023)
C.R. Rao, or Calyampudi Radhakrishna Rao, was certainly one of the most influential statisticians during the 20th century. Born in 1920, he made contributions to statistics such as the famous development of the Cramer-Rao bound and the Rao-Blackwell theorem. The two later notions would prove to be fundamental in statistical estimation and were significantly influential in the approach to modern statistical theory.
Rao’s work in multivariate analysis, especially in the so-called Rao-Blackwell theorem, has applications in econometrics, machine learning, and many other areas. His work was of pathbreaking nature and earned him awards upon awards; today his contributions form a major part of ongoing modern statistical research and application.
Manjul Bhargava (1974-present)
Manjul Bhargava is one of the most famous Indian-American mathematicians of our time. He has collaborated on various sub-problems in number theory and algebra. Born in 1974, Bhargava is popular for his work on quadratic forms, an area which has been enriched by this young Indian mathematician as he was awarded the Fields Medal in 2014, a sort of “Nobel Prize in Mathematics”.
Bhargava’s work has shed much light on number theory, especially on integer factorization and elliptic curves. He also improved the cryptography algorithms used and became a leading figure in the research of mathematics from then on.
Conclusion
India boasts a rich mathematical legacy which stretches back thousands of years in its contributions to both antiquity and modern mathematics. Ranging from the pioneer Aryabhata with his sensational work on zero to Ramanujan’s path-breaking works on number theory, and from Bhaskara II in algebra to current insights of Manjul Bhargava, Indian mathematicians have constantly been at the forefront of pushing knowledge into new vistas in mathematics.
Their work remains a source of inspiration to mathematicians all over the world and indeed remains part of the global mathematical canon that reflects the rich intellectual history of India.