The ancient Indian mathematicians made groundbreaking contributions to the development of modern mathematics. They invented the decimal system and introduced zero as a placeholder, revolutionizing arithmetic. Algebra flourished with solutions to linear and quadratic equations. Trigonometry and trigonometric functions were developed, and π was approximated with remarkable accuracy.
Vedic number words and geometry
The earliest traces of mathematical activity in India can be found in the Vedas, the ancient religious texts of Hinduism. The Vedas contain number words for large numbers, such as shankha (10¹⁷) and padma (10¹⁴), as well as geometric constructions for altars and fire rituals.
Decimal place-value system and zero
The Indians were among the first to develop a decimal place-value system for writing numbers, using symbols for nine digits and a dot or a small circle for zero. The earliest known inscription of this system dates from the 5th century CE, but it may have been used earlier in astronomical texts. The concept of zero as a number, as well as its algebraic and arithmetic properties, was also explored by Indian mathematicians.
Arithmetic and algebra
They developed various methods for performing arithmetic operations, such as addition, subtraction, multiplication, division, square roots, and cube roots. They also invented algorithms for finding solutions to linear and quadratic equations, as well as indeterminate equations of the form ax + by = c. Some of the notable mathematicians who contributed to this field were Aryabhata (5th century CE), Brahmagupta (7th century CE), Bhaskara II (12th century CE), and Mahavira (9th century CE).
Trigonometry
Ancient Indian mathematicians made significant advances in trigonometry, the study of the relations between angles and sides of triangles. They defined the six trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant) and derived formulas for calculating their values for various angles. They also developed methods for finding the sines and cosines of multiple and submultiple angles, as well as the inverse trigonometric functions. Some of the prominent mathematicians who worked on trigonometry were Varahamihira (6th century CE), Aryabhata, Brahmagupta, Bhaskara II, and Madhava of Sangamagrama (14th century CE).
Calculus
They were pioneers in the development of calculus, the branch of mathematics that deals with rates of change, limits, infinite series, and integrals. They discovered many infinite series expansions for trigonometric functions, logarithms, and π, using techniques such as term-by-term differentiation and integration. They also applied calculus to problems in astronomy, geometry, and physics. Some of the remarkable mathematicians who contributed to calculus were Madhava, Nilakantha Somayaji (15th century CE), Jyesthadeva (16th century CE), and Srinivasa Ramanujan (19th-20th century CE).
Geometry, number theory, combinatorics, and the concept of infinity
Other areas of mathematics that were explored by ancient Indian mathematicians include geometry, number theory, combinatorics, and the concept of infinity. Their work spread globally, influencing mathematics in other civilizations and laying the foundation for future discoveries.
The ancient Indian mathematicians made a profound impact on the development of mathematics. Their work is still studied and admired today, and it continues to inspire mathematicians around the world.
