Jayadeva
Jayadeva was a ninth century mathematician.
Contributions
Cyclic Method known as Chakravala method. It is a cyclic algorithm to solve indeterminate quadratic equations.
Solved for x in the equation 61×2 +1 = y2
This was solved in Europe much later in the 17th Century and is commonly known as Lagrange Method. The Lagrange method is complicated while Chakravala is more simple.
Area of combinatorics
Selenius commented on the Chakravala method The method represents a best approximation algorithm of minimal length that, owing to several minimization properties, with minimal effort and avoiding large numbers automatically produces the best solutions to the equation. The chakravala method anticipated the European methods by more than a thousand years. But no European performances in the whole field of algebra at a time much later than Bhaskara’s, nay nearly equal up to our times, equalled the marvellous complexity and ingenuity of chakravala.
Pingala
He was a famous writer before 200 BC. His major work is the Chandas Shastra.
Contributions
Study of Prosody*
Mathematical concepts for describing prosody
First known description of a binary numeral system
Basic idea of the Fibonacci Number** (Maatrameru)
*Prosody is the study of rhythm, intonation, stress and related attributes in speech
**Sequence of numbers starting from zero, one and then every number is a sum of the previous two numbers
Baudhayana
He was a mathematician and a priest. His works are the Sulba Sutra. This sutra gives the rules for the construction of altars. He belonged to the Yajurveda School. His Sutras form a part of the Taittreya of the Krishna Yajurveda.
Contributions
Earliest recorded statement of the Pythagorean Theorem
Pi Value correct to 9 decimal places
Solution for a circle whose area is the same as a given square
Quadratic equations of the forms ax2 = c and ax2 + bx = c
Square root of 2
Diagonals of rectangle bisect each other
Diagonals of rhombus bisect at right angles
Area of a square formed by joining the middle points of a square is half of original
The midpoints of a rectangle joined forms a rhombus whose area is half the rectangle
Geometric solutions (but not algebraic ones) of a linear equation in a single unknown
Brahmagupta
He was the Indian mathematician and astronomer who was head of the observatory at Ujjain. His works are Chadamekala, Brahmasphutasiddanta, Khandakhadyaka, Durkeamynarda. It is believed that the Arabic work Sinhind was a translation of the Brahmasphutasiddanta.
Contributions
Solution to general linear equations
Solution to simultaneous indeterminate equations
Recommended Pulverizers
Cube Roots
Rules for 5 combinations of fractions
Sum of squares and cubes
Earliest Work to use Zero
Operations on negative numbers
Explains Pythogorean Triples
Solves Pell’s equations using Pulverizer (Euclidean Algorithm)
Formulae for cyclic quadrilaterals
Brahmagupta’s theorem describes the length of a diagonal in a cyclic quadrilateral
Construction of figures using right triangles
Sine Table
Establishes that the moon is closer to Earth than the Sun
Methods for calculating the position of heavenly bodies over time
Earth and Heaven are spherical
Earth is moving
Used gravitation to support the Earth’s spherical theory
Brahmadeva
He was the son of Chandrabudha. He was born to the Brahmin family in the Mathura district of Uttar Pradesh. His work includes the Karanaprakasha which is a commentary on the Aryabhatiya.
Contributions
Longitudes of the planets
Problems relating to the daily rotation of the heavens
Eclipses of the sun and the moon
Risings and settings
The lunar crescent
Conjunctions of the planets
Applications of Trignometry to Astronomy
Bhaskara I
Bhaskara I was a mathematician of the 7th century. He was born in Kerala as a Nambudari Brahmin. He and Brahmagupta are the most renowned Indian Mathematicians. His works constitute the commentary on Aryabhatiya called Aryabhatiyabhashya, Mahabhaskariya, Laghubhaskariya. Bhaskara stressed the importance of proving mathematical rules rather than just relying on tradition or expediency.
Contributions
Hindu Arabic Decimal System
Study of Fractions
Numbers Positional System
Variable Equations
Trignometric Formulaes
Approximation for Sine x
Assertion (If p is a prime number, then 1 + (p − 1)! is divisible by p … widely known as the Wilson’s theorem)
Solutions for what is now known as Pell’s equation
First to use a circle for representing zero
Aryabhatta
Aryabhatta is one the greatest mathematicians / astronomers India has seen. He lived during AD 476-550. His famous works are Aryabhatiya and Arya Siddanta. Aryabhatiya covers arithmetic, algebra, plane trigonometry, spherical trigonometry, fractions, quadratic equations, sum of power series and table of sines. His works were translated in Arabic by Al-Khwarizmi, which influenced the adoption of Hindu-Arabic Numerals in Europe from the 12th Century.
Contributions:
Invention of Zero
Arithmetic
Calculation of Longitudes
Decimal Place Valuation
Measuring Earth’s circumference
Hindu Arabic Number System
Pi is irrational
Solutions for Diophantine Equations
Definitions of Sine, Cosine, versine, Inverse Sine influenced the birth of Trignometry
Calendar Calculations for Panchanga
Scientists of India 