Some Indians feel that Indian mathematicians discovered all the mathematical concepts and the Europeans simply took them from India. On the contrary, some European scholars brush aside Indian mathematics and give the credit to Greece. Neither of these views is fully correct.
After seeing the works of all the Indian mathematicians down the ages, one can be absolutely certain that India had great mathematicians who were original, and had produced concepts that were discovered in the western world much later.
It
is very difficult to say with certainty if the west has learnt and borrowed
anything from India in the development of western mathematics except for the
numerals, zero and the concept of infinity. But since contact between the
cultures of India and the West started with the Bactrian Greeks, it
is likely that through them, the Indian thought on Mathematics was
transmitted to the west. it is highly probable that much later through the
Arab Caliphates of Cordoba Grenada, different ideas have been exchanged and
thoughts would have flown both ways. Europeans have also borrowed concepts from
Mesopotamia who in turn may have been influenced by Indian thought and also
influenced it.
But while the Europeans went ahead and developed mathematics further, the Indian mathematics stagnated after the 16th century till Srinivasa Ramanujan came along.
It
is universally acknowledged today that the concept of Zero, Infinity, the
decimal system world uses today as well as the so called Arabic numerals are of
Indian origin. The Indian numerals hvae gone to Europe through the
Arab caliphates in Spain and thus are known as Arabic numerals.
I have gone through Wikipedia for learning more on Indian mathematics and abridged its content below mathematician wise.
Baudhayana (8thCentury BC): He composed the Sulabha Sutras( these are the mathematics required for construction of the sacrificial altars of the Vedas).
Baudhayana’s treatise contains a general statement of the Pythagorean Theorem for the sides of a square and also simple Pythagorean triples. He also gave a square root for the number 2 which is accurate up to 5 decimal places. It should be noted that Baudhayana predates Pythagoras who lived in the 6th century BC.
There were two other Sulabha Sutras composed by Manava (7thcentury BC) and Apastamba (6th century BC).
Pingala(3rd Century BC): He is a musical theorist who authored a Sanskrit treatise on prosody. He stumbled upon the Pascal Triangle and the binomial coefficients despite not having knowledge of the binomial theorem itself. His work also contains the basic idea of Fibonacci numbers. Although his entire work did not survive, a 10th century AD commentary on it by Halayudha exists.
Katyayana(3rd Century BC): He wrote Katyayana Sulabha Sutra which presented a lot of geometry including the general Pythagorean Theorem and also a computation of the square root of 2 to 5 decimal places.
Jain Mathematicians(400 BC to 200 AD): The Jaina mathematicians freed the Indian mathematics from its religious and ritualistic contents. They concentrated a lot on the concept of infinity.
They devised notations for simple powers (and exponents) of numbers like squares and cubes, which enabled them to define simple algebraic equations. Jaina mathematicians were apparently also the first to use the word Shunya (void in Sanskrit) to refer to zero.
Surya Siddhanta (400AD): The author of this treatise is unknown.It contains the roots of modern trigonometry. It uses Sine, Cosine, Tangent and the inverse Sine.
Aryabhata I (476-550AD): he wrote the Aryabhatiya which contained Quadratic equations, Trigonometry and the value of Pi up to 4 decimal places.
Varahamihira
(505-587AD): He wrote the Pancha Sidhhanta which made contributions to
Trigonometry including Sine and Cosine tables up to 4 decimal places and some
formulas relating to them.
Brahmagupta (597-668 AD): In his astronomical work Brahma Sphuṭa Siddhanta , included two chapters devoted to the field of mathematics. Basic operations (including cube roots, fractions, ratio and proportion, and barter)and Practical mathematics (including mixture, mathematical series, plane figures, stacking bricks, sawing of timber, and piling of grain).
Brahmagupta was the first to give rules to compute with zero.
Brahmagupta gave the solution of the general linear equations.
He also went on to solve systems of simultaneous indeterminate equations.
Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals. Given the lengths of the sides of any cyclic quadrilateral,he gave an approximate and an exact formula for the figure's area.
Bhaskara I (600–680 AD): He expanded the work of Aryabhata in his books titled Mahabhaskariya, Aryabhatiya-bhashya and Laghu-bhaskariya.
Hecame out with:
Solutions of indeterminate equations.
An
approximation of the Sine function.
A
formula for calculating the Sine of an acute angle without the use of a
table,correct to 2 decimal places.
AryabhataII (c. 920–1000) wrote a commentary on Shridhara, and an astronomical treatise Maha-Siddhanta. The latter discusses Arithmetic, Algebra and solutions of indeterminate equations.
Shripati Mishra (1019-1066) wrote on permutations and combinations,solution of simultaneous indeterminate linear equation, calculating of planetary longitudes, eclipses and planetary transits.
Bhaskara II (1114-1185) wrote a number of important treatises.Siddhanta Shiromani, Lilavati Ganita, Bija Ganita, Gola Adhyaya and is one of India’s greatest mathematicians. He has contributed on
1. Interest computation.
2.
Arithmetic and Geometric progressions.
3.
Plane Geometry.
4.
Solid Geometry.
5.
Solutions of combinations.
6.
Proof for being divided by zero is infinity.
7.
Proof of the Pythagorean Theorem.
8.
Surds.
9.
Solutions of Quadratic equations, Cubic equations, Quartic equations,
equations with more than one unknown.
10.
Conceived differential calculus.
11.
Compute Pi to 5 decimal places.
12.
Calculated the length of the earth’s revolution around the
sun.
The Kerala school of astronomy and mathematics (1300-1600 AD) was founded by Madhava of Sangamagrama in Kerala, South India and included among its members:
1. Parameshvara,
2.Neelakanta
Somayaji,
3.Jyeshtadeva,
4.Achyuta
Pisharati,
5.Melpathur
Narayana Bhattathiri,
6.Achyuta
Panikkar.
In attempting to solve astronomical problems, the Kerala school astronomers independently created a number of important mathematical concepts. The most important result being the series expansion for trigonometric functions.
The theorems were stated without proof, but proofs for the series for sine, cosine,and inverse tangent were provided a century later in the work written in Malayalam, by Jyesthadeva.
Their discovery of these three important series expansions of calculus, several centuries before calculus was developed in Europe by Isaac Newton and Leibniz was an achievement.However, the Kerala School did not invent calculus; they developed neither a theory of differentiation or integration, nor the fundamental theorem of calculus.
