Indian Mathematical Concepts in European Mathematics

Indian mathematicians introduced the concept of zero, negative numbers, and the decimal system, which revolutionized the way numbers were represented and manipulated in mathematics.

Aryabhata, an Indian mathematician and astronomer, is widely regarded as the father of modern arithmetic. His work, the Aryabhatiya, laid the foundation for many mathematical concepts, including arithmetic operations, fractions, and progressions.

The Pythagorean Theorem, also known as the Indian Theorem or Bhagavata Theorem, is a fundamental theorem in geometry that describes the relationship between the sides of a right triangle.

Madhava of Sangamagrama, an Indian mathematician and astronomer, is credited with developing the concept of the sine function and its series expansion, known as the Madhava series.

The Brahmasphutasiddhanta, written by Brahmagupta, is a comprehensive mathematical text that includes a systematic treatment of indeterminate equations, also known as Diophantine equations.

Bhaskara II, an Indian mathematician and astronomer, developed the concept of the Fibonacci sequence, also known as the golden ratio, and explored its mathematical properties.

The Surya Siddhanta, an ancient Indian astronomical text, contains a detailed discussion of the concept of infinity, including the idea of infinite time and space.

Pingala, an Indian mathematician and grammarian, developed the concept of the Pascal's triangle, also known as Meru Prastara, in his work on prosody and combinatorics.

The Siddhanta Shiromani, written by Bhaskara II, is a comprehensive mathematical text that includes a detailed treatment of trigonometry, including the sine, cosine, and tangent functions.

Madhava of Sangamagrama developed the concept of the Rolle's theorem, which states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the open interval where the derivative is zero.

The Yuktibhasa, written by Jyesthadeva, is a mathematical text that contains a systematic treatment of calculus, including the concepts of limits, derivatives, and integrals.

Madhava of Sangamagrama developed the concept of the Taylor series, which is an infinite series expansion of a function around a given point.

The Ganita Sara Sangraha, written by Mahaviracharya, contains a detailed discussion of the concept of probability, including the calculation of probabilities for various events.

Narayana Pandit, an Indian mathematician and astronomer, developed the concept of the Pascal's law, which states that the binomial coefficients can be arranged into a triangular array, known as Pascal's triangle.