Introduction
Ancient India was one of the greatest periods of scientific and mathematical research, which greatly contributed to laying the foundation for many of the developments we observe today. It covered all branches of mathematics, astronomy, medicine, and metallurgy, where the intellectual brilliance of ancient Indian scholars was highly reflected.

Mathematics Contributions

-Baudhayan (1st millennium BC): He wrote Sulva-Sutra, a fundamental text in geometry. Baudhayan brought out the Pythagorean theorem much before the time of Pythagoras and gave unexcelled approximations for the value of pi and the square root of two.

-Aryabhata (5th century CE): Aryabhata was a pioneer in mathematics and astronomy. He said that the Earth rotates on its axis, a revolutionary concept at his time. He correctly calculated the value of pi and invented the concept of zero as a numeral and as a mathematical concept, advancing the field of mathematics.

-Brahmagupta (7th century CE): Brahmagupta is the most significant contributor to algebra and arithmetic. He gave rules for operations involving zero and negative numbers, solved quadratic equations, and provided solutions for other important algebraic formulas, which became the foundation of modern algebra.

-Bhaskaracharya, (12th century CE): Bhaskaracharya was a genius mathematician who put down the “Cyclic Method” to solve algebraic equations, a method which was only rediscovered in Europe. He also made important contributions to calculus (derivative) among other things.

Contributions to Science

-Kanad (6th century BCE): Kanad was both a philosopher as well as a physicist. He developed the atomic theory that the universe is made of small particles which can’t be divided further: anu. Although much later, improved, it reflected modern atomic theory.

-Varahamihira (6th century CE): Varahamihira, a celebrated astronomer and astrologer, in his treatise Brihat Samhita, has proposed the “earthquake cloud theory,” associating earthquakes with unusual weather conditions and animal behavior. This shows early attempts at understanding and predicting natural phenomena.

-Susruta (700 BCE): Susruta was the first medical pioneer in ancient India. He wrote the Susruta Samhita, a comprehensive treatise on surgery. It deals with rhinoplasty or plastic surgery of the nose, cataract removal, etc. The book shows a wonderful level of medical knowledge and surgical skill.

-Charaka (2nd century CE): Charaka is known as the father of Indian medicine. His Charak Samhita is a foundational text in Ayurveda that gives insightful detail about diseases, how they are caused, and how they should be treated. The document also provides early observations regarding genetics and heredity.

Conclusion

Ancient Indian scientists are credited with making the most significant contributions to mathematics and science. Ideas and discoveries of zero, the decimal system, and the atomic theory are some of the most fundamental ones that have shaped the human course of intellectual history. Such feats depict how ancient India was at the forefront of the most spectacular intellectual and scientific advancement, giving birth to much of the scientific and technological successes that we celebrate today.