Aryabhata, a renowned mathematician and astronomer from the 5th century CE, is widely recognized for introducing the concept of zero as a placeholder and a digit in the Indian numeral system.

The Upanishads, a collection of philosophical and spiritual texts, contain discussions on various mathematical concepts, including infinity, unity, and the relationship between the individual and the universe.

Kanada, the founder of the Vaisheshika school of philosophy, proposed the atomic theory, which states that the universe is composed of five fundamental elements: earth, water, fire, air, and ether.

The Sulba Sutras are a collection of ancient Indian mathematical texts that provide detailed instructions for constructing altars and other ritual structures. They contain valuable information on geometry, including the Pythagorean theorem and the construction of geometric figures.

Bhaskara II, a renowned mathematician from the 12th century CE, discovered the Fibonacci sequence and applied it to solve various mathematical problems, including finding the sum of a series of numbers and solving quadratic equations.

The Nyaya school of philosophy, founded by Gautama, focuses on logic and reasoning as the primary means of acquiring knowledge. It emphasizes the importance of syllogistic reasoning and logical fallacies in understanding the true nature of reality.

Brahmagupta, a brilliant mathematician from the 7th century CE, developed the 'chakravala' method for solving quadratic equations. This method involves converting the quadratic equation into a series of linear equations and solving them iteratively.

The Yoga school of philosophy, founded by Patanjali, focuses on the practice of yoga as a means to achieve liberation from suffering. It emphasizes the importance of self-knowledge, ethical conduct, and meditation in attaining spiritual enlightenment.

Brahmagupta, a renowned mathematician from the 7th century CE, developed a method for calculating the area of a triangle, known as 'Hero's formula'. This formula involves using the lengths of the triangle's sides to calculate its area.

Jainism, an ancient Indian philosophical and religious tradition, emphasizes the importance of non-violence, compassion, and ahimsa as the highest ethical principles. It teaches the practice of non-injury to all living beings and promotes spiritual liberation through self-realization.

Bhaskara II, a brilliant mathematician from the 12th century CE, developed a method for solving cubic equations, known as the 'cubic formula'. This formula involves using the coefficients of the cubic equation to calculate its roots.

Vedanta, an ancient Indian philosophical school, emphasizes the importance of knowledge and wisdom as the means to achieve liberation from suffering. It seeks to understand the true nature of reality and the relationship between the individual soul and the universal consciousness.

Bhaskara II, a renowned mathematician from the 12th century CE, developed a method for calculating the volume of a sphere, known as 'Bhaskara's formula'. This formula involves using the radius of the sphere to calculate its volume.

Yoga, an ancient Indian philosophical school, emphasizes the importance of meditation and self-realization as the means to achieve liberation from suffering. It teaches various techniques of meditation and self-discipline to attain spiritual enlightenment.

Aryabhata, a renowned mathematician from the 5th century CE, developed a method for calculating the circumference of a circle, known as 'Aryabhata's formula'. This formula involves using the diameter of the circle to calculate its circumference.