Baudhayana, a renowned Indian mathematician from the 8th century BCE, is widely recognized for his discovery of the Pythagorean theorem, predating Pythagoras's work.

Gautama Buddha, the founder of Buddhism, established a philosophical school that emphasizes the pursuit of enlightenment, liberation from suffering, and the attainment of nirvana.

Adi Shankara, a prominent philosopher of the Advaita Vedanta school, introduced the concept of 'neti neti' to convey the ineffability and transcendence of Brahman, the ultimate reality.

The Sulba Sutras are ancient Indian mathematical texts that provide detailed instructions for constructing altars and performing rituals, showcasing the advanced geometrical knowledge of the time.

Brahmagupta, a brilliant mathematician of the 7th century CE, introduced the concept of zero as a number and developed the decimal system, revolutionizing the field of mathematics.

The Nyaya school of philosophy, founded by Gautama, places great emphasis on logical reasoning, debate, and the analysis of knowledge, aiming to establish a sound foundation for philosophical inquiry.

Adi Shankara, the renowned Advaita Vedanta philosopher, introduced the concept of 'maya' to describe the illusory nature of the world, asserting that the ultimate reality is Brahman, the unchanging and eternal consciousness.

The Sulba Sutras are ancient Indian mathematical texts that provide detailed instructions for constructing altars and performing rituals, showcasing the advanced geometrical knowledge of the time.

Brahmagupta, a brilliant mathematician of the 7th century CE, introduced the concept of negative numbers and developed methods for solving quadratic equations, significantly advancing the field of mathematics.

The Vaisheshika school of philosophy, founded by Kanada, emphasizes the importance of perception and experience in acquiring knowledge, asserting that the world is composed of indivisible atoms.

Ramanuja, a prominent philosopher of the Vishishtadvaita school, emphasized the importance of 'bhakti' (devotion) as the path to liberation, advocating for a personal relationship with God.

Lilavati, written by Bhaskara II in the 12th century CE, is a comprehensive mathematical treatise that covers various topics, including arithmetic, algebra, geometry, and trigonometry, showcasing the advanced mathematical knowledge of ancient India.

Bhaskara II, a renowned mathematician of the 12th century CE, introduced the concept of the Fibonacci sequence and developed methods for solving indeterminate equations, demonstrating his mastery of advanced mathematical concepts.

The Mimamsa school of philosophy, founded by Jaimini, emphasizes the importance of scriptural authority and the infallibility of the Vedas, focusing on the correct interpretation and application of Vedic rituals and injunctions.

Madhvacharya, the founder of the Dvaita school of philosophy, emphasized the distinctness of the soul and God, asserting that they are two separate and independent entities.