The Atharvaveda, one of the four Vedas, contains numerous hymns and incantations that demonstrate the application of mathematical principles.

Brahmagupta, a renowned mathematician and astronomer, introduced the concept of zero as a number and developed rules for its use in arithmetic operations.

The Sulba Sutras, a collection of mathematical texts composed around 800-600 BCE, provide detailed instructions for constructing altars and performing geometric calculations using the decimal system.

Bhaskara II, also known as Bhaskaracharya, derived the quadratic equation $$ax^2 + bx + c = 0$$ and developed methods for solving it.

Vedanta, one of the six major schools of Indian philosophy, focuses on the ultimate reality of Brahman, the universal consciousness, and the path to liberation through self-realization.

Gautama, also known as Akshapada Gautama, is credited with founding the Nyaya school of Indian philosophy, which emphasizes the importance of logic and reasoning in understanding the world.

Samkhya, one of the six major schools of Indian philosophy, proposes that the universe consists of two fundamental principles: Purusha, the conscious principle, and Prakriti, the material principle.

Patanjali, a renowned sage and philosopher, is credited with authoring the Yoga Sutras, a foundational text that describes the eight limbs of yoga and provides guidance for achieving spiritual liberation.

Vaisheshika, one of the six major schools of Indian philosophy, emphasizes the significance of perception and inference as reliable means of acquiring knowledge about the world.

Vaisheshika, one of the six major schools of Indian philosophy, posits that the universe is composed of multiple independent substances, including atoms, and explores the nature of reality through logical analysis.

Shankara, a prominent philosopher and exponent of Advaita Vedanta, introduced the concept of 'Maya' or illusion, asserting that the phenomenal world is ultimately unreal and Brahman, the absolute reality, is the only true existence.

Madhva, the founder of the Dvaita school of Vedanta, propounded the concept of dualism, asserting that Brahman and the individual soul are distinct and eternally separate entities.

Ramanuja, a prominent philosopher and exponent of Vishishtadvaita Vedanta, emphasized the importance of 'Bhakti' or devotion as the central path to spiritual liberation and union with Brahman.

Nimbarka, the founder of the Dvaitadvaita school of Vedanta, introduced the concept of 'Lila' or divine play, suggesting that Brahman engages in playful and creative activities, resulting in the manifestation of the universe.

Mimamsa, one of the six major schools of Indian philosophy, focuses on the study of the Vedas, emphasizing the importance of ethical conduct, moral values, and the proper performance of rituals in achieving spiritual liberation.