Gautama is the founder of the Nyaya school of philosophy, which is known for its emphasis on logic and epistemology.

The Vaisheshika school of philosophy is known for its atomistic theory, which posits that the universe is composed of indivisible particles called atoms.

Kapila is considered to be the founder of the Samkhya school of philosophy, which is known for its dualistic metaphysics, which posits that the universe is composed of two fundamental principles: purusha (consciousness) and prakriti (matter).

The main goal of the Yoga school of philosophy is to achieve samadhi, a state of deep meditation and spiritual absorption.

Jaimini is the founder of the Mimamsa school of philosophy, which is known for its focus on the interpretation of the Vedas, the sacred texts of Hinduism.

The central concept of the Vedanta school of philosophy is Brahman, the ultimate reality that is the source of all existence.

Buddhism is not one of the six systems of Indian philosophy. It is a separate school of thought that originated in India.

The Nyaya school of philosophy is known for its emphasis on logic and epistemology, which are the study of reasoning and knowledge.

Kanada is the founder of the Vaisheshika school of philosophy, which is known for its atomistic theory.

The main goal of the Samkhya school of philosophy is to achieve moksha, which is liberation from the cycle of birth and rebirth.

Patanjali is the founder of the Yoga school of philosophy, which is known for its emphasis on meditation and spiritual practices.

The Mimamsa school of philosophy is known for its focus on rituals and the interpretation of the Vedas.

Badarayana is the founder of the Vedanta school of philosophy, which is known for its emphasis on the Upanishads, the sacred texts of Hinduism.

The main goal of the Vedanta school of philosophy is to achieve moksha, which is liberation from the cycle of birth and rebirth.