The six district schools of Indian philosophy
The six distinct schools of Indian philosophy, namely Sankhya, Yoga, Nyaya, Vaisheshika, Mimansa, and Vedanta, became fully articulated during the Gupta period.

Overview of the six schools of Indian philosophy
1. Sankhya: Sankhya is one of the oldest philosophical systems in India and focuses on the dualism of matter and spirit. It postulates the existence of two eternal and independent principles - Purusha (consciousness) and Prakriti (nature).

2. Yoga: Yoga is closely related to Sankhya and aims to unite the individual soul with the universal soul through physical and mental practices. It emphasizes meditation, breathing exercises, and ethical disciplines.

3. Nyaya: Nyaya is a system of logic and epistemology. It provides a rational and logical approach to understanding the nature of knowledge and reality. Nyaya relies on inference, perception, comparison, and testimony as valid sources of knowledge.

4. Vaisheshika: Vaisheshika is a system of metaphysics that focuses on the analysis of the material world. It classifies the universe into six categories - substance, quality, action, generality, particularity, and inherence. Vaisheshika also explores the concept of atoms and their combinations.

5. Mimansa: Mimansa is primarily concerned with the interpretation of Vedic texts and rituals. It delves into the nature of dharma (righteousness) and provides guidelines for the performance of sacrificial rituals. Mimansa aims to establish the authority and efficacy of Vedic rituals.

6. Vedanta: Vedanta is a philosophical system that interprets the Upanishads, the concluding part of the Vedas. It emphasizes the ultimate reality of Brahman, the supreme consciousness, and the individual soul's unity with Brahman. Vedanta is further divided into different sub-schools like Advaita, Vishishtadvaita, and Dvaita.

The Gupta period and the articulation of the schools
The Gupta period, which spanned from the 4th to the 6th century CE, is considered a golden age in Indian history. This period witnessed significant advancements in various fields, including philosophy.

During the Gupta period, these six schools of Indian philosophy reached their full articulation. Scholars and philosophers of the time engaged in debates, discussions, and intellectual exchanges, contributing to the development and refinement of these philosophical systems.

The Gupta rulers, such as Chandragupta II and Kumaragupta I, patronized learning and provided support to scholars and universities. This patronage created an environment conducive to the growth and articulation of these philosophical schools.

Prominent philosophers like Ishvarakrishna, Gautama, Vatsyayana, and Shankaracharya played pivotal roles in systematizing and elaborating upon the ideas of these schools. They wrote commentaries, treatises, and philosophical works that provided comprehensive explanations and interpretations of the various concepts and principles.

Overall, the Gupta period was a crucial phase for the development and articulation of the six distinct schools of Indian philosophy. The patronage of the Gupta rulers and the scholarly contributions of eminent philosophers during this period led to a more refined and systematic understanding of these philosophical systems.

The six district school of Indian philosophy Sankhya, Yoga, Nyaya, Vaisheshika, Mimansa, Vedanta became fully articulated during the Gupta period.