From the eighth century to the seventeenth, the great writers of Advaita Vedānta, the non-dualist school of Vedānta, quoted the first three chapters of Gauḍapāda's verses and passed over the fourth. That silence is one clue to the question still asked about him: how much of his thought he owed to the Buddhists among whom he wrote. His verses, 215 of them in four chapters, explain the Māṇḍūkya Upanishad, the shortest of the Upanishads, and go by three names: the Āgamaśāstra, the treatise on the traditional teaching; the Māṇḍūkya-kārikā, the verses on the Māṇḍūkya; and the Gauḍapādīya-kārikā, Gauḍapāda's verses. They are the oldest systematic account of Advaita that survives.
Their central claim is that nothing has ever come into being. The Upanishad describes the self in four conditions, waking, dreaming, dreamless sleep and a fourth beyond all three. Gauḍapāda reasons from the second to the first. The objects of a dream vanish on waking, and what is absent at the beginning and at the end, he argued, is absent in the middle as well; waking experience is no different in kind. The one self, which is Brahman, only seems divided into many selves, as the space inside separate jars seems divided from the space outside them. If nothing is born, there is no bondage to escape. Bondage and liberation are both imagined, and freedom is the recognition that the self, unborn and calm, was never bound. The third chapter teaches a way to that recognition, asparśa-yoga, a "touchless" discipline in which the mind comes to rest without contact with any object.
He wrote among Buddhist philosophers, and he answered them. He cites views of Nāgārjuna, founder of the Madhyamaka school, and of Asaṅga, a founder of the Yogācāra school, which held that the world we experience is a construction of the mind. The fourth chapter borrows their vocabulary so freely that some scholars, T. R. V. Murti and Richard King among them, think another author wrote it. Vidhushekhara Bhattacharya, his editor in 1943, held that the four chapters began as four separate treatises. Whether Gauḍapāda took over Buddhist doctrine or only Buddhist words is the oldest quarrel about him. Murti argued that the self of the Upanishads, which the Buddhists denied, keeps him a Vedāntin; Sengaku Mayeda suggested that Gauḍapāda, and not Śaṅkara, deserves the old charge of being a Buddhist in disguise.
No record of his life survives. Some scholars read his name as a sign that he came from Gauḍa, the old name for Bengal. His date comes from the Buddhists who quote him: Bhāviveka, Śāntarakṣita and Kamalaśīla all cite his verses, and those citations place him around 500. He cannot be earlier than Asaṅga, whom historians place in the fourth century. The tradition makes him a pupil of the sage Śuka and the teacher of Govinda, who in turn taught Śaṅkara; Ānandagiri, a thirteenth-century Advaita writer, tells that he spent time absorbed in meditation at Badarikāśrama in the Himalayas. Read literally, that lineage would bring Gauḍapāda close to the seventh century. The historian Karl Potter suggests that "teacher's teacher" marks reverence rather than a count of generations.
Śaṅkara, the most famous teacher of Advaita, called him his paramaguru, the teacher of his teacher, and cites him often in his commentary on the Brahma Sūtras. A line-by-line commentary on the verses is handed down under Śaṅkara's name. Through Śaṅkara the school came to read the three states of waking, dream and sleep as stages on the way to knowledge of the self, where Gauḍapāda had set liberation apart from all three. The text kept readers even among Advaita's rivals: Rāmānuja and Madhva, who argued that the world and the individual self are real, treated its first chapter as scripture. Also held here is a plain line-by-line commentary on the Sāṃkhyakārikā, Īśvarakṛṣṇa's verses on the Sāṃkhya school, which the tradition ascribes to a Gauḍapāda. It expounds without reservation the Sāṃkhya account of causes that his own verses refute, and most scholars think a different man wrote it. The oldest monastery of the Gauḍa Sārasvat Brahmin community bears his name, and its head carries the title Gauḍapādācārya.