The Tathagatagarbha Sutra and the Srimaladevi Sutra (c. 3rd century CE) teach that all beings possess the tathagatagarbha, the Buddha-embryo, concealed by defilements; the sutra's own similes include gold in filth and a treasure beneath a beggar's floor. The Ratnagotravibhaga systematized the doctrine, and East Asian Buddhism made it central: the Nirvana Sutra's declaration that all beings possess Buddha-nature drove Dogen's Bussho fascicle to insist the grammar matters, all beings are Buddha-nature.
Critics inside Buddhism, including much of the Theravada tradition and the 20th-century Critical Buddhism movement of Hakamaya and Matsumoto, charge that Buddha-nature smuggles an atman, a self, back into the religion of no-self. Defenders reply it is a teaching device for emptiness, not an entity.
Buddha nature is the tradition's answer to the bootstrap problem: you cannot manufacture awakening from delusion, so awakening must be the ground delusion floats on. Practice stops being construction and becomes excavation, the Zen version of the same subtraction Advaita performs on the rope and the snake.
If awakening is innate, what has all this striving been for?