Differing Indian traditions ascribe the first truly Vedantic manuals, the Vedanta sutras (also called Brahma sutras), to two semilegendary figures: the philosopher Badarayana (circa 4th century BC), and a vaguely identifiable sage named Vyasa. To the latter these same traditions also ascribe definitive compilations of the Vedas, as well as a compilation of the later epic poem Mahabharata. Most modern scholars, without totally rejecting the traditions, state that the Sanskrit name Vyasa ("arranger" or "collector,") has been applied to many ancient Hindu authors and compilers.
Whoever first formulated the Vedanta set down its teachings in aphorisms so pithy that they are virtually unintelligible without the aid of interpretation. Different interpretations have given rise to numerous schools of Indian philosophy, the most important being Advaita, or nondualism, founded by the Hindu philosopher and theologian Shankara.
The central problem in Shankara's system of interpretation is the nature of the relation between Brahman and atman, the individual self, breath, or soul. According to Shankara, the two are identical. The individual self, however, is prevented by avidya, or ignorance, from understanding the nondual universal nature of pure being (Brahman). Thus it perceives only separate selves and things (that is, the whole world of material, temporal existence), and never realizes that all separate existences are essentially unreal (these being phenomena produced by maya, the power of illusion mysteriously inherent in and projected from Brahman). As long as the individual self remains without real knowledge, it will blindly look for its true self in the phenomenal world. It remains enmeshed in that world, again and again experiencing samsara, or the series of existences, deaths, and rebirths each unenlightened soul undergoes as a consequence of its karma (its good and evil actions in past existences, which determine the form of future existences). Through the proper knowledge of Vedanta, however, the individual soul recognizes the limitless reality forever existing behind the cosmic veil of maya, realizes that its own true nature is identical with Brahman, and through this self-realization achieves moksha (release from samsara and karma) and Nirvana.
Later modifications of this philosophy were introduced by the philosophers Ramanuja and Madhva. In modern times, Vedanta has received attention outside India through the work of Vivekananda, the Indian interpreter of the work of the Hindu mystic Ramakrishna. In the U.S., for example, in the early 1980s some 1000 members were claimed by the Vedanta Society of America, affiliated with a group with international headquarters at Belur Math, the Ramakrishna Mission chapel near Calcutta..