Who he was
Nāgārjuna probably lived in southern India in the 2nd or 3rd century CE. Almost nothing about his life is certain. His major work is the Mūlamadhyamakakārikā, the "Root Verses on the Middle Way", and the school founded on it became known as Madhyamaka, the Middle Way school.
Emptiness is dependent arising
Nāgārjuna took the Buddha's teaching that everything arises in dependence on conditions and pressed it to its conclusion. If a thing depends on other things to exist, it has no independent essence of its own; it is "empty". So emptiness is not nothingness. It is simply another name for dependent arising. His most quoted verse says that whatever arises dependently is what he calls emptiness, and that this itself is the middle way.
He also taught two truths: a conventional truth, the everyday world in which we speak of people, trees and teachings, and an ultimate truth, their emptiness. The Buddha, he says, taught through both, and without the conventional one the ultimate cannot be understood.
Much of his writing is argument: he takes a claim that something exists independently and shows it leads to contradiction. The point is not to win debates, but to free the mind from clinging to any fixed view.
His influence
Madhyamaka became the philosophical foundation of Tibetan Buddhism, and through Kumārajīva's translations it shaped Chinese Buddhism as well. Nāgārjuna is honoured in both traditions as a "second Buddha".
Why it matters
Madhyamaka becomes one of the major philosophical schools of Mahāyāna, shaping Buddhist thought in India, Tibet and East Asia.
History and tradition
What historians can say
Nāgārjuna's dates and homeland are uncertain, and many later works were attributed to him. Scholars accept the Root Verses as his, and a few other works, such as a letter of advice to a king, with varying confidence. Later tradition also merged him with a tantric master and an alchemist of the same name who lived centuries later.
What Buddhist tradition remembers
Tradition says he lived for six hundred years, and that he brought the Perfection of Wisdom sūtras back from the undersea realm of the nāgas, where they had been kept since the Buddha's time.