Short answers, pulled from the story.
Madhyamaka is a tradition of Buddhist philosophy and practice founded by the Indian monk and philosopher Nāgārjuna, who wrote around the year 150. Its foundational text is his Mūlamadhyamakakārikā, or Root Verses on the Middle Way. The term also refers more broadly to the ultimate nature of phenomena and to the non-conceptual realization of that reality experienced in meditation.
Nāgārjuna, an Indian Buddhist monk and philosopher who wrote around the year 150, founded Madhyamaka. Scholars agree on very few details of his life, though Joseph Walser has proposed that he lived in Amarāvatī, in the east Deccan.
Madhyamaka comes from the Sanskrit word madhya, meaning middle, combined with suffixes that give it the sense of middling or mid-most. It refers to the madhyamā pratipad, the middle path between opposite philosophical extremes.
In Madhyamaka, emptiness means that all phenomena, or dharmas, lack svabhāva, any independent essence, nature, or substance that would give them solid, independent existence. Madhyamaka also holds that emptiness itself is empty, meaning it has no existence of its own and does not point to any transcendental reality beyond phenomena.
Since the 4th century CE, Madhyamaka has been the dominant interpretation of Buddhist philosophy within Tibetan Buddhism, and it has also strongly influenced East Asian Buddhist thought. Its influence spread alongside the spread of Buddhism across Asia.
Madhyamaka holds that nothing truly arises because none of the four logical possibilities for arising, from itself, from something other, from both, or from no cause, can be shown to hold up. Nāgārjuna concluded that the arising people experience is a mere appearance, comparable to the arising experienced in a dream.