The Madhyamika school of Buddhist philosophy, which taught 'Shunyata' (emptiness), was founded by:

The Madhyamika (Middle Way) school of Mahayana Buddhist philosophy was founded by Nagarjuna, who taught the doctrine of "Shunyata" (emptiness).

About Nagarjuna:

• He lived around the 2nd century CE (approximately 150-250 CE).
• He is believed to have been a Brahmana from south India, possibly from the Andhra region, who became a Buddhist monk.
• He is associated with the Satavahana kings; according to tradition, he wrote a letter of advice ("Suhrllekha") to a Satavahana king.
• The site of Nagarjunakonda, in the Krishna valley of Andhra Pradesh, is named after him and was a great Buddhist centre.
• He is considered one of the most important philosophers of Mahayana Buddhism, and is sometimes called the "second Buddha".
• His main work is the "Mulamadhyamakakarika" ("Fundamental Verses on the Middle Way").

His teaching:

• "Shunyata" (emptiness): all things are "empty" of independent, permanent existence (svabhava), because they arise in dependence on other things.
• This does not mean that nothing exists, but that nothing exists independently.
• His philosophy avoids the two extremes of eternalism (things exist permanently) and nihilism (nothing exists), hence the name "Middle Way".
• He developed the idea of "two truths": the conventional truth (the world as it appears) and the ultimate truth (emptiness).
• His school is also called "Shunyavada".

Other Mahayana schools:

• "Yogachara" (Vijnanavada): taught that only consciousness (mind) is real; founded by the brothers Asanga and Vasubandhu (4th century CE).
• Dignaga and Dharmakirti were great Buddhist logicians.

Influence:

Nagarjuna's ideas greatly influenced Tibetan, Chinese and Japanese Buddhism.

Why not the other options?

• ✗Vasubandhu and Asanga founded the Yogachara school.
• ✗Dignaga was a Buddhist logician.