The correct answer is option 1: Nagarjuna. Nagarjuna was associated with the formulation of the basic ideas of Mahayana Buddhism.

Option 2: Kashyapa Matanga, also known as Mahakashyapa, was a disciple of Gautama Buddha and a prominent figure in early Buddhism. However, he is not specifically associated with the formulation of Mahayana Buddhism.

Option 3: Menander was a Greco-Bactrian king who ruled in Northwestern India during the second century BCE. While he patronized Buddhism and is known for his support of Buddhist institutions, he is not directly linked to the formulation of Mahayana Buddhism.

Option 4: Kanishka, a Kushan Empire ruler, played a significant role in the spread of Buddhism and was a supporter of Mahayana Buddhism. However, he did not formulate the basic ideas of Mahayana Buddhism.

Thus, option 1, Nagarjuna, is the correct answer as he is associated with the formulation of the basic ideas of Mahayana Buddhism.