Named after Janos Bolyai - Hungarian mathematician (1802-1860).
Bolyai is an old lunar crater that is located in the southern hemisphere on the far side. This crater has been heavily eroded and worn by subsequent impacts, leaving only a deformed remnant of the original rim that is overlaid by a multitude of lesser craters. The most notable of these is Bolyai D along the northeast rim and Bolyai W to the northwest. (wikipedia entry)
A crater is a circular depression likely created by an impact event. On the Moon they are named after deceased scientists, polar explorers, astronauts or cosmonauts.