"In what fields have Buddhist monks excelled?"
Martial arts? Some other arts. Propagating a religion. Overcoming what seem to many people to be overwhelming motivations, such as the motivation to eat or to avoid extreme amounts of pain, convincing people that they are wise, maybe some memory and rapid cognition feats.

If you count Stoics as Buddhists, as I would, governing Rome & providing that part of the content of Christianity for lack of which the ancient world seems most alien.