[Cronos]

may have carried the idea of the gymansium back to China where they were modified into martial arts institutes which began about that period.

Actually, the idea of Martial arts started in the Southern parts of the Indian continent. There is still a martial art form there that dates to pre-Buddhist times. This martial art form (or similar kinds) was taken by Indian Buddhist missionaries sent by the Indian Emperor Ashoka to China. The Chinese (and later the Japanese) used this and developed the higher martial arts.

[Eternal_Bear]

Some of the Greeks in Central Asia converted to Buddhism. They were in contact with both China and India and would have been the natural intermediaries for the conduit of culture. The Greek gynmasia or the schools of physical culture existed in Central Asia before Ashoka. We know they existed because the foundations of their cities indicate this and it was a prerquisite for Hellenistic culure. The hypothesis that the Chinese borrowed the idea of martial arts academies remains just that, I suspect that they will contend that ther system was developed independently of foreign cultures.