Q: Was Tai Chi originally taught at the Wudang Mountain?
A: There is no simple answer to this question. There are no verifiable historical sources that indicates any form of Tai Chi practice in the temples of Wudang Mountain before the 1980s. The mountain is today home of several independent schools of martial arts and Tai Chi that teaches in traditional black Daoist priest attire. The popularity of the legends of Wudang Mountain is mainly due to a great number of movies and martial arts tales that praise the supernatural powers of the Daoists. Much like the Shaolin monastery that is immensely popular with tourists from both China and abroad. Both places have schools for martial art with a considerable reputation, but it is doubtful how much of the original tradition that is actually carried on in these schools. In the old days there were without doubt all sorts of Buddhist and Daoist practices as well as martial arts. However, there is, to the best of my knowledge, absolutely no evidence of a long tradition of Tai Chi practice on Wudang Mountain. There are many styles of Wushu, or Kungfu, taught in the area today but their lineages are obscure. This link points to an overview of newer Wudang history. The two oldest masters mentioned are Zhu Cheng De 朱诚德 (1889-1990) and Guo Gao Yi 郭高一 (1921-1996). Their lineages of Tai Chi are not clearly indicated.
The monks on Wudang Mountain could very likely have been practicing Tai Chi alongside other internal martial arts, but it remains a mystery who they studied from. The lineage that is claimed today has Zhang Sanfeng as its founder, a person that is taken by numerous Daoist sects merely as a legendary figure. The Wudang lineage also claim that Wang Zongyue and Jiang Fa was transmitting Tai Chi on Wu Dang, but we know for certain that Wang Zongyue was a student of the Li Family and Jiang Fa resided in the vicinity of the Chen Family.