The article On the Historical Mystery of Zhang Sanfeng by Simon Cox, on the history of Tai Chi Chuan and its connection to Zhang Sanfeng is great. I’ll just quote a couple of paragraphs from near the end, but recommend you read the whole thing for context:

It seems like Tai Chi was really a Republican era (1912-1949) category that became a sort of umbrella term for various Chinese martial arts that are practiced slowly, containing such multitudes as the ancient martial arts of Chen village, the later arts of the Yang family, and the weird things people were doing at Wudang, in Zhaobao village, and even the government-created variations on these styles.  From this view, asking which style started it all is rather meaningless.  The historical connections simply aren’t there.  From the densest of historical positions, there is no evidence anyone practiced anything called Tai Chi Fist before the 20th century. It arises as a high prestige category in the context of post-Qing Chinese nationalism. Every slow-ish martial art in China seems to have been automatically re-branded as a form of Tai Chi.

According to the Yang Family oral tradition, Yang Luchan 杨露禅 (1799-1872), the founder of the style, called his art variously Cotton Fist 綿拳 or Transforming Fist 化拳, and it was only during his time in Beijing that a Confucian scholar Weng Tonghe 翁同龢 (1830-1904) witnessed him demonstrating his style and wrote a poem about how it embodied the principles of Tai Chi.  According to this oral tradition it was after this event that the art came to be known as Tai Chi Fist.  This story was first published in the 1930’s and is almost certainly apocryphal.  But even if we take it at face value, we arrive at the inevitable conclusion that Tai Chi Fist was an appellation applied first to Yang family martial arts and then later, during the first decades of the 20th century, expanded to include Wudang and Chen styles.

Simon Cox – On the Historical Mystery of Zhang Sanfeng