The term "t'ai chi ch'uan" translates as "supreme ultimate fist", "grand supreme fist", "boundless fist", "supreme ultimate boxing" or "great extremes boxing". The chi in this instance is the Wade–Giles transliteration of the Pinyin jí, and is distinct from qì (ch'i, "life energy"). The concept of the taiji ("supreme ultimate"), in contrast with wuji ("without ultimate"), appears in both Taoist and Confucian Chinese philosophy, where it represents the fusion or mother of Yin and Yang into a single ultimate, represented by the taijitu symbol Taijitu - Small (CW).svg. T'ai chi ch'uan theory and practice evolved in agreement with many Chinese philosophical principles, including those of Taoism and Confucianism. T'ai chi ch'uan training involves five elements, taolu (solo hand and weapons routines/forms), neigong & qigong (breathing, movement and awareness exercises and meditation), tuishou (response drills) and sanshou (self defence techniques). While t'ai chi ch'uan is typified by some for its slow movements, many t'ai chi styles (including the three most popular – Yang, Wu, and Chen) – have secondary forms with faster pace. Some traditional schools of t'ai chi teach partner exercises known as tuishou ("pushing hands"), and martial applications of the taolu's (forms') postures. In China, t'ai chi ch'uan is categorized under the Wudang grouping of Chinese martial arts – that is, the arts applied with internal power. Although the term Wudang suggests these arts originated in the Wudang Mountains, it is simply used to distinguish the skills, theories and applications of neijia ("internal arts") from those of the Shaolin grouping, waijia ("hard" or "external") martial art styles. Since the first widespread promotion of t'ai chi ch'uan's health benefits by Yang Shaohou, Yang Chengfu, Wu Chien-ch'uan, and Sun Lutang in the early 20th century, it has developed a worldwide following among people with little or no interest in martial training, for its benefit to health and health maintenance. Medical studies of t'ai chi support its effectiveness as an alternative exercise and a form of martial arts therapy. It is purported that focusing the mind solely on the movements of the form helps to bring about a state of mental calm and clarity. Besides general health benefits and stress management attributed to t'ai chi ch'uan training, aspects of traditional Chinese medicine are taught to advanced t'ai chi ch'uan students in some traditional schools. Some other forms of martial arts require students to wear a uniform during practice. In general, t'ai chi ch'uan schools do not require a uniform, but both traditional and modern teachers often advocate loose, comfortable clothing and flat-soled shoes. The physical techniques of t'ai chi ch'uan are described in the "T'ai chi classics", a set of writings by traditional masters, as being characterized by the use of leverage through the joints based on coordination and relaxation, rather than muscular tension, in order to neutralize, yield, or initiate attacks. The slow, repetitive work involved in the process of learning how that leverage is generated gently and measurably increases, opens the internal circulation (breath, body heat, blood, lymph, peristalsis, etc.). The study of t'ai chi ch'uan primarily involves three aspects: Health: An unhealthy or otherwise uncomfortable person may find it difficult to meditate to a state of calmness or to use t'ai chi ch'uan as a martial art. T'ai chi ch'uan's health training, therefore, concentrates on relieving the physical effects of stress on the body and mind. For those focused on t'ai chi ch'uan's martial application, good physical fitness is an important step towards effective self-defense. Meditation: The focus and calmness cultivated by the meditative aspect of t'ai chi ch'uan is seen as necessary in maintaining optimum health (in the sense of relieving stress and maintaining homeostasis) and in application of the form as a soft style martial art. Martial art: The ability to use t'ai chi ch'uan as a form of self-defense in combat is the test of a student's understanding of the art. T'ai chi ch'uan is the study of appropriate change in response to outside forces, the study of yielding and "sticking" to an incoming attack rather than attempting to meet it with opposing force. The use of t'ai chi ch'uan as a martial art is quite challenging and requires a great deal of training.
When tracing t'ai chi ch'uan's formative influences to Taoist and Buddhist monasteries, there seems little more to go on than legendary tales from a modern historical perspective, but t'ai chi ch'uan's practical connection to and dependence upon the theories of Sung dynasty Neo-Confucianism (a conscious synthesis of Taoist, Buddhist, and Confucian traditions, especially the teachings of Mencius) is claimed by some traditional schools. T'ai chi ch'uan's theories and practice are believed by these schools to have been formulated by the Taoist monk Zhang Sanfeng in the 12th century, at about the same time that the principles of the Neo-Confucian school were making themselves felt in Chinese intellectual life. However, modern research casts serious doubts on the validity of those claims, pointing out that a 17th-century piece called "Epitaph for Wang Zhengnan" (1669), composed by Huang Zongxi (1610–1695 A.D.), is the earliest reference indicating any connection between Zhang Sanfeng and martial arts whatsoever, and must not be taken literally but must be understood as a political metaphor instead. Claims of connections between t'ai chi ch'uan and Zhang Sanfeng appeared no earlier than the 19th century. History records that Yang Luchan trained with the Chen family for 18 years before he started to teach the art in Beijing, which strongly suggests that his art was based on, or heavily influenced by, the Chen family art. The Chen family are able to trace the development of their art back to Chen Wangting in the 17th century. It has been suggested that the Taiji of Chen Village had been strongly influenced by the arts of the Shaolin Monastery, which resided in the same region and in rather close proximity. What is now known as "t'ai chi ch'uan" appears to have received this appellation from only around the mid-1800s. There was a scholar in the Imperial Court by the name of Ong Tong He who witnessed a demonstration by Yang Luchan at a time before Yang had established his reputation as a teacher. Afterwards Ong wrote: "Hands holding Taiji shakes the whole world, a chest containing ultimate skill defeats a gathering of heroes." Before this time the art may have had a number of different names, and appears to have been generically described by outsiders as zhan quan (??, "touch boxing"), mian quan (??, "soft boxing") or shisan shi (???, "the thirteen techniques").