Cheng Wu-ji (1063~1156), a native of Liaoshe (now Yanggu County, Shandong) during the Song Dynasty. According to Zhang XiaozhongZhujie Shanghan Lun‧Postscript, Cheng was still alive and well at the age of over 90 in 1156, indicating that he was born between 1066 and 1156. After the Jingkang Incident (1126), Liaoshe became part of the Jin territory, and thus he became a subject of the Jin Dynasty. Coming from a family of Confucian physicians, he was intelligent, knowledgeable, and had a broad memory. He specialized in the study of cold-damage disease for several decades. His works include Zhujie Shanghan Lun in 10 volumes (1144), Cold-Damage Disease Mingli Lun in 3 volumes (1142), and Yaofang Lun in 1 volume. He annotated the classics with theories and used theories to prove the classics, clarifying and proving principles, making him the first to annotate the Cold-Damage Disease Treatise and a representative figure of the cold-damage disease school. His foundational work was arduous and greatly influential, providing endless inspiration and earning high praise from medical practitioners.

Song Dynasty's Yan Qizhi commented: "Cheng Gong of Liaoshe, with his extensive discussions and mastery of the art, coming from a family of learning, annotated the Cold-Damage Disease in ten volumes, which he showed to me. Within the 397 methods, he analyzed similarities and differences, clarified hidden profundities, discussed pulse theory, distinguished yin and yang, making the external and internal clearly evident, and the methods of sweating and purging clearly understood. After the 112 formulas, he explained the origins of the names, highlighted the main medicinal properties, differentiated the weights of the ten kinds of formulas, revealed the uses of the seven emotions, distinguished the appropriate tastes, and clarified the suitability of tonification and purgation, all while referencing the Neijing and drawing on various theories. His method of differentiation is most appropriate, truly what previous sages did not mention and later scholars did not know. He deeply understood the profound meaning of Zhongjing."

In terms of academic thought, Cheng Wu-ji was both broad and meticulous, achieving deep understanding through self-study. He referenced the Neijing and Nan Jing to elucidate the theories of Zhongjing, and had unique insights into differentiating external and internal, deficiency and excess, greatly influencing the development of cold-damage disease theory in later generations.

1. To annotate the classics with theories, and to verify the classics with theories. Zhang Zhong-jing in the preface to his Treatise on Cold Damage Diseases mentioned that he compiled works such as Suwen, Nine Volumes, and Eighty-One Difficulties. Cheng Wu-ji often cited theories from the Inner Canon and Difficulties to elucidate Zhang Zhong-jing's theories, analyzing the pathogenesis, treatment principles, and formulas. This not only made the Inner Canon, Difficulties, and Cold Damage Diseases interconnected and integrated, but also achieved the effect of combining the classics with theories to verify the classics. It clarified the principles of Cold Damage Diseases and substantiated the Inner Canon and Difficulties, which is the success of his scholarly approach. For example, using the Lingshu to explain the "Minor Green-Blue Dragon Decoction" entry, which states "if the exterior of Cold Damage Diseases is not resolved and there is water qi below the heart," it is believed that "if the exterior of Cold Damage Diseases is not resolved and there is water retention below the heart, then water and cold will clash, leading to lung cold and qi rebellion, hence retching fever and cough. The Classic of Acupuncture says: 'Cold form and cold drink injure the lung, as the two colds interact, both internal and external are injured, hence qi rebels and ascends,' this pertains to the kidney." The Classic of Acupuncture mentioned in the text comes from the Lingshu﹒Evil Qi Zang-Fu Organ Disease Form Chapter, and Cheng annotated the phrase "qi rebels and ascends," correcting the error in the current version of Lingshu which states "qi pathway ascends." Another example is the annotation of Cold-Extremities Decoction: "Neijing says: 'Cold excess within is treated with sweet heat;' also says: 'Cold excess element being restricted is balanced with pungent heat.' Liquorice Root and Ginger-Aconite combination is a major pungent and hot formula, which can disperse the qi of yin and yang." This uses the principles of Suwen﹒Zhizhenyao Da Lun Four Properties and Five Flavors to explain Zhang Zhong-jing's formulation principles, mutually verifying and elucidating each other, with reason and evidence.
2. To discern and prove theories, and to differentiate similarities and differences. His work Cold-Damage Disease Mingli Lun (Theory of Clarifying Principles) consists of 50 chapters, starting from "fever" and ending with "relapse due to overexertion." It meticulously analyzes the pathogenesis, location, and nature of 50 major symptoms in the Cold-Damage Disease Treatise, distinguishing the different manifestations caused by various etiologies. This provides valuable clinical diagnostic experience and can be considered the earliest "symptom differentiation and diagnosis" text in the Cold-Damage Disease Treatise. As Yan Qizhi commented, "It aims to define the body, classify types, and analyze syndromes. If there are differences in questioning, it clarifies them; if there are similarities that are not, it distinguishes them. It diagnoses internal and external causes for shivering, differentiates yin and yang for dysphoria. Delirious speech and unconscious murmuring are now clearly seen as deficiency or excess; reversal cold of limbs and syncope are classified by depth. Starting with fever and ending with relapse due to overexertion, it comprises 50 chapters, titled Mingli Lun (Theory of Clarifying Principles), truly capturing the essence of Changsha Gong (Zhang Zhongjing)." This evaluation is indeed fair.
3. Detailed Analysis of Formula Preparation.Cheng Wu-ji analyzed the formulas in the Cold-Damage Disease Treatise and made significant contributions to the classification of formula preparation. Building on Chen Cang-qi's statement that "medicines have the functions of dispersing, unblocking, tonifying, purging, lightening, weighting, astringing, lubricating, drying, and moistening, these ten are the general categories of medicine," Cheng explicitly proposed the concept of "ten kinds of formulas." Moreover, based on the Neijing (Inner Canon) and materia medica, he introduced the "seven types of formulas," stating, "The use of formula preparation lies in the seven types: large, small, slow, urgent, odd, even, and complex. Thus, the essence of formula preparation is to achieve the functions of these seven types, which must be rooted in the generation of qi and flavor, thereby completing the formula." He also believed that "only Zhang Zhongjing's formulas are the ancestors of all formulas," and that "the preparation of formulas cannot surpass this." Additionally, in his Formula Treatise, he selected 20 commonly used formulas for cold-damage disease and provided explanations. For example, he discussed Jianzhong Tang and Cinnamon Twig Decoction in terms of odd, even, large, and small preparations: "Some say Cinnamon Twig Decoction releases the exterior with a small amount of Peony Root, while Jianzhong Tang warms the interior with a larger amount of Peony Root, not realizing the difference in their preparation for near and far conditions. For near conditions like skin pathogens, the dosage is small, as in Cinnamon Twig Decoction where Peony Root assists Cinnamon Twig in dispersing, not the same as Jianzhong Tang; for far conditions like heart and abdominal pathogens, the dosage is large, as in Jianzhong Tang where Peony Root assists glue to strengthen the spleen, not the same as Cinnamon Twig. Neijing says: 'For near conditions, odd or even, prepare a small dose; for far conditions, odd or even, prepare a large dose.' This is what it means." It is evident that Cheng Wu-ji's discussions on cold-damage disease formulas largely follow the Neijing and materia medica, serving as a model for formula preparation, and his "seven types of formulas" became a standard for later generations.

In summary, Cheng Wu-ji had profound medical knowledge and rich clinical experience. His most outstanding academic achievement was his research on the Cold-Damage Disease Treatise, which played a pivotal role in the formation of the cold-damage disease school and greatly influenced later scholars in this field, making a significant contribution to the development of medicine.