This communication explores issues of the relation of commentary and education surrounding the life, work, and legacy of Zheng Xuan 鄭玄 (127–200 CE). It is to Zheng Xuan, more than any other commentator, whom we owe our understanding of the Confucian Classics, and it thus behoves us to ask how he knew what he knew, and whether or not he was abjectly wrong. What we learn about his educational background is both typical and atypical: typical in that he, like most exegetes, had a broad background including mathematics and the astral sciences, but atypical in the sense that he actively avoided imperial institutions for academic advancement and the performance of royal rites. In light of his lack of living experience in this regard, the canonisation of Zheng Xuan’s commentary of the ritual classics is odd. To reflect on this disconnect, I submit for your consideration an example from the Book of Etiquette & Ceremonial concerning the arrangement of archery targets for the ‘Big Shoot’ (da she 大射). There, what Zheng Xuan does is forward philological arguments for converting a variety of anthropometric and object-based measuring units into the standard chi 尺 (23.1 cm) so that he can abstract the Classics’ descriptions into a maths problem, which leads him to physically impossible results. What is curious is that scholars like Kong Yingda 孔穎達 (574–648 CE) and Jia Gongyan 賈公彥 (fl. 637 CE) who were responsible for Zheng Xuan’s canonisation do not correct him but rather attempt to supply his calculations with mathematical proofs in their subcommentaries. As the results remain physically impossible, however, we realise that the commentarial tradition in this case is divorced from any historical or contemporary reality. Ritual (li 禮) is very much a study defined by numbers (shu 數), and the lesson that I wish to draw from this case is that there is a lot to learn about a classical commentator's modus operandi by taking such things in his educational background like mathematics into account.