Avian eggs are products of consumer demand, with modern methodologies for their morphometric analysis used for improving quality, productivity and marketability. Such studies open up numerous prospects for the introduction of artificial intelligence (AI) and deep learning (DL). We first consider the state of the art of DL in the poultry industry, e.g., image recognition and applications for the detection of egg cracks, egg content and freshness. We comment on how algorithms need to be properly trained and ask what information can be gleaned from egg shape. Considering the geometry of egg profiles, we revisit the Preston-Biggins egg model, the Hügelschäffer's model, universal egg models, principles of egg universalism and "The Main Axiom", proposing a series of postulates to evaluate the legitimacy and practical application of various mathematical models. We stress that different models have pros and cons, and using them in combination may yield more useful results than individual use. We consider the classic egg shape index alongside other alternatives, drawing conclusions about the importance of indices in the context of applying DL going forward. Examining egg weight, volume, surface area and air cell calculations, we consider how DL might be applied, e.g., for egg storage. The value of DL in egg studies is in pre-incubation egg sorting, the optimization of storage periods and incubation regimes, and the index representation of dimensional characteristics. Each index can thus be combined to provide a synergy that is on the threshold of many scientific discoveries, technological achievements and industrial successes facilitated through AI and DL.