Thank you for the comments on geometry predictions, offering geometry as a door to disclose deeper meanings, and beginnings of Egyptian mathematics. These views have been opposed by many over the years, as you have noted.
There are, of course, other historical paradigms that tend to pry open long lost Old Kingdom mathematics. One paradigm, or metaphor, is the traditional and most common method, astronomy, the mother of mathematics, as reported by the history of mathematics community, and others. Sarton's discussion of Egyptian astronomy, related to Babylonian astronomy, and other issues is worth reading.
For myself, I prefer the broader point of view, one that reaches out to China, India, Mayans and several other great cultures of the world. Many of the great cultures used modular arithmetic, the theory of rational number remainders, written in exact ways, a metaphor that appeared in the Egyptian Middle Kingdom, not in Egyptian astronomy (as needed), but in scribal weights and measures.
Babylonian scholars, like Neugebaur, have suggested that the earliest Babylonian astronomical methods, not directly built upon modular arithmetic, formed the basis for Egyptian astronomy. Babylonian scholars have also suggested that Babylonian weights and measures names and units formed the basis of Egyptian weights and measures.
My view is that the Egyptian texts report large chunks of their culture's mathematics in remainder arithmetic, an early form of modular arithmetic. Predictions concerning the contents of Egyptian astronomy, forming the basis of Egyptian mathematics, is the topic that I enjoy pondering.