Milo, the Rhind Mathematical Papyrus announces all secrets, and then offers nothing more than rather dry calculations. This can't be all there is about Egyptian mathematics. I claim that we see only the level for beginners, but the same problems can be solved on the level of advanced pupils. RMP 33 on the advanced level can be formulated like this (my proposition): A cube measures 37 by 37 by 37 fingers. Calculate the diagonal of the volume in palms, and then the volume itself in cube cubits. First you have to draw up the number column for the square root of 3, or consult it as written on a wall of the scribe's office. Choose the line 56 97 168. Multiply 37 fingers by 168 and divide the result by 97 and you get the diagonal in fingers. Divide it again by 4 and you get the diagonal in palms. Abbreviate the calculations by dividing 37 fingers by a factor of 97/42 = 1 "3 '2 '7 and you get the diagonal in palms (numbers given in the RMP). Now calculate the volume in cube cubits. If you carry out the rather demanding calculation involving high numbers, and if you proceed correctly, you are rewarded with a fine surprise: the volume measures practically 1 "3 '2 '7 cube cubits.
I claim that we see only a part of Egyptian mathematics and have to restore the rest, namely wooden objects visualizing a problem (in the case of RMP 33 perhaps a chest whose outer measures are 41 by 41 by 41 fingers, and whose inner measures are 37 by 37 by 37 fingers) on whose surfaces the problems were written, and the apparatus of simple yet clever additive algorithms such as number columns and number sequences. We have to combine math history with math archaeology and experimental math history, as too many sources (papyri, leather rolls, and the teaching materials) are lost.