I’m not sure what the author had in mind when he wrote the paper, but its light-hearted content reveals well how to structure a math paper: (1) state the problem and why the reader should care about it, (2) state how the paper builds on prior work, (3) summarize the main results, and then (4) develop them in theorem-proof style.

An economics paper in the same spirit (though of course economics addresses more practical problems than mathematics, in this case whether one should leave the toilet seat up or down) shows quite well how to present and develop an economic model [0].

0. https://jaypilchoi.com/wp-content/uploads/2021/06/Economic-I... [PDF]