Axiomatising mathematical objects is actually a relatively recent development in the history of math: it wasn't until the late 19th century that the approach was introduced. It eventually caught on and is now how modern students learn about algebraic structures.
Defining objects axiomatically is much easier to do in the math world than in the real world. If you want to give yourself a real head-scratcher, try to come up with a list of penguin axioms!
Administrative note: we will be away for a few days next week, so expect the next comic to be ready closer to the end of March.