Why isn’t the fundamental theorem of arithmetic obvious? (2011)
In math school we had a saying: &quot;obvious means easy to prove&quot;. So the problem is about recognizing the difference between proofs and non-proofs. The hard but satisfying way to learn that difference is to start with axioms. Take some simple system of axioms that holds for Z, and try to prove the FTA from these axioms alone. Then check that the axioms aren&#x27;t satisfied by Z[sqrt(-5)], or the even numbers, or some other ring where the FTA doesn&#x27;t hold.