The problem with this formulation is that one can convince the audience that something is right when it isn't. Example: 31 is prime, 331 is prime, 3331 is pr

The problem with this formulation is that one can convince the audience that something is right when it isn't. Example: 31 is prime, 331 is prime, 3331 is prime, 33331 is prime, ... 33333331 is prime, therefore 333333331 must be prime (while in fact it's divisible by 17). I'm not arguing one should never look at proofs and take everything for granted. I'm saying that rigorous proofs going down all the way to Peano axioms are unnecessary. In fact, most math people actually use, including linear algebra, calculus, Fourier transform predates Peano axioms.