Math is perfect (in principle), but mathematicians are not (because they are humans), hence the mathematics that (human) mathematicians do is influen… - Doron Zeilberger

Programming is much much harder than doing mathematics.

Many of the successes of `fancy' mathematics are due to sociological and linguistic reasons. They are really high-school-algebra arguments in disguise. Once you strip the fancy verbiage off, what remains is a bare (and much prettier, in my eyes) argument in high-school mathematics, or at most, in Freshman linear-algebra and (formal!) Calculus. For example, I am (almost) sure that Wiles's proof would be expressible in simple language, and if not, there would be a much nicer proof that would.

Mathematics is so useful because physical scientists and engineers have the good sense to largely ignore the "religious" fanaticism of professional mathematicians, and their insistence on so-called rigor, that in many cases is misplaced and hypocritical, since it is based on "axioms" that are completely fictional, i.e. those that involve the so-called infinity.