Programming is much much harder than doing mathematics. - Doron Zeilberger

Algorithms existed for at least five thousand years, but people did not know that they were algorithmizing. Then came Turing (and Post and Church and Markov and others) and formalized the notion.

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.

Conventional wisdom, fooled by our misleading "physical intuition", is that the real world is continuous, and that discrete models are necessary evils for approximating the "real" world, due to the innate discreteness of the digital computer.