[StJacques]

". . . 2) Mathematics is invented to describe the real world; things that do not work are discarded; it would be surprising that mathematics were not effective. . . ."

Are you a closet "Nominalist" Doctor Stochastic? Do you believe Mathematics reflects an objective reality or do things just work the way they do in Mathematics because of the meaning we give to definitions?

This is one of my favorite debates in all philosophy.

[Doctor Stochastic]

I'm not sure these are exclusive. We do attempt to give definitions that reflect what we think the world is.