What god has to do in mathematics
He picks from uncountably many sets simultaneously without an algorithm.
He preserves us from sets of measure zero and the non-measurables. In his loving arms infinity minus infinity equals whatever we need it to. He takes five loaves of spheres and two small spheres and feeds the host.
He makes the inaccessible cardinals. He stops the inaccessible cardinals from accessing us
He is risen, he is lifted, and he is Born.
He transubstantiates our mortal filters into ultrafilters for free.
He knows the truth of the continuum hypothesis but saves us from it.
He lets us pretend we can do functional analysis, keeping our intersections dense by tucking away the invisible point we could never reach.
Quietly he makes actual of potential infinity.
Silently he transfers the evaluation strategy from heaven (the meta-language) to earth (the source language).
He forgives us our renormalizations.
When we are weak and know only subspace, he carries our functional to the full space.
Ultimately he makes it all cohere. The accidents of our conditionals are treatable as unconditional. “I am that I am”, what makes the axioms hold.
Various atheists try to do without him and do not prevail.
- The joke was initially supposed to be about actual mostly-unacknowledged holes in the theoretical structure: ridiculously strong assumptions, suppressed premises, things we ignore and which we get away with.
But Choice is too well-known and contested to be a great example and I ended up just covering a bunch of nonconstructive results, which aren't as mysterious as I'd like to justify the "god did it" gag.
Basically I don't know obscure unacknowledged issues. But someone who does could write a good version of this post.