The audacity of math
I thought this statement by physicist Brian Greene in an interview with Terry Gross was particularly lucid, stating an assumption that is too often left unarticulated:
"Underlying (physics, theories of the universe and) everything that we're talking about, in fact underlying everything I do in my entire life, pretty much, is a firm belief that mathematics is a sure-footed guide to how reality works. If that's wrong, then all bets are off."
I don't know enough math theory to argue that the math does not do what the mathematicians assume it does. I assume it's at least in parts analogous to philosophy of language, though, and there the attempts to nail down language so that we can be at least a little sure of the correspondence between our language and the world are insanely messy, at best. Maybe math is a "sure-footed guide" to reality, but the question, "why do you think so?" seems to open up a void that falls away forever.
The radicalness of this assumption, this half-submerged idea about how math isn't constructed but is, kind of takes my breath away.