The limits of mathematics I think that most people would agree that though everything else seems to be uncertain, that at least mathematics gives us universal truths. Unfortunately, that's not the case. All truths in mathematics are local. No form of mathematics applies to everything. And no matter how you define a mathematical system, there will always be valid statements within it which are true but which can't be proved within that mathematical system.
Inconsistent systems are uninteresting.
But even a consistent system may not yield practical results. A mathematical system is an artificial construct which may or may not be applicable to a real system. Geometry is an example, or rather geometries, for there are many. Euclidian geometry, the granddaddy of them all, starts as does any mathematical systems with a small set of axioms. An axiom is a statement which is assumed to be true.