The contrast drawn here is between two kinds of claim. A mathematical proposition follows from stated axioms by deduction, so once proved it cannot be undone by anything observed in the world. A scientific proposition rests on evidence gathered so far, and remains open to revision if new measurements do not fit.

This is why mathematics can appear more secure. Its results accumulate without being overturned, whereas physics has repeatedly replaced accepted accounts, as Newtonian mechanics was superseded as a general theory by relativity.

Einstein presented this esteem as resting on a misunderstanding, and went on to argue that mathematical certainty is bought at a price: it holds only within a chosen system of axioms and says nothing in itself about reality. In his formulation, propositions that are certain do not refer to the world, and those that refer to the world are not certain.