Mathematics is often taken as a kind of path to true. But its
methods are not as simple as is popularly made out. Although
mathematical systems are often described axiomatically, this is
not how these systems are born. Its often their final form, or
rather the form that they are expressed in to bring out their
most important properties and to make it look as though they are
almost inevitable. Though this is as much psychological for a
certain kind of mind. An example is calculus: Archimedes
investigated integration synthetically but could not put it on a
formal axiomatic system ala euclid. Its development stalled
until Newton/Leibniz utilised the coordinitisation of geometry
to begin to fully realise its capability. It was of course
noticed that these 'fluzions' were not fully rigorous, and
Berkelys criticism of 'ghosts of departed quantities' stung. It
wasn't until Cauchy developed the idea of a limit that the
foundations of calculus began to be put on a rigourous basis.
Now there are a plethora of different