<p>Although I think frozen-tears view is correct for certain aspects or time periods in mathematics, I don’t believe it is applicable to pure math today. For the last 200 years or so, mathematicians have been attempting to solidify the foundations of math(as a branch of logic), mainly by restricting the number of axioms(or starting assumptions). Sure, there was a bit of trial and error, a little testing of the waters to find the most simple axioms that keep the desired structure, but that is mostly done with- the axioms are set(ok so if you bring up the axiom of choice, we can talk). </p>
<p>At this point, we have a self-consistent logical structure, where theorems are not tweaked to fit reality, but are either true or false(or both-stupid Godel). This means if a mathematical theorem doesn’t jive with reality, we don’t just throw it out or modify it as frozen-tears suggested.</p>
<p>So the question is, restated, why does a logical system based on such a simple starting point have describe reality so well? Why do the theorems about groups apply to molecules? Why do physicists always find such convenient mathematical structures like Calub-Yau shapes to hang their theories on? (I’ve got the feeling most of the posters aren’t mathematicians, come on Ben where are you?)</p>