The Accidental Astrophysicists
An anonymous reader recommends a ScienceNews story that begins: "Dmitry Khavinson and Genevra Neumann didn't know anything about astrophysics. They were just doing mathematics, like they always do, following their curiosity. But five days after they posted one of their results on a preprint server, they got an email that said 'Congratulations! You've proven Sun Hong Rhie's astrophysics conjecture on gravitational lensing!'... Turns out that when gravity causes light rays to bend, it can make one star look like many. But until Khavinson and Nuemann's work, astrophysicists weren't sure just how many. Their proof in mathematics settled the question."
Mathematics results are physically relevant. News at 11.
The wikipedia article on gravitational lensing has a neat animation produced with a numerical model. I wouldn't make it your desktop background though because it might warp your file icons.
Some might, but I wouldn't.
Mathematics has its own ontology - namely the axioms that it is based upon.
It has no need for a separate epistemology - it is what it is, and that's that.
Propositional calculus, on which Russell, Frege and Wittgenstein based their mathematical philosophy (which I see as applicable to all rational thought) is itself the root of mathematics - thus mathematics (or logic, however you wish to phrase it) is fundamental to philosophy, rather than philosophy being fundamental to mathematics.
You can't have an ontology without maths - epistemologies are more equal, but essentialy the whole of philosophy is based on the propositional calculus, which is only one of many possible formulations of mathematics.
One swallow does not a fellatrix make