My current research in metaphysics is pointing me towards structural realism. There are actually a number of different positions that go by the name of structural realism. There are also positions that don't go by that name, but which could... Zuse, Wolfram, Tegmark, Ladyman have written books and articles that are relevant. Structural realism, in all of its forms, is basically a contemporary pythagoreanism: the world is made of mathematics. This can be approached in terms of philosophy of science. Here it would mean that the physical world is isometric with the mathematical formulas that describe it: it *is* the mathematics that describes it. It can also be approached in terms of philosophy of mathematics. Something more or less like platonism - mathematical objects as we know them are simply real. They're not derived from concepts or operations. Finally, it can be approached from the direction of computer science: the world is a computer program. The universe is a giant computer. I incline towards some kind of combination between all three of these versions.

For now I'm treating "metaphysics" as an effort to put together a coherent structural realist position. My sense, though, is that even if one were able to describe the entire universe in terms of a single formula, one would still have the question: why this formula? And the most rational answer to the question would be in terms of some kind of subjectivity or decision.

There would be a lot to be gained by the effort of putting Badiou's mathematical ontology in conversation with structural realism. I'm sure most analytic philosophers and physicists would want to get rid of the subject altogether, but I'd incline towards actually transcendentalizing it even more than Badiou does, putting it in conversation with the cosmogonical ideas of Lurianic kabbalah.