“I read sentences like “I believe the Frobenioid associated to a number field is something close to the finite etale covers of Spec(OF) (equipped with some log structure) together with metrized line bundles on them, although it’s probably more complicated”.”

And the scary part is, that’s someone trying to reduce Shinichi Mochizuki’s work to the usual old stuff! I mean, everyone in that business knows you should look at the finite etale covers of Spec(O_F), and so on. What’s weird about Mochizuki’s work is that he claims to be using ideas from the foundations of mathematics – set theory – to create new ‘universes’ in which to do math. And then, he’s claiming to take mathematical structures from one universe and transport them to another.

If you look at his homepage, you’ll see a sign saying ‘Inter-universal geometer’ next to a picture of him staring bravely off into space. That gets the idea across as well as anything.

But here’s a passage from his 4th paper:

“In particular, one must continue to extend the universe, i.e., to
modify the model of set theory, relative to which one works. Here, we recall in passing that such “extensions of universe” are possible on account of an existence axiom concerning universes, which is apparently attributed to the “Grothendieck school” and, moreover, cannot, apparently, be obtained as a consequence of the conventional ZFC axioms of axiomatic set theory [cf. the discussion at the beginning of §3 for more details]. On the other hand, ultimately in the present series of papers [cf. the discussion of [IUTchIII], Introduction], we wish to obtain algorithms for constructing various objects that arise in the context of the new schemes/universes
discussed above — i.e., at distant Θ^±\ell NF-Hodge theaters of the log-theta-lattice — that make sense from the point of view the original schemes/universes that occurred at the outset of the discussion.”

- OK, I’ll bite: where can I find your fiction writing..?