Funny. One would imagine that filtering stuff like this should be very easy, because stuff in math either makes sense, or not, at least to someone knowledgeable in the field.
Print out a copy of this paper. Take it to the nearest university campus. Ask math grad students and profs to look it over. I suspect almost all of them will ask if it's some kind of joke, or simply tell you it doesn't make any sense.
That's the filter we expect to apply. But the journal this was submitted to doesn't use a math filter; it uses a "did you pay me $500" filter, which isn't really useful for identifying legitimate mathematics.
I performed a variant of my suggested experiment. I went on facebook and found a friend of mine, who has a B.S. in mathematics and did some coursework toward a Masters.
It took him about 5 minutes to identify it as a hoax. And he was distracted (with facebook, football, and his 3 year old.)
12:14pm HIM: My first thought: "Holy crap, there's a ton here I don't even remember..."
12:14pm ME: second thought?
12:15pm HIM: Second thought: "Is this legit? It's all over the place..."
12:15pm ME: third thought?
12:16pm HIM: "This is starting to look like something thrown together to appear like a legit math paper."
12:17pm ME: Thanks. That's adequate. It actually is.
12:17pm HIM: Yeah, I was about to say I was 100% certain after one more glance.
EDIT: my wife and I both have advanced math degrees, and we spent the morning laughing at this paper. But since we already knew it was a hoax from the HN post, we weren't valid targets for this experiment. My friend didn't know anything about it before this chat, so he was a valid experimental target. I think his response is adequate to demonstrate that this paper wouldn't pass peer review by actual mathematicians working for a legitimate journal.
And how. I still can't breathe quite right. I still think differentiable category theory was my favorite bit, but I'll admit the recent paper by Pythagoras has appeal.
