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I think a lot of people don't appreciate how open mathematicians are, in general, to work "outside the field" - it's especially baked into the DNA through lessons like e.g. Ramanujan.

This guy though, knows what the right way to present the idea would be, but for some reason (ego? knowing it's weak/broken? pique?) chose not to.

Further, in certain cases (P =? NP is one I know of) it has been proven that certain types[0] of proofs cannot possibly work -- and yet people keep offering "proofs" of those bound-to-be-wrong types.

[0] Not sure if 'types' is the right word? Using it colloquially. Maybe 'classes' would be more accurate?

It's subtle, because some of the impossibility proofs are effectively saying that any real proof needs to be somehow sensitive to whether it's in an imaginary universe with oracles, so they can _fail_ in them!

It really is mind-bending stuff -- I have only the vaguest idea of how these proofs could work, but you summarized it beautifully.

As an aside, this is also perhaps also one of the best motivating examples of the idea of "oracles" in math. ("Ok, assume we can do $IMPOSSIBLE_THING... now what?" :) )

> It's not the discussion that makes you a crank. It's publishing a paper claiming you have solved something that you haven't even begun to understand. It's bypassing peer review. It's ignoring all the literature out there and claiming that is somehow a virtue.

You've effectively said that people can't post things on ArXiV unless they're up to your unstated standards; otherwise, they're just "cranks".

Also, no one is "bypassing peer review" by posting on ArXiV and/or YouTube, nor have I seen anyone claim "a virtue" of any sort. Where are you getting all this? From the abstracts?

> It just wastes everyone's time. For example, this paper. It would take a lot of time to sit down and work through the math until I find a specific error in it. But the barren abstract and reference sections strongly suggest that would be a huge waste of my time and energy.

Well, since you've now admitted that you haven't read his work, it seems like everything you said earlier really must be coming from the abstracts alone.

> It just wastes everyone's time. For example, this paper. It would take a lot of time to sit down and work through the math until I find a specific error in it. But the barren abstract and reference sections strongly suggest that would be a huge waste of my time and energy.

Who's time is wasted? The random people who volunteer to read his ArXiV submissions and/or YouTube videos? Really, the only waste of time I've seen is your ad hominem comment in a HN post that isn't even about the author you're blatantly criticizing.

> Mochizuki pulled this stunt with the ABC conjecture. Wasted YEARS of mathematicians' time just to arrive at the conclusion it was all elaborate mathematical smoke and mirrors. The guy is an egotistical asshole with a messiah complex, and managed to burn a lot of PhD students by chasing his red herring. Not cool.

And that's why we must all attack Mochizuki whenever we see his name, right? Do you know Nick? Is he egotistical? Does he have a messiah complex? Are you just going on a tangent now? Are you just math trolling?

The standard being applied here is just that the work is correct. Polson's paper on RH is wrong.

It is bad practice to post incorrect results and not retract them when this is pointed out.

> It is bad practice to post incorrect results and not retract them when this is pointed out.

And it's good practice to take shots at people whenever you see their name?

Also, no, there's no "practice" that says you can't keep a mistake posted on ArXiV or YouTube. That just sounds like something you've made up to justify attacking someone.

And who's pointing this out to him?

Oh damn, I hit a nerve, huh?

Not trolling, I am serious. It took Peter freakin Scholze to finally settle the debate over Mochizuki's work. What came out of it? What else could Scholze have been working on instead of spending time finding the incredibly subtle gaps in logic that he used to construct his false theory?

What Mochizuki did was wrong is because he was utterly uncooperative with the mathematics community, he would answer questions only with more papers that never addressed the concerns being raised, and he was offended that so much scrutiny was applied.

Has Nick made an effort to educate people on the incredible breakthrough he has made? How many lectures has he given on it? Any conference videos on YouTube? Because I'll watch them. Mochi is an extreme example, so I'm sure he's not trying to do anything wrong. He should just retract the paper and keep working on it. An interested volunteer can tell him what is specifically wrong, and that's all that needs to happen.

Peer review isn't a great modern invention. It's better to publish things out in the open and allow discussion of them. If we perform code reviews out in the open and it has proven exceptionally successful then I don't see why we wouldn't encourage the same for scientific research. The fact that peer reviews happen in private makes the whole process opaque to outsiders, and it simply creates artificial barriers.

If you have valid criticisms of something, you can make them in public and help everyone involved grow.

> It's bypassing peer review.

Unfortunately, if you aren't already part of the in-crowd, getting peer review at all can be very difficult, if you have any type of unorthodox idea. Because, you guessed it, you get labelled as a "crank", so why bother wasting time reviewing your paper?