On the other hand, let me say that I did spend some time reading some of the materials on his webpage. His short "textbook" had the most details -- including some details that were not supplied on my requests here -- and I think there is definitely some interesting mathematical content there. What he has written is incomplete by any standard -- there are, for instance, whole blank sections in the text -- and it is way underexplained from the pedagogical side (I.e., given that we agree that most freshman calculus students actually get very little out of the formal definitions of limits and derivatives, is there any reason to believe that replacing one technical foundation they ignore with another technical foundation they will mostly ignore is going to make any significant difference?). But as a mathematician I definitely enjoyed parts of his work and acquired insight from them. When I have the time I would like to take some notes on it and think harder about how or why to incorporate some of these ideas into my teaching (probably not at the calculus level, but that's okay).

I feel the need for some concluding paragraph summing up my take on the situation, but I guess it's pretty clear that I find it rather strange and have very mixed feelings about it. That will have to do for now.

Since posting comments does not cause anything to bump, it can be carried on harmlessly by those who want to participate in the thread, while all others can ignore it. Given this, I don't see that fedja and misha should stop unless/until they decide to do so themselves.

I'm also inclined to agree with Andrew, but have to admit that if this discussion were taking place on ML's own blog then I would be even less likely to read it. The fact I do occasionally check the discussion going on in that comment thread is more to do with the calibre of the "defenders of the orthodoxy" than with it belonging on MO.

By the way, I and at least 3 other people down-voted the answer in a much earlier state lacking any worthwhile content (it was basically just a denunciation combined with a link at that point).

Now, is a public discussion of controversial issues appropriate for MO?

I'll say "no". Not because I don't think that these discussions are important, but actually because I think that they are important enough to have somewhere where they can actually be easily followed and participated in than stuffed in the comments on a question that most people won't look at.

Discussions and MO just don't fit well together!

Maybe it is time it were moved to a blog or email or...?

"Promotion of obscurantism" -- you know, some people say that about higher topos theorists, too.

Yeah, but those people don't know what they're talking about. First of all, everything is as precisely defined, and the underlying ideas are easy to grok. As usual, the devil is in the details (the underlying ideas are far simpler than the underlying ideas in algebraic geometry, for instance (of course not that I'm implying that algebraic geometers are obscurantists either (quite the opposite, in fact))).

If that still isn't convincing, I suggest that such people take a look at Lurie's DAG I, where he applies the general theory to show that the fundamental category of a stable $\infty$-category (the definition of this is extremely elegant) is a triangulated category, where the shift autoequivalence (whatever you call it) (resp. its inverse) is induced by the natural suspension functor (resp. loop functor).

Documentary? Are you talking about the Rodney Dangerfield comedy film?

Yes.

+1 to Andy.

@Harry: there are many literary critics, and I wouldn't paint them all with the same tarbrush. Perhaps you are thinking of a certain type or school of literary critic?

Me being me, I'm going to respond with a quote from Hardy's Apology:

Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain.

Which does not answer your question, but having gone to the library and looked through the massive tomes of literary criticism, I can say for sure that 99% of it is pure nonsense. I recall the scene in the (completely true and not at all fictional) documentary Back to School:

Diane: You didn't write this paper, Thornton... And I'll tell you something else: Whoever did write this doesn't know the first thing about Kurt Vonnegut!
[cut to Thornton's dorm suite]
Thornton Melon: [on the phone] ... and another thing, Vonnegut! I'm gonna stop payment on the check!
[Kurt tells him off]
Thornton Melon: Fuck me? Hey, Kurt, can you read lips, fuck you! Next time I'll call Robert Ludlum!
[hangs up]

May be it is just me, but I feel a little uneasy reading all this discussion about personal details. I am not sure Misha employment status (and other juicy information about him) is relevant to the question. Can we close this thread please ? Thank you.

Long

However, Misha/Michael, whatever his employment status, doesn't do himself any good carrying on as he does. He is really, as Pete found out, insulting to his interlocutors.

It sounded to me that nielkj was suggesting that the mathematicians there were just about as fawning in their attentions to said critic as the paparazzi, in other words that we mathematician-types are equally taken in by superficial trappings of reputation. (It's perhaps a little ironic to be talking about reputation here however!)

The individual in question was a famous literary critic.

To be fair, this person was a literary critc. Not only do I not have respect for them, I also think that they do active harm through promotion of obscurantism.

@nielkj: I personally am not "worried" whether Misha has a PhD, but since he seems not to be very capable of having a civil conversation about his chosen topic, I thought it might be good to counterbalance any impression that he is a <i>complete flake</i> with the observation that he does have a substantial mathematical background. I don't see that registering that data point is in any way elitist -- it is consonant with what you wrote in the last sentence of your first comment here.

The interactions I had with him on Armstrong's blog did not, however, suggest that he was in any way a deep thinker; what I saw was a great deal of sloppiness. Are you seriously comparing him to Gromov?

Note also: I guess I took from your advice not to try to argue with him. I didn't realize that I shouldn't try to question him for understanding!

About the biographical data: I couldn't find any evidence that Mr. Livshits has a PhD (which is not to say of course that he doesn't have one). His own resume lists a 1974 Master's degree in Leningrad and that he spent five years as a graduate student at Brandeis. He has one MathSciNet publication.

Let me also say that I am sincerely interested in the ideas expressed in the responder's post, although I don't yet understand them very well and feel that, perhaps, they are not being expressed very clearly. In any case, in that it is a program for doing calculus without limits, it is 100% on target as an answer to the question.

[@Yemon: I have no idea what you're talking about. But that's okay with me if it's okay with you. :)]

As to what should be done with this: for a non-CW question this is gaming the system. And I think the moderators probably have established practice of dealing with this (warning + suspension etc). For CW questions, you can always downvote it again: downvoting community wiki answers does not incur a penalty on the voter.