[ArtB]

> And most mathematicians have been reluctant to invest the time necessary to understand the work because they see no clear reward: it is not obvious how the theoretical machinery that Mochizuki has invented could be used to do calculations.

I find this _deliciously_ ironic since that is the position most students have towards mathematics in general (replace "calculations" with "anything relevant in their lives").

[embiaa]

I am a research mathematician. I don't think this quote is an accurate reflection of how 99% of experts feel about Mochizuki's work. Most experts expect that if Mochizuki's work is correct (and even if not) it contains a lot of valuable ideas. Proofs of this kind are almost never mathematical dead ends - they are difficult because they require fresh insights and these insights can always be applied to other areas.

Mathematics is not solely about the proof. Good mathematics is about the communication of the proof and the ideas in it. I think it is fair to say Mochuzuki's work is not being communicated effectively. Though I am not saying the problem lies with Mochizuki alone.

[iso-8859-1]

After Perelman's proof, there have been some "filling in of details". [1] Would you say that Perelman's proof is comparable, and that he could also have been more pedagogical? Do you see any parallel at all?

It sounds to me as if you are implying, that it is Mochizuki's responsebility to be pedagogical. If being pedagogical is good (because it is more social?), how is mathematics different from any other discipline? Surely one ought to be social in every regard.

If the proof turn out to be correct, would you still say Mochizuki communicated it wrong?

[1]: https://en.wikipedia.org/wiki/Grigori_Perelman#Verification

[embiaa]

From what I understand (not exactly my area) Perelman's proof was quite intelligible. Yes there were lots of details to fill in, but for the expert it was clear how this should be done. Perelman's proof also had a long background (it implemented ideas outlined by Hamilton earlier) so for experts it made a lot of sense. I don't think there is a lot of similarity between the two situations.

Research is a social activity. Being a successful researcher means being social. What social means depends on the norms of the relevant field. Yes, we should reflect on those norms and allow innovators to push boundaries but for the science to evolve it has to take everyone with it.

Mochizuki and those around him have a responsibility only if they want take part in the mathematical community - which I think and hope they do.

I am taking the word of experts in the area of arithmetic geometry who say there isn't being enough done to communicate his ideas. Regardless of whether he is right or wrong (really it isn't about this - it is about whether his new ideas have merit - the proof of the abc conjecture would be strong evidence for this) I think the current situation speaks for itself.

Edit: Also, you are entirely correct, we are humans, we should be social in every regard!

[znfi]

I'm not qualified to answer this, but I remember this rather interesting talk where Richard Taylor talks about this somewhat, and there is some discussion of the ABC Conjecture even if somewhat tangentially: https://www.youtube.com/watch?v=eNgUQlpc1m0&t=25m40s

[asgard1024]

There is a quote from Mochizuki himself in the article: [my proof] "constitutes a sort of faithful miniature model of the status of pure mathematics in human society"