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I want to ask a more general question that relates to a renowned mathematician’s recent proposed proof of a famous hypothesis, which seems to be widely considered not even close to being correct – that it’s not just not correct, it’s “not even wrong”.

Since now, all the top mathematicians have declined to comment on his proof, seemingly out of respect for the mathematician.

So my general question is: for a well-established mathematician, shouldn’t they be given feedback, even if their work isn’t correct? Why not give a rejection, so that they are informed?

I would think that a long-time mathematician who has won the top awards in their lifetime can actually handle the criticism – they wouldn’t have become a master at their craft without overcoming a great deal of failures and negativity in their career. In that sense, it is actually more respectful to tell a researcher when they are wrong.

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    This post appears to relate to a very specific individual with a unique set of circumstances. As such, I've deleted the comments identifying the individual and am taking the (rather heavy-handed) approach of closing this question. I welcome discussion on Academia Meta if the group thinks this is inappropriate. – eykanal♦ Sep 26 '18 at 18:31
  • People should, please, distinguish between criticizing the person and critiquing the mathematics. They aren't at all the same thing. – Buffy Sep 26 '18 at 19:02
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    My impression is that there have been previous efforts to give this kind of feedback on previous attempts on other problems, perhaps even this one. Bear in mind that not everything which occurs is documented online and announced on blogs, etc – Yemon Choi Sep 27 '18 at 8:59
  • Why not give a rejection, so that they are informed? Under such circumstances one could expect that the work would indeed be rejected if it were submitted to a journal. As Yemon says, not everything relevant which occurs will be announced on blogs. – Mark Meckes Oct 1 '18 at 12:11
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The person we're talking about has his place in mathematics cemented whatever he says or does in the latter days of his career. The mathematicians who have been asked to comment on the latest claim know this and do not feel the need to tarnish his reputation by commenting publicly on it. Those who know him well may choose to tell him in private what they think, which he may or may not accept.

At its core, this is a very private story about aging and all of its associated effects. It is magnified by the fact that the person in question is a giant in his field and the public nature that comes along with everything he says. But I'm sure all of us with aging parents/friends/loved ones can relate to the fact that there are no easy ways to deal with this; dealing with it in public does not seem the right approach to me.

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    I strongly agree with this answer, and want to add that the only people who I personally think less of is the committee that somehow decided it would be appropriate to invite him to present the “proof” at such a public venue. – Stella Biderman Sep 26 '18 at 12:52
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    @StellaBiderman -- indeed. – Wolfgang Bangerth Sep 26 '18 at 15:32
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Don't. That would be a one-word answer (somewhat ironic). But to generalize the question, be very careful of giving negative feedback to anyone, ever (whether a mathematician or otherwise). Most people just don't like it. If it is imperative, try to show factual things that are actually wrong, and why (I once showed a Computer Science professor that the steps in his program were needed to run backwards, which when he understood, he appreciated). If you do give the negative feedback, be sure to maintain politeness and courtesy at all times.

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    Indeed. There are two main good reasons to give negative feedback: to help someone improve, and to prevent bad work getting accepted by the mathematical community. The former is appropriate when one’s in a mentorial or close collaborative role, when refereeing/editing submissions, and generally not otherwise. The latter is appropriate when bad work is otherwise liable to get accepted with its errors overlooked. Neither of these applies in the present example (except for close friends/colleagues of the mathematician in question, but they already know the full situation better). – PLL Sep 26 '18 at 17:32