Etiquette on giving negative feedback on a top mathematician's work 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.
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.