Exercise 2: Why the Later-Found Gap Doesn't Mean the Announcement Was Premature — Possible Solution
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Announcing a proof and having it undergo real peer review afterward is
the NORMAL, expected process for genuinely difficult mathematics, not
a sign that the announcement itself was rushed or dishonest. A proof
of this real scale and complexity - drawing on years of highly
specialized, cutting-edge mathematics - simply cannot be fully checked
by the author alone before public presentation; verification by other
experts is a real, necessary part of how mathematics is actually
confirmed, not an afterthought.

Wiles's June 1993 lectures presented a genuinely complete, carefully
worked-out argument, built on real years of dedicated effort - it
wasn't a rough sketch or a bluff. Nick Katz, as a serious reviewing
colleague working carefully through the details, found a genuine, real
gap in one specific part of the argument - exactly the kind of subtle
error that can hide in even a fundamentally sound, honestly-presented
proof of this complexity, the same way Chapter 7's own Four Color
Theorem later had a real error found by Ulrich Schmidt despite being
a genuinely serious piece of work.

What would actually indicate a premature or dishonest announcement is
different: presenting something known to be incomplete as finished, or
refusing to acknowledge and work to fix a real problem once
identified. Wiles did the opposite - he accepted Katz's finding,
spent roughly another year working to close the gap, and didn't
publish a corrected, complete proof until he and Richard Taylor had
genuinely resolved it.

ANSWER: Peer review discovering a genuine error after a public
announcement is the normal, expected way mathematics gets verified,
not evidence the original announcement was dishonest or premature -
Wiles presented a real, carefully-developed argument in good faith,
and his response to Katz's finding (spending a year working to
genuinely fix the gap rather than dismissing it) is itself evidence of
honest, careful mathematical practice, not the opposite.

WHY THIS WORKS AS AN ANSWER
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This explains why post-announcement peer review catching errors is
normal scientific/mathematical process rather than a red flag, and
identifies what Wiles's actual real response reveals about his own
good faith.