[FOM] FLT Decisive by Normal Math Standards

[Harvey Friedman]

I would like to point out that FLT is considered a completely
established mathematical theorem by what has come to be normal
mathematical standards for a famous widely recognized statement.

Consider these ingredients.

1. A proof was published in a major Journal after it was refereed with
unusual care. That unusual care consisted of dividing the paper into
many parts (perhaps 6 or so), with independent referees. The referees
were well aware that it was important that the Journal - and therefore
they - get it right.

2. The process already passed a serious test by finding a serious
error in the first round.

3. After the fix and publication, and after having been looked at
seriously by many experts in many seminars, no issues have arisen for
many years.

This is much more than one has for an ordinarily fine result.

Now perhaps people are not doubting this, but being rather focused on
whether the proof was done in ZFC.

But the refereeing process probably didn't even touch this question.
Rather, they probably focused totally on whether or not the proof
meets the standard criteria that has been used in algebraic geometry
and allied fields for  long periods of time.

Probably none of the referees nor the author had any interest in the
question of whether ZFC suffices. They generally have the point of
view that mathematics is not built on any axiomatic framework and that
axiomatic frameworks are a separate subject and have nothing to do
with mathematical practice or the process by which mathematicians
accept the validity of papers and results.

This is the way the math community operates. However, the situation
will of course radically change during this Century in spectacular
ways, as enough of just the right kind of path breaking results get
established.

Harvey Friedman