[FOM] FLT Decisive by Normal Math Standards

[W.Taylor at math.canterbury.ac.nz]

Quoting Harvey Friedman <hmflogic at gmail.com>:

> CAN WE AND HOW CAN WE MAKE MATHEMATICAL RESULTS CERTAIN OR MORE
> CERTAIN THAN THEY ARE NOW?

Very good question.

> You and I think that the foundational assumptions underlying a
> mathematical proof are of great importance, but mathematicians to my
> knowledge, have never acknowledged any importance in this. Part of the
> problem is that they remain deliberately unfamiliar with foundations,
> and don't care. This is not new, and will continue until the dam
> breaks (for them) in the new f.o.m. revolution ongoing this century.

And again...

> All of this culminated by around 1920 with ZFC, and since then
> mathematicians assume that there are no foundational problems, and
> don't even bother to look when they *feel* good about proofs. This is
> not going to change until the current f.o.m. revolution reaches a
> significantly higher level of intensity.

And again...

> But compared to the non mathematical world, pure mathematics is
> completely singularly in great shape, foundationally, and in terms of
> certainty. Of course I am interested, at least as much as you, in
> issues of certainty, witness the above in all caps. But I don't expect
> hardly any normal mathematicians to care at all - at least until the
> damn breaks later this century. You have to demonstrate a crisis
> before they care.

Could you perhaps be more specific about this coming revolution, especially
regarding the nature of the "dam breaking", that is going to focus
the attention of mathematicians with great force?

Bill Taylor



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