[FOM] FLT Decisive by Normal Math Standards

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

Quoting David Fernandez Breton <djfernan at umich.edu>:

> As I've learned throughout the years, there are at least two kinds of
> mathematicians: those (like me, and I suspect also like you) who were first
> attracted to mathematics because of its very specific epistemic situation
> (because of the fact that, once proved, a mathematical statement seems to
> be much more certain than most everyday statements, and even than
> scientific statements),

Hear hear!

> "the combinatorial thinking, or to put it more bluntly, the cleverness"
> (I'm paraphrasing here), the thrill of solving a problem, the degree of
> abstraction, etc.)

I suspect a considerable overlap here.

> This obviously relates to my previous point above, but also: I think you're
> getting this backwards. Math has not always been this "paradise of rigour",
> which has just stopped being so in recent times.

It's never been that, of course.  Hippasus, Archimedes, Euler, Cantor
and many others were prepared to bypass full rigour for a while.

  On the contrary, for the
> longest time (with possibly the only exception of Euclid's elements),
> mathematics was an activity where the primary objective was to obtain
> results, rather than to be rigorous. Looking at most proofs from two or
> three centuries ago, they look much more like the kind of intuitive
> arguments that physicists do than like modern times proofs. The whole
> concern about foundational issues is relatively recent, its embryo probably
> first arose about halfway through the XIX century, and it only took full
> force in the early XX century. Considering that math has been around for
> millenia,

I quote, though I've forgotten who from, that

** The applied STANDARDS of rigour have varied a lot from time to time,
    place to place, and person to person, but

** The CONCEPT of rigour have hardly changed at all.

It seems to me that the list is trying to place the FLT results
somewhere in one or the other of these areas; but which and how far
I cannot yet determine.

Bill Taylor


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