Re: Amateur takes on Wiles's work

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 09/11/04 

Date: Sat, 11 Sep 2004 09:38:46 +0200

jstevh@msn.com (James Harris) writes:

> And as for myself, I'm quite capable of showing how the null test
> works with actual proofs, as in fact it logically has to work.

Well then why don't you?

I've asked you repeatedly to do just that. I've asked you to give an
example of your null test because this supposed test looks like
nonsense to me. I've given my argument expressing why your test does
nothing at all useful and your claims about keystone steps are just
silly (each proof has *one* step that is somehow more important than
all the rest -- from a literally logical viewpoint that is just a
silly notion).

But, these are just words you say. You don't find them persuasive.
Fine. *Show us* an example of your test so that we can evaluate
whether there's anything to it. Now, normally you give us examples
when we ask for definitions. And, if you were competent with
definitions, I wouldn't be asking for an example (namely, you haven't
said what you mean by "contradict", which is ambiguous in this
context). So instead I ask for an example.

And you say you're quite capable, but I provided a trivial example
nonetheless. It is fully formalized so there's no doubt about what
counts as a step. It's not an "indirect" proof, so your spurious
claim that proofs by contradiction *are* null tests doesn't apply.

So have at it, then. Show us which step is the keystone step and
explain why that step and only that step is the keystone step.

Once again, here it is.

,----[ Proof ]
| 1. 0 < 1 Ax.
| 2. 0 + 1 = 1 Ax.
| 3. 0 < 0 + 1 Subst.
| 5. (A x)(A y)( x < y -> x + 1 < y + 1 ) Ax.
| 6. (A y)( n < y -> n + 1 < y + 1) UE
| 7. n < n + 1 -> n + 1 < (n + 1) + 1 UE
| 8. (A x)( x < x + 1 -> x + 1 < (x + 1) + 1) UI
| 9. 0 < 0 + 1 & (A x)( x < x + 1 -> x + 1 < (x + 1) + 1)
| &I
| 10. ( 0 < 0 + 1 & (A x)( x < x + 1 -> x + 1 < (x + 1) + 1) ) ->
| (A x)( x < x + 1 ) Ax.
| 11. (A x)( x < x + 1 ) MP
`----

If there's anything you don't understand (like the notation), just say
so. I'm willing to translate it to plainer English while still
retaining the formal character.

> I think it's obnoxious to you only if you think that his work fails,
> but you hate the idea of the social embarrassment, and shame for that
> truth to come out, so you claim I'm being obnoxious as if society is
> all that matters in mathematics.

I don't quite understand this, either. You keep saying that there's a
conspiracy among mathematicians to accept each other's work just to
keep up appearances and keep the money and respect flowing.

Call me crazy, but that kind of arrangement seems incompatible with
*this* view.

,----[ 3c65f87.0408151150.bfff343@posting.google.com ]
| I couldn't understand it then, but I think I understand better now as
| I've been told that academics is a dog-eat-dog world and academics
| only care about their own research and routinely fight to push down
| research from others, including their own students, unless they can
| steal credit for the ideas as their own.
`----

Now, if mathematicians only care about themselves, then they should
refute Wiles's proof (because such refutations would be big news).
Also, they should probably encourage amateurs with big discoveries,
because they can get co-authorship (likely) and attach their names to
it.

Anyway, who cares about that. Now, about the null test example.... 

-- 
Jesse F. Hughes
"Truth is common stuff, ready to your hand, but lies you have to make
yourself, and you can't be sure they are any good until you've
used them --- and then it's too late."   John Steinbeck

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