Re: Gist of surrogate factoring theorem

From: N. Silver (mathelp_at_worldnet.att.net)
Date: 04/10/05 

Date: Sun, 10 Apr 2005 04:05:12 GMT

JSH wrote:

> So the theorem as it is gives you what has
> never before been seen, guaranteed an infinite
> supply of potentially non-trivial solutions to a
> difference of squares.

As I understand it, we have no guarantee, nor even
an indication that your algorithm makes progress;
i.e., gets closer to a non-trivial solution after arbitrarily
many iterations.

> Math people are trained to believe that what can be
> simply done has already simply been done,...

It's not about training. It's about having common sense.
If a lot of knowledgeable, hard-working mathematicians
fail to solve a problem, one may want to conclude that
most naive approaches have been tried and lead to dead
ends.

> They didn't convince me, so I went looking, and I found
> the surrogate factoring theorem.

A statemant, not proved, is a conjecture, not a theorem.