FOM: F.O.M./pure math; general intellectual interest

[Harvey Friedman]

Lou writes:

>Just a few remarks. I find the notion "general intellectual interest"
>suspect.

>The connection between some pure mathematics and complexity
>questions was brought up by you, not by me.

No. You brought it up when we had a hot exchange on the fom, in the last
paragraph of your posting Re: FOM: OpenMindedComparison, 12:10, 10/24/97.
"...And complexity theory uses nowadays a fair amount of number theory." So
I brought it up this time before you did, since you were going to anyways,
as you did before. Ahhh - Steve's archives!

>...if applications of fom related research
>to complexity are brought up by you, it seems not unreasonable to
>mention number theory in this connection too.

I did not mention applications of fom related research to complexity. I
mentioned something far more significant: that complexity theory has a
strikingly similar intellectual structure and style to fom, and that its
origins are close to the origins of fom - and also its general intellectual
interest. One could argue the case that complexity theory is part of fom,
although I shy away from going that far.

>When in an earlier message I said that I was not inclined to compare
>fom highlights with, say, number theory highlights (as to their
>"general intellectual interest"), this has to do with my finding
>the notion "general intellectual interest" suspect, and also that
>I do not believe in some kind of linear order of such matters.

When in an earlier message I said that I was inclined to compare fom
highlights with, say, number theory highlights (as to thier general
intellectual interest), this has to do with a major difference in the
intellectual value systems represented by the two endeavors. We are talking
about very great differences in kind, and I picked a way of looking at this
difference in kind (through "general intellectual interest") so that it
translates into something that looks like a huge difference in degree, in
order to help make the difference in kind understood.

But now the big question for you is: what do you mean by "suspect"? I think
you will agree that your use of the word "suspect" is quite vague. You
could mean quite a number of things, or maybe all of them; but I think it
is best for you to elucidate this.

>FOM
>has its place in mathematics, though indeed we differ greatly, it
>seems, as to what that place is.

Maybe we don't disagree on FOM's place in mathematics so much. However, we
probably disagree on the places (areas of) mathematics and FOM have in the
wider intellectual universe.

BOTTOM LINE: Please tell us what you mean by "suspect" so that we can
continue this brawl. I take it that you are conceding by default the point
I made about the relative general intellectual interest of P=NP and the
abc-conjecture and Lang's conjectures, but instead question the
significance of that difference.