FOM: social construction of mathematics?

[Vaughan Pratt]

It seems to me that there is some truth to both sides, that mathematics
is there all along, *and* it is what we make of it.  It's almost like a
game, on the one hand we are given the chaos inherent in any non-r.e.
theory and can't change that part of it.  But on the other it is up to us
to find the beauty in what we are given.  This is the game called
mathematics.

I would compare mathematics to diamond jewelry.  You can't substitute
glass, the experts know the difference and you have to hunt for the real
stuff and use only what nature gives you.  But neither can you say that
the jewelry was there in the earth all along.  Some of the diamonds
in the world will never be discovered before we either disappear as a
race or dismantle the world (perhaps to extract the remaining minerals).
And not all that is discovered is of jewelry quality.  And even then it
takes an expert to recognize and cut the good diamonds to display their
features at their best.

On the other hand well-honed theorems seem more robust than well-cut
diamonds.  The closest analogy I could come up with to the risk of
destroying the stone when cleaving it is to be scooped on a good theorem.

Vaughan Pratt