FOM: The origin of mathematics?

[JoeShipman@aol.com]

In her column in Parade magazine today, Marilyn vos Savant answers a reader's
query about the ultimate principles on which the universe operates as follows:

"I'd say physics alone covers the territory.  Chemistry falls under the
heading of physics, biology falls under the heading of chemistry, thought
processes fall under the heading of biology, and mathematics falls under the
heading of thought.  I think."

Of course Marilyn missed an opportunity (by not beginning with "Physics falls
under the heading of mathematics") to make a funny joke with a profound point,
namely the mystery that our biologically-determined thought processes somehow
manage to arrive at the mathematics on which everything else depends,
including our thought processes.  

Does physics fall "under" mathematics?  Obviously modern physics is
inconceivable without lots of abstract mathematics.  It may not be completely
explained by mathematics, because the universe could have different laws than
it actually does (though there is a strong emphasis in theoretical physics
nowadays on the degree of mathematical necessity of those laws and the lack of
"choice" a Creator could have had).  I would also argue that there may be true
mathematical statements which can only be "proved" with the help of physics
(see some earlier posts of mine and my published papers "Cardinal conditions
for strong Fubini theorems" and "Aspects of computability in physics", cited
in earlier posts).

Marilyn vos Savant's attitude towards mathematics appears to be "anti-
foundational" in the sense of Hersh or Tymoczko.  But does mathematics really
belong "at the other end" of her hierarchy from where she places it, or is the
situation more complicated?

-- Joe Shipman