🚀 go-pugleaf

Gary Merrill writes:

>You can take a mathematician and lock him in his little office with just
>some writing materials and he will (a) be pretty happy, and (b) be able
>and willing to do anything of a mathematical nature.  Even a committed
>*theoretical* physicist will be very distressed under such circumstances
>since he has not way to determining whether his theories (however abstract)
>are *good* ones.

I hope you have not tried this experiment, because I don't think I, at
least, would stay happy for long in this little office.  Seriously, I
think your picture refers to an idealized "pure" mathematician who is
content to prove theorems without any interest in whether they are
useful for science.  I can cite my heroes -  Newton, Leibniz, Lagrange,
Laplace, Euler, Gauss, the Bernoulli crew, Fourier, Hilbert, von Neumann, Weyl,
etc. - as examples of mathematicians who DID care deeply about the
applicability of math.  Any thought experiments with mathematicians
should be run on some of this crowd.  And any theory of what mathematics
is that doesn't note where ideas like the Fourier transform came from is
wanting.  

You can say that these folks were sometimes acting qua theoretical
physicist, if you want to squirm out of this issue.  I don't think that
one can separate things out like that - e.g., Gauss did not say "today I
will do some mathematics and prove Gauss' law; tomorrow I will be a
theoretical physicist and apply this law to electricity."