> It seems to me that in order for a scientific study to be considered
> part of mathematics, it must meet two criteria:
> 1) its practicioners make heavy demands on their math
> 2) its practitioners in turn make original mathematical contributions
> which find their homes in other branches of math, or at least that the
> study presents problems which cause other people to develop new
> mathematical techniques to solve.
>
> On the other hand, statistics does not meet the second criteria.
> Although statisticians make considerable use of techniques from other
> branched of mathematics, they do not return the favor. As far as I
> know (please correct me if I'm wrong), even such a basic entity as
> the normal distribution has no uses in mathematics (other than in
> probability and statistics). Therefore I can claim that statistics is
> NOT a branch of mathematics.
Eh? Apart from a minor rescaling of variables the normal distribution is
the error function, which is essential in most work on diffusion problems.
And statisticians like Kolmogorov have contributed significantly to
measure theory.
> Gibbs and Heaviside contributed to vectors, and Einstein had something
> to do with tensors, but these are about the last examples of original
> mathematical work coming from the field of physics.
What about Berry's work on the Riemann zeta function and quantum
mechanics? The JWKB method for asymptotics of the solutions of
differential equations, in which J was a seismologist (1924) and W, K
and B were quantum theorists (1926). Then there's catastrophe theory and
chaos theory (Kolmogorov again, inm the KAM Theorem)
John Harper, School of Mathematical and Computing Sciences,
Victoria University, Wellington, New Zealand
e-mail john.harper@vuw.ac.nz phone (+64)(4)471 5341 fax (+64)(4)495 5045