"Once a mathematical algorithm has been found, the claim as a
whole must be further analyzed. If it appears that the
mathematical algorithm is implemented in a specific manner to
define structural relationships between the physical elements of
the claim (in apparatus claims) or to refine or limit claim steps
(in process claims), the claim being otherwise statutory, the
claim passes muster under 101. If, however, the mathematical
algorithm is merely presented and solved by the claimed invention,
as was the case in Benson and Flook, and is not applied in any
manner to physical elements or process steps, no amount of
post-solution activity will render the claim statutory; nor is it
saved by a preamble merely reciting the field of use of the
mathematical algorithm.
Various indicia are helpful in determining whether a claim as a
whole calls merely for the solution of a mathematical algorithm.
For instance, if the end-product of a claimed invention is a pure
number, as in Benson and Flook, the invention is nonstatutory
regardless of any post-solution activity which makes it available
for use by a person or machine for other purposes. If, however,
the claimed invention produces a physical thing, such as the
noiseless seismic trace in In re Johnson (what this case involved
will be indicated infra) the fact that it is represented in
numerical form does not render the claim nonstatutory."