The Court did not agree with Flook's assertion that the existence of a limitation to a specific field of use made the formula patent-eligible. The majority opinion said of this argument:
A competent draftsman could attach some form of post-solution activity to almost any mathematical formula; the Pythagorean theorem would not have been patentable, or partially patentable, because a patent application contained a final step indicating that the formula, when solved, could be usefully applied to existing surveying techniques.
The court moderated that assertion by agreeing that not all patent applications involving formulas are patent-ineligible by saying, "Yet it is equally clear that a process is not unpatentable simply because it contains a law of nature or a mathematical algorithm." Patents involving formulas, laws of nature, or abstract principles are eligible for patent protection if the implementation of the principle is novel and unobvious—unlike this case, in which it was conceded that the implementation was conventional. Accordingly, in Flook's case, there was no "other inventive concept in its application," and thus no eligibility for a patent.
Summary Totally from Wikipedia, here.