Under the U.S. patent statute, patents may be granted for any new and useful process, machine, manufacture or composition of matter. Over the years, however, case law has put a gloss on this general statement and created certain limitations on what is patentable. Among the types of inventions that have been denied patent protection by case law are inventions in the form of pure algorithms and methods of doing business.

In a recent case, In re Schrader, the Court of Appeals for the Federal Circuit (CAFC) denied patent protection to Schrader's claimed method whereby parcels of real property or other things are sold at auction by a procedure of bidding and determining optimum prices that, according to Schrader, "is usefully but not necessarily performed with the aid of a computer." The basis of the court's decision was that it considered what Schrader was seeking to patent was a mathematical algorithm.

In reaching its decision, the CAFC applied the following two-step test: first, determine whether a mathematical algorithm is recited directly or indirectly in the claim; if it is, then determine whether the claimed invention as a whole is no more than the algorithm itself.

Thus, if the claim is directed to a mathematical algorithm that is not applied to or limited by physical elements or process, the claim is non-statutory. "However, when the mathematical algorithm is applied to one or more elements of an otherwise statutory process claim ... the requirements of [the statute] are met."

Since the CAFC considered that Schrader's process was a mathematical optimization procedure and thus a mathematical algorithm was implicit in the claim, the court addressed the second step. The CAFC found that there was nothing about the steps set out in the claim that reflect a physical change, effect or result and, since the second step of the test was not met, the method was unpatentable. The court distinguished Schrader from cases where patentable subject matter was found when the claims involved the transformation or conversion of subject matter representative of physical activity, such as Arrhythmia Research Technology v. Corazoniz Corp. where an algorithm was applied to data obtained from electrocardiograph signals that were representative of human cardiac activity and In re Taner where the data in question were seismic reflection signals representing discontinuities below the earth's surface.

This decision is in contrast with the famous decision in Paine Webber v. Merrill Lynch, where the Federal District Court of Delaware, had found Merrill Lynch's system for processing and supervising subscriber accounts to be patentable subject matter because the court was "unable to find any direct or indirect recitation of a procedure for solving a mathematical problem" in the claimed system. A factor in that case may also have been that the invention was claimed as a system rather than a process and thus the claim at least implied a requirement for use of appropriate hardware.