The Easiest Line To Draw would be simply to say that if an invention is physical, then it should be patentable, and if it is abstract, then it should not be. But what do we do with inventions that involve both the physical and the abstract? For example, the case of Diamond v. Diehr involved a rubber-curing machine that relied on a significant amount of software to control the machine's timing. The U.S. Supreme Court ruled in 1981 that the patent was for industrial equipment, not an abstract algorithm, and thus the overall patent—software plus machine—was valid. But the court left a key question hanging: how much physical invention is necessary before the overall device is patentable? If all of the inventiveness is in the algorithm, which is then applied in a trivial manner to a simple machine, is the overall patent okay?

In a long series of rulings, culminating in 1994 with In re Alappat and In re Lowry, the U.S. Court of Appeals for the Federal Circuit ruled that an uninventive physical component added to an inventive abstract component makes the whole patentable. In other words, "a new algorithm to calculate Fourier transforms" is not patentable, but "a stock PC on which is programmed a new algorithm to calculate Fourier transforms" has enough of a physical component to be patentable.

Further, the court ruled that since a computer is so integral to a computational algorithm, patent examiners are obliged to assume that one exists. If an application is for "a pure computational algorithm," then the examiner must read it as if the words "a computer on which is programmed" had been prepended to the description of the algorithm.

This is the bottom of the slippery slope: there is no longer any meaningful barrier to the patenting of abstract algorithms. The use of any inventive mathematical algorithm that requires more calculation than can be reasonably done by hand is now patentable.

Another Approach Might Be to distinguish between the pure mathematical algorithm, which should not be patentable, and its application to real-world problems, which should be.

For example, the case of Gottschalk v. Benson concerned the patentability of a program to convert between binary-coded decimal and plain old binary. Evidently, this was too close to unapplied pure math; the Supreme Court struck down the patent in 1972, because "the patent would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself."

In contrast, State Street Bank and Trust Co. v. Signature Financial Group Inc. was a suit over alleged infringement of State Street's patented system for doing the bookkeeping for a suite of mutual funds. The system did not push around physical objects, but the Court of Appeals for the Federal Circuit ruled that the share prices and other numbers it derived still have a real, tangible effect and may therefore be considered to be a valid subject for a patent. So this attempt to distinguish the patentable from the unpatentable is too unreliable.