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U.S. Patent and Trademark Office, Computer Programs and Mathematical Algorithms (Sept. 1989).


In September 1989, the U.S. Patent and Trademark Office published a set of guidelines on the patentability of mathematical algorithms. In these guidelines, the PTO interpreted the law to encourage greater consistency in examination procedures among the different groups which handled patent applications that include mathematical algorithms.

Applicable Patentability Test[]

The PTO relied upon the two-part test of In re Freeman[1] as modified by In re Walter[2] and In re Abele[3] as the proper legal analysis of mathematical algorithm-statutory subject matter cases. Part 1 of the test is to determine whether a mathematical algorithm is recited, directly or indirectly, in the claims. The guidelines warn that, since mathematical algorithms have been determined not to fall within the Section 101 statutory class of a "process," applicants may attempt to circumvent the nonstatutory subject matter rejection by drafting mathematical algorithms as "apparatus" claims. The guidelines require that the claim first be inspected to determine whether the claim recites a mathematical algorithm. Noting that such a determination is not always possible by inspection of the claim, the guidelines indicate "careful interpretation of each claim in light of its supporting disclosure."[4]

Part 2 of the test is to determine whether the mathematical algorithm is "applied in any manner to physical elements or process steps." The guidelines suggest that the Abele rule be followed, wherein the claim is viewed without the mathematical algorithm to determine whether what remains is "otherwise statutory." If it is, the claim does not become nonstatutory simply because it includes a mathematical algorithm. Citing Parker v. Flook, and recognizing that the line between a patentable "process" and an unpatentable "principle" is not always clear, the PTO suggests some “useful guidelines” synthesized from the court decisions, that should aid in drawing the line between a patentable process and an unpatentable "principle.” The PTO issued guidelines resulting from leading court decisions:

1. If the only limitation other than the mathematical algorithm is insignificant or nonessential “post solution activity,” the claimed subject matter is nonstatutory.[5]
2. A mathematical algorithm is not rendered statutory by "attempting to limit the use of the formula to a particular technological environment," so that "field of use" or "end use" limitation in the claim preamble do not suffice to constitute statutory subject matter.[6]
3. If the only claim limitations in addition to the mathematical algorithm are data gathering steps which "merely determined values for the variables used in the mathematical formulae used in making the calculations," such steps are insufficient to change a nonstatutory method of calculation into a statutory process.[7]
4. The PTO suggests that it is useful to analyze whether there is transformation of something physical into another form. A distinction is made between transformation of matter in one physical state to another physical state, which is a statutory process in electrical arts, and mathematical manipulation of “data" which is not a statutory process.
5. Structural limitations in method claims have a limited effect on patentability. While such limitations are not improper, they are not generally to be given patentable weight unless they affect or form an essential part of the process.[8]


The analysis of the guidelines were used before the Federal Circuit in the Solicitor’s brief for the Commissioner in In re Grams,[9] the first reported decision by the Federal Circuit in this area. The subsequent case of In re Iwahashi[10] indicated how mathematical algorithms in apparatus claims should be handled by the PTO.


  1. 573 F.2d 1237, 197 U.S.P.Q. (BNA) 464 (C.C.P.A. 1978) (full-text).
  2. 618 F.2d 758, 205 U.S.P.Q. (BNA) 397 (C.C.P.A. 1980) (full-text).
  3. 684 F.2d 902 (C.C.P.A. 1982) (full-text).
  4. In re Johnson, 589 F.2d at 1070, 1079, 200 U.S.P.Q. (BNA) 199 (C.C.P.A. 1978) (full-text).
  5. Parker v. Flook, 437 U.S. 584, 590 (1978) (full-text).
  6. Diamond v. Diehr, 450 U.S. 175, 191 (1981) (full-text).
  7. In re Richman, 563 F.2d 1026, 1030, 195 U.S.P.Q. (BNA) 340 (C.C.P.A. 1977) (full-text).
  8. In re de Castelet, 562 F.2d 1236, 1244, 195 U.S.P.Q. (BNA) 439 (C.C.P.A. 1977) (full-text).
  9. 888 F.2d 835 (Fed. Cir. 1989) (full-text).
  10. 888 F.2d 1370, 12 U.S.P.Q.2d (BNA) 1908 (Fed. Cir. 1989) (full-text).