Parker v. Flook: Post-Solution Activity Cannot Save an Algorithm

Parker v. Flook, 437 U.S. 584 (1978), refined the algorithm-eligibility principle of Gottschalk v. Benson by confronting a subtler claim: one that did not seek to patent a formula in the abstract, but instead limited it to a specific technological field and added a concluding step. Dale Flook claimed a method for updating “alarm limits” during the catalytic conversion of hydrocarbons, using a mathematical formula to compute new limits from measured process variables. In a 6–3 decision written by Justice Stevens, the Court held the claim patent-ineligible under 35 U.S.C. § 101. The formula was the only novel element; limiting it to the petrochemical field and adding the conventional step of adjusting an alarm limit was not enough to make the underlying principle patentable.

At a glance

• Case: Parker v. Flook, 437 U.S. 584 (1978), Docket No. 77-642
• Court: Supreme Court of the United States, on certiorari to the Court of Customs and Patent Appeals
• Decided: June 22, 1978; 6–3
• Opinion: Justice Stevens, for the Court; Justice Stewart dissenting (joined by Chief Justice Burger and Justice Rehnquist)
• Subject matter: Patent eligibility under § 101 of a method for computing and updating alarm limits using a mathematical formula
• Holding: A claim whose only novel feature is a mathematical algorithm is not patent-eligible merely because it is confined to a particular field of use and adds conventional post-solution activity

Alarm limits and the claimed method

In many industrial operations, an “alarm limit” is a threshold value for a measured variable — temperature, pressure, or flow rate — that, when crossed, signals an abnormal condition. During the catalytic conversion of hydrocarbons, the appropriate alarm limits change as operating conditions change, so the limits must be updated over the course of the process. Flook’s application claimed a method for updating alarm limits that had three steps: measuring the present value of a process variable, using a mathematical algorithm to calculate an updated alarm limit, and adjusting the actual alarm limit to the newly calculated figure.

The only asserted point of novelty was the mathematical formula used in the second step — a “smoothing” algorithm for computing the updated value. The application did not claim any new measuring device, any new way of determining the input variables, or any new chemistry; it acknowledged that measuring process variables and adjusting alarm limits were already known. The patent examiner rejected the claims as directed to nonstatutory subject matter, but the Court of Customs and Patent Appeals reversed, reasoning that because the claim was limited to the catalytic-conversion field and did not wholly preempt the formula, it escaped Benson. The Acting Commissioner of Patents sought review.

Treat the algorithm as prior art

The Court agreed that Flook’s claim, unlike the claims in Benson, did not entirely preempt the mathematical formula — the formula could still be used outside the catalytic-conversion setting. But it rejected the conclusion that a limited field of use saved the claim. The Court reasoned that a patentable invention must be sought in the application of a law of nature or mathematical formula, not in the discovery of the formula itself: “a patent claim must be considered as a whole,” but the process of analysis requires treating the underlying mathematical principle as though it were “well known” prior art. On that premise, the question becomes whether the claim contains any “inventive concept” in the application of the formula beyond the formula itself.

Applying that test, the Court found nothing patentable remaining. Once the algorithm was assumed to be part of the prior art, Flook’s claim contained no novel or inventive application. “The only difference between the conventional methods of changing alarm limits and that described in respondent’s application rests in the second step — the mathematical algorithm or formula,” the Court explained. The steps of measuring variables and adjusting alarm limits were “the very definition of conventional.” Because the sole innovation lay in the algorithm, and the algorithm was itself an unpatentable principle, the claim as a whole did not describe patent-eligible subject matter.

The rejection of post-solution activity

The Court’s most enduring contribution was its treatment of “post-solution activity.” Flook had argued that the final step — using the computed number to adjust an alarm limit — was a physical, practical application sufficient to confer eligibility. The Court disagreed and warned that such a rule would swallow the exclusion of abstract principles. “The notion that post-solution activity, no matter how conventional or obvious in itself, can transform an unpatentable principle into a patentable process exalts form over substance,” the Court wrote. It offered a memorable illustration: “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 was equally careful about what it was not deciding. It disclaimed any holding that a process is unpatentable simply because it uses a mathematical formula, computer program, or digital computer, and it stressed that its decision reflected the “established rule that a scientific principle… cannot support a patent unless there is some other inventive concept in its application.” The opinion acknowledged the difficulty of the underlying policy questions and, echoing Benson, suggested they were ultimately matters for Congress.

Open questions

Flook left a genuine tension in the law that the Court would grapple with three years later in Diamond v. Diehr. Flook directed courts to treat the algorithm as prior art and to search the remainder of the claim for an inventive concept; Diehr insisted that a claim be assessed “as a whole” without dissecting out the formula, and it upheld a rubber-curing process that used the Arrhenius equation. Commentators have long debated whether the two decisions are consistent, and both remain good law. The Court’s later framework in Mayo Collaborative Services v. Prometheus Laboratories and Alice Corp. v. CLS Bank substantially revived Flook’s methodology, adopting a step that asks whether a claim’s elements beyond the ineligible concept supply an “inventive concept” — the very phrase Flook used. How to reconcile that inquiry with Diehr’s whole-claim command continues to generate litigation.

Implications

• A limited field of use is not enough. Confining a formula to a particular technological area does not, by itself, make an otherwise ineligible algorithm patentable under § 101.
• Post-solution activity does not confer eligibility. Adding a conventional step after the formula produces its result — recording, displaying, or acting on the number — cannot transform an unpatentable principle into a patentable process.
• The algorithm is treated as known. Under Flook, courts assume the mathematical formula is prior art and look for an inventive concept elsewhere in the claim; if the rest is conventional, the claim fails.
• Seek genuine application, not window dressing. Eligibility requires a real inventive application of a principle, not a draftsman’s trick of attaching a field of use or a trivial final step.

Frequently asked questions

What did Parker v. Flook hold? The Court held that a method for updating alarm limits during catalytic conversion was not patent-eligible under 35 U.S.C. § 101. The only novel feature was a mathematical formula, and adding a specific field of use plus conventional post-solution activity did not transform the unpatentable principle into a patentable process.

What is “post-solution activity”? Post-solution activity is a routine step tacked onto a mathematical formula after the formula produces its result, such as recording or acting on the number the formula generates. The Court held that such conventional activity cannot make an otherwise unpatentable algorithm eligible; otherwise any principle could be patented by adding a trivial final step.

How should a claim reciting an algorithm be analyzed under Flook? Flook directs that the mathematical algorithm be treated as though it were already known prior art. The claim is then examined to see whether the application contains any “inventive concept” beyond the formula itself. If the remaining elements are conventional, the claim is ineligible.

Authorities and sources

• Parker v. Flook, 437 U.S. 584 (1978), Docket No. 77-642 (decided June 22, 1978). Justia; Cornell Legal Information Institute.
• Oral argument and case summary via Oyez.
• Later revival of the “inventive concept” inquiry: Mayo Collaborative Services v. Prometheus Laboratories, Inc., 566 U.S. 66 (2012). Justia.
• The 6–3 vote, Stevens authorship, Stewart dissent, and alarm-limit facts corroborated by Wikipedia: Parker v. Flook.