Parker v. Flook
437 U.S. 584 (1978)

Annotate this Case

U.S. Supreme Court

Parker v. Flook, 437 U.S. 584 (1978)

Parker v. Flook

No. 77-642

Argued April 25, 1978

Decided June 22, 1978

437 U.S. 584



Respondent's method for updating alarm limits during catalytic conversion processes, in which the only novel feature is a mathematical formula, held not patentable under § 101 of the Patent Act. The identification of a limited category of useful, though conventional, post-solution applications of such a formula does not make the method eligible for patent protection, since, assuming the formula to be within prior art, as it must be, O'Reilly v. Morse, 15 How. 62, respondent's application contains no patentable invention. The chemical processes involved in catalytic conversion are well known, as are the monitoring of process variables, the use of alarm limits to trigger alarms, the notion that alarm limit values must be recomputed and readjusted, and the use of computers for "automatic process monitoring." Pp. 437 U. S. 588-596.

559 F.2d 21, reversed.

STEVENS, J., delivered the opinion of the Court, in which BRENNAN, WHITE, MARSHALL, BLACKMUN, and POWELL, JJ., joined. STEWART, J., filed a dissenting opinion, in which BURGER, C.J., and REHNQUIST, J., joined, post, p. 437 U. S. 598.

Page 437 U. S. 585

MR. JUSTICE STEVENS delivered the opinion of the Court.

Respondent applied for a patent on a "Method for Updating Alarm Limits." The only novel feature of the method is a mathematical formula. In Gottschalk v. Benson,409 U. S. 63, we held that the discovery of a novel and useful mathematical formula may not be patented. The question in this case is whether the identification of a limited category of useful, though conventional, post-solution applications of such a formula makes respondent's method eligible for patent protection.


An "alarm limit" is a number. During catalytic conversion processes, operating conditions such as temperature, pressure, and flow rates are constantly monitored. When any of these "process variables" exceeds a predetermined "alarm limit," an alarm may signal the presence of an abnormal condition indicating either inefficiency or perhaps danger. Fixed alarm limits may be appropriate for a steady operation, but during transient operating situations, such as start-up, it may be necessary to "update" the alarm limits periodically.

Respondent's patent application describes a method of updating alarm limits. In essence, the method consists of three steps: an initial step which merely measures the present value of the process variable (e.g., the temperature); an intermediate step which uses an algorithm [Footnote 1] to calculate an updated alarm limit value; and a final step in which the actual alarm limit is adjusted to the updated value. [Footnote 2] The only difference

Page 437 U. S. 586

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. Using the formula, an operator can calculate an updated alarm limit once he knows the original alarm base, the appropriate margin of safety, the time interval that should elapse between each updating, the current temperature (or other process variable), and the appropriate weighting factor to be used to average the original alarm base and the current temperature.

The patent application does not purport to explain how to select the appropriate margin of safety, the weighting factor, or any of the other variables. Nor does it purport to contain any disclosure relating to the chemical processes at work, the monitoring of process variables, or the means of setting off an alarm or adjusting an alarm system. All that it provides is a formula for computing an updated alarm limit. Although the computations can be made by pencil and paper calculations, the abstract of disclosure makes it clear that the formula is primarily useful for computerized calculations producing automatic adjustments in alarm settings. [Footnote 3]

The patent claims cover any use of respondent's formula for updating the value of an alarm limit on any process variable involved in a process comprising the catalytic chemical conversion of hydrocarbons. Since there are numerous processes of that kind in the petrochemical and oil-refining industries, [Footnote 4] the claims cover a broad range of potential uses of the method. They do not, however, cover every conceivable application of the formula.

Page 437 U. S. 587


The patent examiner rejected the application. He found that the mathematical formula constituted the only difference between respondent's claims and the prior art, and therefore a patent on this method "would, in practical effect, be a patent on the formula or mathematics itself." [Footnote 5] The examiner concluded that the claims did not describe a discovery that was eligible for patent protection.

The Board of Appeals of the Patent and Trademark Office sustained the examiner's rejection. The Board also concluded that the "point of novelty in [respondent's] claimed method" [Footnote 6] lay in the formula or algorithm described in the claims, a subject matter that was unpatentable under Benson, supra.

The Court of Customs and Patent Appeals reversed. In re Flook, 559 F.2d 21. It read Benson as applying only to claims that entirely preempt a mathematical formula or algorithm, and noted that respondent was only claiming on the use of his method to update alarm limits in a process comprising the catalytic chemical conversion of hydrocarbons. The court reasoned that, since the mere solution of the algorithm would not constitute infringement of the claims, a patent on the method would not preempt the formula.

The Acting Commissioner of Patents and Trademarks filed a petition for a writ of certiorari, urging that the decision of the Court of Customs and Patent Appeals will have a debilitating effect on the rapidly expanding computer "software" industry, [Footnote 7] and will require him to process thousands of additional

Page 437 U. S. 588

patent applications. Because of the importance of the question, we granted certiorari, 434 U.S. 1033.


This case turns entirely on the proper construction of § 101 of the Patent Act, which describes the subject matter that is eligible for patent protection. [Footnote 8] It does not involve the familiar issues of novelty and obviousness that routinely arise under §§ 102 and 103 when the validity of a patent is challenged. For the purpose of our analysis, we assume that respondent's formula is novel and useful, and that he discovered it. We also assume, since respondent does not challenge the examiner's finding, that the formula is the only novel feature of respondent's method. The question is whether the discovery of this feature makes an otherwise conventional method eligible for patent protection.

The plain language of § 101 does not answer the question. It is true, as respondent argues, that his method is a "process" in the ordinary sense of the word. [Footnote 9] But that was also true of the algorithm, which described a method for converting binary-coded decimal numerals into pure binary numerals,

Page 437 U. S. 589

that was involved in Gottschalk v. Benson. The holding that the discovery of that method could not be patented as a "process" forecloses a purely literal reading of § 101. [Footnote 10] Reasoning that an algorithm, or mathematical formula, is like a law of nature, Benson applied the established rule that a law of nature cannot be the subject of a patent. Quoting from earlier cases, we said:

"'A principle, in the abstract, is a fundamental truth; an original cause; a motive; these cannot be patented, as no one can claim in either of them an exclusive right.' Le Roy v. Tatham, 14 How. 156, 55 U. S. 175. Phenomena of nature, though just discovered, mental processes, and abstract intellectual concepts are not patentable, as they are the basic tools of scientific and technological work."

409 U.S. at 409 U. S. 67.

The line between a patentable "process" and an unpatentable "principle" is not always clear. Both are "conception[s] of the mind, seen only by [their] effects when being executed or performed." Tilghman v. Proctor,102 U. S. 707, 102 U. S. 728. In Benson, we concluded that the process application in fact sought to patent an idea, noting that

"[t]he mathematical formula involved here has no substantial practical application except in connection with a digital computer, which means that, if the judgment below is affirmed, the patent would wholly preempt the mathematical formula and, in practical effect, would be a patent on the algorithm itself."

409 U.S. at 409 U. S. 71-72.

Respondent correctly points out that this language does not apply to his claims. He does not seek to "wholly preempt the mathematical formula," since there are uses of his

Page 437 U. S. 590

formula outside the petrochemical and oil refining industries that remain in the public domain. And he argues that the presence of specific "post-solution" activity -- the adjustment of the alarm limit to the figure computed according to the formula -- distinguishes this case from Benson and makes his process patentable. We cannot agree.

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. 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. [Footnote 11] The concept of patentable subject matter under § 101 is not "like a nose of wax, which may be turned and twisted in any direction. . . ." White v. Dunbar,119 U. S. 47, 119 U. S. 51.

Yet it is equally clear that a process is not unpatentable simply because it contains a law of nature or a mathematical algorithm. See Eibel Process Co. v. Minnesota Ontario Paper Co.,261 U. S. 45; Tilghman v. Proctor, supra. [Footnote 12] For

Page 437 U. S. 591

instance, in Mackay Radio & Telegraph Co. v. Radio Corp. of America,306 U. S. 86, the applicant sought a patent on a directional antenna system in which the wire arrangement was determined by the logical application of a mathematical formula. Putting the question of patentability to one side as a preface to his analysis of the infringement issue, Mr. Justice Stone, writing for the Court, explained:

"While a scientific truth, or the mathematical expression of it, is not patentable invention, a novel and useful structure created with the aid of knowledge of scientific truth may be."

Id. at 306 U. S. 94.

Funk Bros. Seed Co. v. Kalo Co.,333 U. S. 127, 333 U. S. 130, expresses a similar approach:

"He who discovers a hitherto unknown phenomenon of nature has no claim to a monopoly of it which the law recognizes. If there is to be invention from such a discovery, it must come from the application of the law of nature to a new and useful end."

Mackay Radio and Funk Bros. point to the proper analysis for this case: the process itself, not merely the mathematical algorithm, must be new and useful. Indeed, the novelty of the mathematical algorithm is not a determining factor at all. Whether the algorithm was in fact known or unknown at the time of the claimed invention, as one of the "basic tools of scientific and technological work," see Gottschalk v. Benson,

Page 437 U. S. 592

409 U.S. at 409 U. S. 67, it is treated as though it were a familiar part of the prior art.

This is also the teaching of our landmark decision in O'Reilly v. Morse, 15 How. 62. In that case, the Court rejected Samuel Morse's broad claim covering any use of electromagnetism for printing intelligible signs, characters, or letters at a distance. Id. at 56 U. S. 112-121. In reviewing earlier cases applying the rule that a scientific principle cannot be patented, the Court placed particular emphasis on the English case of Neilson v. Harford, Web.Pat.Cases 295, 371 (1844), which involved the circulation of heated air in a furnace system to increase its efficiency. The English court rejected the argument that the patent merely covered the principle that furnace temperature could be increased by injecting hot air, instead of cold into the furnace. That court's explanation of its decision was relied on by this Court in Morse:

"'It is very difficult to distinguish it [the Neilson patent] from the specification of a patent for a principle, and this at first created in the minds of the court much difficulty; but after full consideration, we think that the plaintiff does not merely claim a principle, but a machine, embodying a principle, and a very valuable one. We think the case must be considered as if the principle being well known, the plaintiff had first invented a mode of applying it. . . .'"

15 How. at 56 U. S. 115 (emphasis added). [Footnote 13] We think this case must also be considered as if the principle or mathematical formula were well known.

Respondent argues that this approach improperly imports into § 101 the considerations of "inventiveness" which are the proper concerns of §§ 102 and 103. [Footnote 14] This argument is based on two fundamental misconceptions.

Page 437 U. S. 593

First, respondent incorrectly assumes that, if a process application implements a principle in some specific fashion, it automatically falls within the patentable subject matter of § 101 and the substantive patentability of the particular process can then be determined by the conditions of §§ 102 and 103. This assumption is based on respondent's narrow reading of Benson, and is as untenable in the context of § 101 as it is in the context of that case. It would make the determination of patentable subject matter depend simply on the draftsman's art, and would ill serve the principles underlying the prohibition against patents for "ideas" or phenomena of nature. The rule that the discovery of a law of nature cannot be patented rests not on the notion that natural phenomena are not processes, but rather on the more fundamental understanding that they are not the kind of "discoveries" that the statute was enacted to protect. [Footnote 15] The obligation to determine what type of discovery is sought to be patented must precede the determination of whether that discovery is, in fact, new or obvious.

Second, respondent assumes that the fatal objection to his application is the fact that one of its components -- the mathematical

Page 437 U. S. 594

formula -- consists of unpatentable subject matter. In countering this supposed objection, respondent relies on opinions by the Court of Customs and Patent Appeals which reject the notion

"that a claim may be dissected, the claim components searched in the prior art, and, if the only component found novel is outside the statutory classes of invention, the claim may be rejected under 35 U.S.C. § 101."

In re Chatfield, 545 F.2d 152, 15 (CCPA 1976). [Footnote 16] Our approach to respondent's application is, however, not at all inconsistent with the view that a patent claim must be considered as a whole. Respondent's process is unpatentable under § 101 not because it contains a mathematical algorithm as one component, but because, once that algorithm is assumed to be within the prior art, the application, considered as a whole, contains no patentable invention. Even though a phenomenon of nature or mathematical formula may be well known, an inventive application of the principle may be patented. Conversely, the discovery of such a phenomenon cannot support a patent unless there is some other inventive concept in its application.

Here it is absolutely clear that respondent's application contains no claim of patentable invention. The chemical processes involved in catalytic conversion of hydrocarbons are well known, as are the practice of monitoring the chemical process variables, the use of alarm limits to trigger alarms, the notion that alarm limit values must be recomputed and readjusted, and the use of computers for "automatic monitoring alarming." [Footnote 17] Respondent's application simply provides a new and presumably better method for calculating alarm limit

Page 437 U. S. 595

values. If we assume that that method was also known, as we must under the reasoning in Morse, then respondent's claim is, in effect, comparable to a claim that the formula 2

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