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." The examiner concluded that the claims did not describe a discovery that was eligible for patent protection.

6

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" 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 pre-empt 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 pre-empt 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,' and will require him to process thousands of addi

"The term "software" is used in the industry to describe computer programs. The value of computer programs in use in the United States in 1976 was placed at $43.1 billion, and projected at $70.7 billion by 1980 according to one industry estimate. See Brief for the Computer & Business Equipment Manufacturers Assn. as Amicus Curiae 17-18, n. 16.

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

III

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. 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. But that was also true of the algorithm, which described a method for converting binary-coded decimal numerals into pure binary numerals,

8 Title 35 U. S. C. § 101 provides:

"Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title."

Section 100 (b) provides:

"The term 'process' means process, art or method, and includes a new use of a known process, machine, manufacture, composition of matter, or material."

The statutory definition of "process" is broad. See n. 8, supra. An argument can be made, however, that this Court has only recognized a process as within the statutory definition when it either was tied to a particular apparatus or operated to change materials to a "different state or thing." See Cochrane v. Deener, 94 U. S. 780, 787-788. As in Benson, we assume that a valid process patent may issue even if it does not meet one of these qualifications of our earlier precedents. 409 U. S., at 71.

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 § 101.10 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, 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 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, 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 pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself." 409 U. S., at 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

10 In Benson we phrased the issue in this way:

"The question is whether the method described and claimed is a 'process' within the meaning of the Patent Act." Id., at 64.

Opinion of the Court

437 U.S. 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." 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, 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.12 For

11 It should be noted that in Benson there was a specific end use contemplated for the algorithm-utilization of the algorithm in computer programming. See In re Chatfield, 545 F. 2d 152, 161 (CCPA 1976) (Rich, J., dissenting). Of course, as the Court pointed out, the formula had no other practical application; but it is not entirely clear why a process claim is any more or less patentable because the specific end use contemplated is the only one for which the algorithm has any practical application.

12 In Eibel Process Co. the Court upheld a patent on an improvement on a papermaking machine that made use of the law of gravity to enhance the flow of the product. The patentee, of course, did not claim to have discovered the force of gravity, but that force was an element in his novel conception.

Tilghman v. Proctor involved a process claim for "the manufacturing

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 94.

Funk Bros. Seed Co. v. Kalo Co., 333 U. S. 127, 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,

of fat acids and glycerine from fatty bodies.'" The Court distinguished the process from the principle involved as follows:

"[T]he claim of the patent is not for a mere principle. The chemical principle or scientific fact upon which it is founded is, that the elements of neutral fat require to be severally united with an atomic equivalent of water in order to separate from each other and become free. This chemical fact was not discovered by Tilghman. He only claims to have invented a particular mode of bringing about the desired chemical union between the fatty elements and water." 102 U. S., at 729.