The Long Reach of the Mathematics Patentability Exception is Overbroad and Absurd – Part II

In Part I of this series we examined the mathematics exception to patentability and the historical underpinnings of its justification. In Part II, we will continue to examine the case history around patenting of mathematic principles.

MacKay Shows Mathematical Expressions of Scientific Truths are not Patentable

The rule that principles in science or laws of nature are not patentable was specifically applied to mathematical expressions in 1939, when the Supreme Court in Mackay Co. v. Radio Corp., 306 U.S. 86, decided patentability for “patent, No. 1,974,387, for a directive antenna system for use in radio communication,” where the “patent discloses and claims invention of a V antenna structure made in conformity to the Abraham formula.”

The court in Mackay presented the law saying, “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” (emphasis added).

Although Le Roy and Morse did not discuss mathematical expressions, the court’s statement in Mackay is logical based on the idea that, if principles in science or laws of nature are not patentable, then the mathematical expression of that scientific truth is also not patentable by association. However, note that Mackay did not say that all mathematical expressions are not patentable, only mathematical expressions of scientific truth.

Benson Finds That One Formula is Not Patentable

In 1972, the Supreme Court in Gottschalk v. Benson, 409 U. S. 63 (“Benson”) cited Mackay and other cases to reiterate that the mathematical expression of scientific truth is not patentable. Further, the Benson Court decided, “The 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.”  The Court in Benson gave a lengthy explanation on why this one particular mathematical formula was unpatentable. However, the Court did not declare that all mathematical formulas were unpatentable.

Flook Declares All Mathematical Formulas Ineligible with an Unjustified and Absurd Simile

Parker v. Flook, 437 U.S. 584, 594–95 (“Flook”) is a Supreme Court case from 1978 regarding a “method for updating alarm limits during catalytic conversion processes” which arguably killed the patentability of all mathematics. The Flook opinion is a collection of illogical and incorrect statements, perhaps because the Court did not understand mathematics and thus was not worried about using logic—a field of mathematics—or following rigorous steps to reach its conclusions.

There are three errors in the Flook decision: 1) any mathematical formula is like a law of nature, 2) previous cases justified that all mathematical formulas are not patentable, and 3) justifying the patentability rejection, citing from previous cases (e.g., Benson, Mackay, Funk Bros., Morse, Neilson), by conflating the concepts of law of nature and mathematics.

The reason for granting certiorari is even questionable, “The Acting Commissioner of Patents and Trademarks [Mr. Parker] 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 additional patent applications. Because of the importance of the question, we granted certiorari.”  It is shocking and outrageous that the Commissioner would ask to destroy inventor’s patent rights just because it would be too much work for the Office. This selfish motive to abolish inventor rights, even if their rights were protected by patent law, did not seem to bother the Court. In fact, the Court helped Acting Commissioner Parker by creating a new category of ineligible subject matter.

Justice Stevens delivered the Flook opinion and, right from the outset, the first paragraph contains a false statement, “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.”  As described above, Morse dealt with principles in science or law of nature, not mathematical formulas. Morse’s rejected claim 8 did not have a mathematical formula, but a reference to electro-magnetism. Also note that prior art should not be a factor in determining patent eligibility.

The next statement in the summary is to say that virtually everything claimed is well known, “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.’”  However, at least according to patent law, whether something is well known is a question of newness and novelty, not a question for patent eligibility.

Stevens said, “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.”

Three Justices dissented and Justice Stewart disagreed with Justice Stevens on the impropriety of considering prior art for subject-matter patentability, “The Court … strikes what seems to me an equally damaging blow at basic principles of patent law by importing into its inquiry under 35 U. S. C. § 101 the criteria of novelty and inventiveness. Section 101 is concerned only with subject-matter patentability. Whether a patent will actually issue depends upon the criteria of §§ 102 and 103, which include novelty and inventiveness, among many others.”  “But in my view the claimed process clearly meets the standards of subject-matter patentability of § 101.”

Gone is the rigorous analysis the court used in Morse to show how scientific principles and laws of nature did not conform with patent law, such as, “This is required by the patent laws of England and of the United States” (Morse). Instead, Justice Stevens mixed patent-law sections to justify unpatentability, a practice that has steadily grown over the years and to which we have unfortunately become accustomed.

Furthermore, Justice Stevens misrepresented Benson, “The only novel feature of the method is a mathematical formula. In Gottschalk v. Benson, 409 U. S. 63 (1972), we held that the discovery of a novel and useful mathematical formula may not be patented” (emphasis added). However, this is not what the Supreme Court said in Benson. The only time the word “novel” appears in Benson is to cite Mackay, “”[w]hile a scientific truth, or the mathematical expression of it, is not a patentable invention, a novel and useful structure created with the aid of knowledge of scientific truth may be” (emphasis added). The Benson opinion stated that a novel structure may be patentable, while still preserving the idea that the mathematical expressions of scientific truth were not patentable, not that all mathematical formulas were not patentable.

Justice Stevens in the Flook opinion casually slips in the idea that, “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.”  Justice Stevens did not explain why a mathematical formula is like a law of nature, which means that there is no real justification for why all mathematical formulas are not patentable. Maybe there was an implicit assumption that all of mathematics serves to discuss laws of nature, but such an assumption would be wrong. Previous cases were clear in referring to mathematical expressions of scientific truth, but in just one sentence Justice Stevens justified that all mathematical formulas were not patentable. Justice Stevens then cited at length from previous cases about patentability of laws of nature as if doing so would justify excepting mathematics.

Modern Cases Perpetuate the Unjustified Exception

The precedent set in Flook has remained unchanged to this day. The Supreme Court in Diamond v. Diehr, 450 U. S. 175, 185 (1981), provided the infamous and often repeated statement that “a mathematical formula, like a law of nature, cannot be the subject of a patent.”  In Bilski v. Kappos, 561 U. S. 593, the Supreme Court cited Diehr but changed the wording to formally hold that a mathematical formula is not patentable, independently of its association with a law of nature, stating, “Diehr explained that while an abstract idea, law of nature, or mathematical formula could not be patented.”  Finally, the Supreme Court in SAP America v. Investpic LLC. flatly stated, “mathematical calculations and formulas are not patent eligible.”

The justification for why mathematics is not patentable (np) can be summarized, with some help from mathematical notation, as follows:

Patentability Should Focus on What is Claimed, Not How the Invention is Described

Mathematics has many functions, such as providing a language to describe relationships, methodologies to prove truth using logic, algorithms to derive new relationships, procedures to solve problems, statistics to analyze data, and so forth. The descriptive power of mathematics may be used to describe, not just laws of nature and scientific principles, but also many other phenomena. Morse and other early cases provided excellent reasons why these scientific principles were not eligible subject matter according to patent law.

The assertion that mathematics is “like a law of nature” is wrong and must be corrected. The implicit assumption that mathematics can only be used to describe laws of nature is incorrect; mathematics may be used to describe other concepts beyond laws of nature.

Morse taught us that patentability may be denied when the invention is not properly described in the specification. Mathematics provides a descriptive language, and patentability should be based on how the invention is described, so a person skilled in the art would be able to practice the invention. The way the invention is described should not matter to patentability, and only the content of the invention should matter. Saying that something mathematically described cannot be patented is the same as saying that inventions described in French are not patentable.

Justice must look beyond the descriptive medium and focus on what is described. If the claimed novelty is a law of nature, then the invention is not patentable. If the claimed novelty is not a law of nature, then the invention is patentable based on the terms and conditions provided by law.

The U.S. Patent and Trademark Office’s OCT2019 Patent Eligibility Guidance is therefore wrong when it says, “there are instances where a formula or equation is written in text format that should also be considered as falling within this grouping [of mathematical concepts].” An invention claiming “calculating the force of the object by multiplying its mass by its acceleration” or claiming “F= ma” would not be patentable just because it uses or hides mathematics, but because it represents a law of nature. Let’s focus on what is claimed and not the format used in the claim. This way, we can eliminate the illogical conclusion that something without mathematics falls under the mathematical-concepts category.

Further, the mathematical exception is absurd, and one can use mathematical logic to prove this by reductio ad absurdum. Any composition of matter may be described in a mathematical formula. For example, a composition of matter M that includes three elements A, B, and C in a defined proportion can be expressed as M=k₁A+k₂B+k₃C, where k₁, k₂, and k₃ are the coefficients indicating their relative proportion. We can deduce the following:

This means that all compositions of matter would be ineligible, contrary to the clear, express intent of the law. Conclusion: the judicial exception that all mathematical formulas are not patentable is absurd, q.e.d.

The absurd justification in Flook that all mathematics is unpatentable because mathematics is like a law of nature must be corrected to enable inventors to use mathematics as a descriptive media when laws of nature are not involved. Making all mathematical formulas unpatentable is overbroad, because, as Aristotle would say, mathematically encoded by Morse,

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