“Our ancestors discovered long ago that mathematics is everywhere and that everything involves mathematics…. If we declare mathematical concepts as ineligible subject matter, then everything would be ineligible.”
The mathematics exception for subject matter eligibility is overbroad because it was improperly justified under the premise that mathematics is like a law of nature. This is absurd because mathematics is everywhere, and excepting mathematics means excepting virtually everything.
The Mathematics Exception to Subject Matter Eligibility
Recent court decisions declare that “[m]athematical calculations and formulas are not patent eligible,” SAP Am., Inc. v. InvestPic, LLC, 898 F.3d 1161 (2018)(“SAP AM.”), based on older decisions, such as Parker v. Flook, 437 U.S. 584 (1978) (“Flook”) and Gottschalk v. Benson, 409 U.S. 63 (1972) (“Benson”).
The USPTO’s Update on Subject Matter Eligibility of October 2019 (“OCT2019 PEG”) states, “The 2019 PEG defines ‘mathematical concepts’ as mathematical relationships, mathematical formulas or equations, and mathematical calculations,” and “where a formula or equation is written in text format that should also be considered as falling within this grouping.” This means that one can have a mathematical concept without even writing any mathematics. The USPTO can assert this illogical and absurd statement because the justification for the underlying mathematical exception itself is also illogical and absurd.
What is Mathematics?
Everyone knows what mathematics is, but there is no universally accepted definition. Galileo Galilei said, “Mathematics is the language in which God has written the universe.” One of mathematics’ functions is to serve other sciences like physics, chemistry, engineering, manufacturing, accounting, machine learning, etc., by providing tools to precisely define concepts and manipulate those concepts easily and with scientific rigor.
Mathematics provides a descriptive language that can be used to describe virtually everything in a precise manner. Mathematics can be used to describe not only laws of nature, but also many other concepts, such as defining proportions to combine materials, expressing a cost function to be optimized by a machine-learning algorithm, predicting the winner of a football game, determining if a premise is logical or absurd, charting and predicting the growth of cases in a pandemic, and so forth.
If I say, “Alice is The Supreme Court’s worst decision,” it would seem that my opinion has nothing to do with mathematics. Nonetheless, I can use mathematics to represent this opinion as follows:
My opinion is now written as a mathematical concept; this is just an example of how virtually everything can be expressed mathematically. Our ancestors discovered long ago that mathematics is everywhere and that everything involves mathematics, as shown in the following two quotes:
The so-called Pythagoreans applied themselves to mathematics and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything.
— Aristotle, In Metaphysics (circa first century BCE)
In my opinion, everything happens in nature in a mathematical way.
— René Descartes, 1640
The logical conclusion is that if we declare mathematical concepts as ineligible subject matter, then everything would be ineligible. Let us see how we got into this absurd situation and the justifications that the courts have provided for the mathematics patentability exception.
Justification Begins with English Common Law and Le Roy
Le Roy v. Tatham, 14 How. 156, 175, is a case from 1852 regarding machinery used for making pipes and tubes, an improved application of air to produce heat in fires, forges, and furnaces, where bellows or other blowing apparatus are required. The Supreme Court in Le Roy stated that principles in science or laws of nature are not patentable. The legal discussion by the Court centered on the patentability of a “principle,” and the Court cautioned, “The word principle is used by elementary writers on patent subjects, and sometimes in adjudications of courts, with such a want of precision in its application, as to mislead.” It seems like “principle” was in the 19th century what “abstract” is today.
Le Roy discussed precedent from U.S. and English cases by noting, for example, that “in the case of the Househill Company v. Neilson, Webster’s Patent Cases, 683, ‘A patent will be good, though the subject of the patent consists in the discovery of a great, general, and most comprehensive principle in science or law of nature, if that principle is by the specification applied to any special purpose, so as thereby to effectuate a practical result and benefit not previously attained’” (emphasis added). The opinion did not refer to all principles, just principles in science or laws of nature.
These principles in science or laws of nature are not patentable, as deemed by the Court in saying, “It is admitted, that a principle is not patentable. 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. Nor can an exclusive right exist to a new power, should one be discovered in addition to those already known. Through the agency of machinery, a new steam power may be said to have been generated. But no one can appropriate this power exclusively to himself, under the patent laws. The same may be said of electricity, and of any other power in nature, which is alike open to all, and may be applied to useful purpose by the use of machinery” (emphasis added).
Morse Shows Scientific Principles are Not Covered by U.S. Law
O’Reilly v. Morse, 56 U.S. 62 (“Morse”) is a landmark case from 1853 related to the infancy of the telecommunications industry. Samuel F. B. Morse, a historical painter, made “discoveries in relation to electro-magnetism” during a return trip from Europe in October 1832. In the Supreme Court’s opinion, a lengthy discussion about various research performed in Europe and US at the time precedes the Court’s conclusion that “Morse was the first and original inventor of the electro-magnetic telegraph,” which used Morse code. Morse continued making improvements to the basic concept, including the subject of the patent in question regarding the problem of signal attenuation over great distances.
Both O’Reilly and Morse were in the process of laying electrical wire between cities for the electro-magnetic telegraph, “telegraphs along lines, amounting, in the aggregate, to upwards of four thousand five hundred miles, whereby telegraphic communication was established between the principal cites of the United States, from New Orleans to Boston.” O’Reilly entered into a contract with Morse to lay wire, but O’Reilly later decided that Morse’s patent was invalid and proceed to operate without a license and “constructed a line of posts and suspended metallic wires thereon, from the city of Louisville, in the District of Kentucky, by way of Bardstown, to Nashville, in the State of Tennessee.”
Most of Morse’s patent claims were validated by the court, but a patentability issue arose with claim 8, which covered “the use of the motive power of the electric or galvanic current, which I call electro-magnetism, however developed, for making or printing intelligible characters, letters, or signs, at any distances, being a new application of that power” (emphasis added). Greedy Morse—or maybe his greedy patent attorney—wanted to claim, as his invention, not only the present uses of electro-magnetism, but also any future uses of it.
The court referred to English common-law cases and Le Roy to discuss patentability. “If the Court of Exchequer had said that Neilson’s patent was for the discovery, that hot air would promote ignition better than cold, and that he had an exclusive right to use it for that purpose, there might, perhaps, have been some reason to rely upon it. But the court emphatically denied his right to such a patent.” “And the [Le Roy] court held that he was not entitled to a patent for this newly-discovered principle or quality in lead; and that such a discovery was not patentable. But that he was entitled to a patent for the new process or method in the art of making lead pipe.”
When it came to addressing U.S. law in the Morse opinion, Justice Taney made a rigorous, deliberate effort to show that the act of Congress would not justify granting a patent for a principle, “independently of judicial authority, we do not think that the language used in the act of Congress, can justly be expounded otherwise.” The reasoning is based on the concepts of enablement in the specification and too-broad claiming. There was no judicially created exception, just the terms and conditions on which a patent could be obtained.
The 6th section [of the act of 1836] directs who shall be entitled to a patent, and the terms and conditions on which it may be obtained. It provides that any person shall be entitled to a patent … But before he receives a patent, he shall deliver a written description of his invention or discovery, ‘and of the manner and process of making, constructing, using, and compounding the same, ‘in such exact terms as to enable any person skilled in the art or science to which it appertains, or with which it is most nearly connected, to make, construct, compound, and use the same.
Justice Taney then wrote, “This court has decided, that the specification required by this law is a part of the patent; and that the patent issues for the invention described in the specification.” Under this reasoning, claim 8 was deemed too broad, going beyond what Morse had invented. The opinion stated, “[Morse] claims an exclusive right to use a manner and process which he has not described and indeed had not invented, and therefore could not describe when he obtained his patent. The court is of opinion that the claim is too broad, and not warranted by law.” In particular, the opinion noted that:
Yet this claim can derive no aid from the specification filed. It is outside of it, and the patentee claims beyond it. And if it stands, it must stand simply on the ground that the broad terms above-mentioned were a sufficient description, and entitled him to a patent in terms equally broad. In our judgment the act of Congress cannot be so construed.
Because claim 8 did not meet the terms and conditions of the Patent Act, claim 8 was held invalid, not because of a judicially-created exception, but because “[t]he words of the acts of Congress above quoted show that no patent can lawfully issue upon such a claim.” In the words of the court, “[f]or he claims what he has not described in the manner required by law. And a patent for such a claim is as strongly forbidden by the act of Congress, as if some other person had invented it before him.”
In Part II of this series, we will continue to examine the case history through to today, ultimately arriving at the conclusion that the mathematics exception must be corrected to facilitate important innovations.
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