The Long Reach of the Mathematics Patentability Exception is Overbroad and Absurd – Part 1

By Jose Nunez
April 27, 2020

“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 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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The Author

Jose Nunez

Jose Nunez is a registered patent attorney at Schwegman Lundberg & Woessner. His practice includes patent prosecution (US and foreign), patent validity, and strategic IP counseling, in a broad range of technical arts, including computer software and hardware, networking, semiconductor manufacturing, network storage, gaming (including virtual and augmented reality, controllers, head-mounted displays), data analysis, machine learning, virtual machines, and security.

For more information or to contact Jose please visit his Firm Profile Page.

Warning & Disclaimer: The pages, articles and comments on do not constitute legal advice, nor do they create any attorney-client relationship. The articles published express the personal opinion and views of the author as of the time of publication and should not be attributed to the author’s employer, clients or the sponsors of Read more.

Discuss this

There are currently 15 Comments comments.

  1. Patent Princess April 27, 2020 9:17 am

    Very nicely written, looking fwd to Part II.

    Love how you mathematically represented your thoughts on Alice.

    101 needs a major precedential makeover asap.

  2. American Cowboy April 27, 2020 10:13 am

    I have heard numerous non-patent attorneys say “I went to law school so I would not have to learn math.” Apparently some of them made it to Scotus.

  3. Ternary April 27, 2020 12:46 pm

    Nice article, Jose. And I agree with you. I am looking forward to part 2. However, I am not sure what the Morse decision has to do with math. I understand that you want to discuss “scientific principles” and judicial exceptions. (O’Reilly v Morse is of course cited in Alice). I am curious how you piece this all together.

    Under Alice, the Morse code would probably be rejected in its entirety (not just claim 8) as being directed to an abstract idea, as coding was well known in transmission of messages.

    The “electro-magnetic principle” (in 1840) in Morse has nothing to do with Maxwell’s electromagnetism published in 1865 (at least not deliberately). It refers to what we nowadays would call electro-mechanics, such as in relays. The relay in a telegraph works as an amplifier. A small signal activates a switch (“signal lever” in Morse) that provides a “refreshed” (or “relayed”) signal from a battery for instance. This made it possible to transmit signals, basically without any distance limit. It is a technology, not a scientific principle.

    My initial reaction about this case, way back, reading about “electro-magnetic” without realizing its intended meaning, timeline and context, was similar to probably many nowadays. What? Claiming e.m. field devices for now and in the future. That is not realistic. However, it is not what Morse claims.

    Morse’s claim 8 is, I believe, fully supported by the specification. SCOTUS is just plainly wrong.

    For some reason (lack of schooling in sciences?) SCOTUS misinterprets and continues to misinterpret the science of claimed inventions. Starting with Morse.

    I am looking forward to your further analysis of the case history.

  4. Jose April 27, 2020 4:23 pm

    Cowboy, that’s funny! I was extremely tempted to make a joke around those lines, but decided to stick to the facts. But, I think that there may a lot of truth to that.

  5. Jose April 27, 2020 4:30 pm

    Thanks Ternary. Eileen has part 2, so I’m sure she’ll post it pretty soon. The problem is not with Morse; the problem is with Flook. But discussing Morse was necessary to show the evolution of the exception. I think the analysis in Morse is correct. It was very refreshing to see how, in 1853, the Court respected the law and justified the decision based on the acts of Congress, not judicial exceptions. Completely opposite to today where the Court is happy to focus patentability analysis on absurd and poorly-justified exceptions.

  6. stepback April 28, 2020 1:06 pm

    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.

    Hi Jose,

    These propositions are ripe for philosophical debate.

    Of course the minute a proposition begins with “Everyone knows” or “Common sense tells us …” then it becomes taboo to point out the fallacies in the proposition.

    I’ll take on the challenge nonetheless.
    No. Almost no one knows what mathematics truly is is. How many skilled mathematicians do you believe exist in the American population? How many people can comprehend the exponential function? You get your answer from how people behave in the COVID-19 pandemic. A rally to open up and let the function rip again? Really?

    Modern physics tells us that Euclidean geometry (and its concept of extensibility to the infinitely small and infinitely large) is completely wrong. There is no such thing in the universe as a perfectly straight line of zero width and infinite length. As scale goes toward zero we hit atomic particles, exclusion zones and quantum effects. As scale goes to infinity even photons do not travel in perfectly straight lines because their paths are bent by gravitational forces. And of course Einstein recognized that velocity of masses cannot go to infinity and beyond. No. God did not write the universe in the form of man-made mathematical principles. We are merely guessing, approximating, trying to model what we perceive; and for the most part we are wrong.

    Science is not a thing. It is a process. We pose falsifiable hypothesis and wait for someone with insight (like Einstein, Heisenberg, etc.) to demonstrate the error in our hypothesis. Hopefully but not necessarily, we are converging toward something closer to the way our universe actually works.

    All the noises we make are man-made. They are not “fundamental” principles of reality. The black robed wizards of the high courts are the last people to be trusted in understanding what the “fundamentals” truly are. Yet they are 101% confident that they sit at the top of the pile.

  7. Josh Malone April 28, 2020 3:48 pm

    I agree with Professor Adam Mossoff that Morse’s Claim 8 was a reasonable description of the invention under the laws at that time.

  8. Night Writer April 29, 2020 9:44 am

    I think that claim 8 is more properly framed as a problem of enablement.

    A patentee is entitled to a scope of enablement for the claims.

    If you read Alice carefully, you will see the justification for Alice is that the claims were unconstitutionally granted because they are too broad and may thus inhibit innovation. That is the holding of Alice.

    There is this odd relationship between “abstract”, “enablement”, and “maths”.

    Basically, if you read Stevens carefully you will see that he believes in a conscious mind that performs calculations outside the brain.

  9. stepback April 29, 2020 12:22 pm

    Josh @7
    Thank you for the link to Mossoff’s 2014 paper.

  10. Anon April 29, 2020 2:50 pm

    @ 8: “ That is the holding of Alice.

    No. That is not.

    Please stop using legal terms incorrectly. NO amount of careful reading supports an incorrect reading that sounds good to you.

  11. stepback April 30, 2020 11:08 am

    NW @8
    I suggest reading the paper that Josh @7 cites.
    It’s a long read and I’m only halfway through it. But it certainly sheds new light on the concept of reading things outside the context in which they were written. In other words, one can easily take a claim or other passage out of its original environment and twist its meaning in whatever nose-of-wax direction one wants.

    In science, math can serve as a modeling tool and/or as a descriptive tool.
    In law, judges can twist reality to whatever ideology serves them.

    If they don’t like those new-fangled computer gizmos they can shoot them down. If they don’t understand the new biotechnology methods, they can bury those as well. Innovation is as innovation does. Meaning; it does not have to be “innovation” in a positive direction. Innovation simply means change; change that the folks seeing it were not aware of before. We are witnessing changes of historical proportions both in patent law and elsewhere. IMHO, not good ones.

  12. Jose April 30, 2020 11:20 am

    @6: Thanks for the insights. I’m not much for philosophical debate, but much more interested in a fair and RATIONAL patent system. I agree with you that some judges should be put at the frontline for finding treatment and a vaccine, since it is so easy. It’s about time they stop killing technology just because they do not understand it; or at least, using the laws that Congress made to determine what qualifies for a patent, instead of subjective, unreasonable criteria.

  13. Anon April 30, 2020 2:28 pm

    Jose @12,

    As you lead in with “I’m not much for philosophical debate,” you might want to realize the landmine you step on with your next statement of “much more interested in a fair and RATIONAL patent system.”

    The words of ‘fair’ and ‘rational’ are tripwires of different — and often incompatible philosophies.

    One cannot merely assume that the notion of fair and rational that one ascribes to is the same notion that others ascribe to.

    For example there was a mini-series earlier this year in which a guest author used the term Rational Actor. It was pointed out that those destroying the patent system WERE Rational Actors — Efficient Infringers are (after all) aiming for efficiency for their ends.

  14. stepback May 1, 2020 3:38 am

    Anon @13

    My first instinct was to bite my tongue on the “fair and rational” line.

    But since you rang in on that bell let’s not forget another set of actors who find it fair and rational to efficiently dispose of patent claims on a summary judgment basis.

    We’re talking about harried district court judges who often have a large docket of federal criminal cases to deal with. Along comes this esoteric case dealing with counter-intuitive patent law. What better way to get rid of the pesky case than by way of a subjective decision that the invention is one of those I-know-it-when-I-see-it abstractly-directed ones lacking an I-know-it-when-I-feel-it something significantly more?

    What we are dealing with here is a happy coalition of judges and efficient infringers who together find the current system very “fair and rational”.

    As for the crushed under foot inventor, who cares?

  15. Anon May 1, 2020 8:01 am

    Thanks stepback, a worthy addition to a nominal list of Rational Actors.

    ‘Rational’ is very much a tripwire (one can easily think of plenty of rationalizations that occur.