Is a mathematical algorithm necessarily in itself patent-ineligible subject
Is a process implemented in software necessarily in itself
patent-ineligible subject matter?
Quotation from Funk Bros. v. Kalo
For patents cannot issue for the discovery of
the phenomena of nature. See Le Roy v. Tatham, 14 How. 156, 175. The qualities
of these bacteria, like the heat of the sun, electricity, or the qualities of
metals, are part of the storehouse of knowledge of all men. They are
manifestations of laws of nature, free to all men and reserved exclusively to
none. 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. See Telephone Cases, 126 U.S. 1, 532-533; DeForest Radio Co. v.
General Electric Co., 283 U.S. 664, 684-685; Mackay Radio & Tel. Co. v.
Radio Corp., 306 U.S. 86, 94; Cameron Septic Tank Co. v. Saratoga Springs, 159
F. 453, 462-463.
Quotations from Gottschalk v. Benson:
Court stated in Mackay Co. v. Radio Corp., 306 U. S. 86, 94, that “[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.” That statement followed the longstanding rule
that “[a]n idea of itself is not patentable.” Rubber-Tip Pencil Co.
v. Howard, 20 Wall. 498, 507. “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. As we stated in Funk Bros. Seed Co.
v. Kalo Co., 333 U. S. 127, 130, “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.” We dealt there
with a “product” claim, while the present case deals with a
“process” claim. But we think the same principle
It is conceded that one
may not patent an idea. But in practical effect that would be the result if the
formula for converting BCD numerals to pure binary numerals were patented in
this case. 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
Quotations from Parker v. Flook:
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
As the Court of
Customs and Patent Appeals has explained, “if a claim is directed
essentially to a method of calculating, using a mathematical formula, even if
the solution is for a specific purpose, the claimed method is
nonstatutory.” In re Richman, 563 F. 2d 1026, 1030
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.
[Note that the
dictum that “once that algorithm is assumed to be within the prior art,
the application, considered as a whole, contains no patentable invention”
was repudiated in Diehr.]
Quotations from Diamond v. Diehr:
certiorari to determine whether a process for curing synthetic rubber which
includes in several of its steps the use of a mathematical formula and a
programmed digital computer is patentable subject matter under 35 U. S. C.
In Benson, we held
unpatentable claims for an algorithm used to convert binary code decimal numbers
to equivalent pure binary numbers. The sole practical application of the
algorithm was in connection with the programming of a general purpose digital
computer. We defined “algorithm” as a “procedure for solving a
given type of mathematical problem,” and we concluded that such an
algorithm, or mathematical formula, is like a law of nature, which cannot be the
subject of a patent.
the respondents here do not seek to patent a mathematical formula. Instead, they
seek patent protection for a process of curing synthetic rubber. Their process
admittedly employs a well-known mathematical equation, but they do not seek to
pre-empt the use of that equation. Rather, they seek only to foreclose from
others the use of that equation in conjunction with all of the other steps in
their claimed process.
earlier opinions lend support to our present conclusion that a claim drawn to
subject matter otherwise statutory does not become nonstatutory simply because
it uses a mathematical formula, computer program, or digital computer. In
Gottschalk v. Benson we noted: “It is said that the decision precludes a
patent for any program servicing a computer. We do not so hold.“ 409 U.
S., at 71. Similarly, in Parker v. Flook we stated that “a process is not
unpatentable simply because it contains a law of nature or a mathematical
algorithm.“ 437 U. S., at 590. It is now commonplace that an application
of a law of nature or mathematical formula to a known structure or process may
well be deserving of patent protection. See, e. g., Funk Bros. Seed Co. v. Kalo
Inoculant Co., 333 U. S. 127 (1948); Eibel Process Co. v. Minnesota &
Ontario Paper Co., 261 U. S. 45 (1923); Cochrane v. Deener, 94 U. S. 780 (1877);
O'Reilly v. Morse, 15 How. 62 (1854); and Le Roy v. Tatham, 14 How. 156 (1853).
As Justice Stone explained four decades ago:
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.” Mackay Radio & Telegraph Co. v. Radio Corp.
of America, 306 U. S. 86, 94 (1939).
We think this statement
in Mackay takes us a long way toward the correct answer in this case. Arrhenius'
equation is not patentable in isolation, but when a process for curing rubber is
devised which incorporates in it a more efficient solution of the equation, that
process is at the very least not barred at the threshold by §
I suggest that relying on the above
quotations (and any similar quotes from Benson, Flook and
Diehr) for the proposition that there is an established judicial
exception for mathematical algorithms per se is wishful thinking.
Accordingly I now present an argument that mathematical algorithms are not
We start with Bilski v.
The Court's precedents provide three specific
exceptions to § 101's broad patent-eligibility principles: “laws of
nature, physical phenomena, and abstract ideas.” Chakrabarty, supra, at
309, 100 S.Ct. 2204. While these exceptions are not required by the statutory
text, they are consistent with the notion that a patentable process must be
“new and useful.” And, in any case, these exceptions have defined
the reach of the statute as a matter of statutory stare decisis going back 150
years. See Le Roy v. Tatham, 14 How. 156, 174-175, 14 L.Ed. 367 (1853). The
concepts covered by these exceptions are “part of the storehouse of
knowledge of all men… free to all men and reserved exclusively to
none.” Funk Brothers Seed Co. v. Kalo Inoculant Co., 333 U.S. 127, 130, 68
S.Ct. 440, 92 L.Ed. 588
Any suggestion in this
Court's case law that the Patent Act's terms deviate from their ordinary meaning
has only been an explanation for the exceptions for laws of nature, physical
phenomena, and abstract ideas. See Parker v. Flook, 437 U.S. 584, 588-589, 98
S.Ct. 2522, 57 L.Ed.2d 451 (1978). This Court has not indicated that the
existence of these well-established exceptions gives the Judiciary carte blanche
to impose other limitations that are inconsistent with the text and the
statute's purpose and design. Concerns about attempts to call any form of human
activity a “process” can be met by making sure the claim meets the
requirements of § 101.
Then on to Mayo v.
The Court has long held that this provision
contains an important implicit exception. “[L]aws of nature, natural
phenomena, and abstract ideas” are not patentable. Diamond v. Diehr, 450
U.S. 175, 185, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981); see also Bilski v. Kappos,
561 U.S. ___, ___, 130 S.Ct. 3218, 3233-3234, 177 L.Ed.2d 792 (2010); Diamond v.
Chakrabarty, 447 U.S. 303, 309, 100 S.Ct. 2204, 65 L.Ed.2d 144 (1980); Le Roy v.
Tatham, 14 How. 156, 175, 14 L.Ed. 367 (1853); O'Reilly v. Morse, 15 How. 62,
112-120, 14 L.Ed. 601 (1854); cf. Neilson v. Harford, Webster's Patent Cases
295, 371 (1841) (English case discussing same). Thus, the Court has written that
“a new mineral discovered in the earth or a new plant found in the wild is
not patentable subject matter. Likewise, Einstein could not patent his
celebrated law that E=mc2; nor could Newton have patented the law of gravity.
Such discoveries are ‘manifestations of ... nature, free to all men and
reserved exclusively to none.’” Chakrabarty, supra, at 309, 100
S.Ct. 2204 (quoting Funk Brothers Seed Co. v. Kalo Inoculant Co., 333 U.S. 127,
130, 68 S.Ct. 440, 92 L.Ed. 588
“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.” Gottschalk v. Benson, 409 U.S. 63, 67, 93 S.Ct. 253, 34 L.Ed.2d 273
(1972). And monopolization of those tools through the grant of a patent might
tend to impede innovation more than it would tend to promote
The Court has recognized, however, that too
broad an interpretation of this exclusionary principle could eviscerate patent
law. For all inventions at some level embody, use, reflect, rest upon, or apply
laws of nature, natural phenomena, or abstract ideas. Thus, in Diehr the Court
pointed out that “‘a process is not unpatentable simply because it
contains a law of nature or a mathematical algorithm.’” 450 U.S., at
187, 101 S.Ct. 1048 (quoting Parker v. Flook, 437 U.S. 584, 590, 98 S.Ct. 2522,
57 L.Ed.2d 451 (1978)). It added that “an application of a law of nature
or mathematical formula to a known structure or process may well be deserving of
patent protection.” Diehr, supra, at 187, 101 S.Ct. 1048. And it
emphasized Justice Stone's similar observation in Mackay Radio & Telegraph
Co. v. Radio Corp. of America, 306 U.S. 86, 59 S.Ct. 427, 83 L.Ed. 506
“‘While 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.’” 450 U.S., at 188, 101 S.Ct. 1048 (quoting Mackay Radio, supra,
at 94, 59 S.Ct. 427).
See also Funk Brothers, supra,
at 130, 68 S.Ct. 440 (“If there is to be invention from [a discovery of a
law of nature], it must come from the application of the law of nature to a new
and useful end”).
So now I move in for the
In the most recent cases related to patent-eligibility under
Section 101, namely Bilski and Mayo, the Supreme Court affirmed
that laws of nature, natural phenomena and abstract ideas are not in themselves
patent-eligible subject matter. In Bilski, the Court declined to
recognise an additional per se exclusion for business methods. This
would imply that the Supreme Court would not now recognize and affirm an
exception for mathematics per se. If mathematical subject matter is not
patent-eligible, then the justification for this must be on the grounds either
that it is the expression of a law of nature, a natural phenomenon, or an
abstract idea, or else that it is in itself an abstract idea. Benson,
Flook and Diehr suffice to establish that mathematical formulae
and equations are not patent-eligible under Section 101, and moreover the
formulae and equations at issue in those cases represent laws of nature or
abstract ideas. It is certainly established that some mathematical algorithms
are patent-ineligible, and that, in particular, that algorithms for converting
binary-coded decimal representations of integers to binary are not
Let us suppose that a mathematical algorithm is not a
law of nature. Is it then guaranteed to be an “abstract idea”? To
show that it is an abstract idea, it is surely not sufficient to show merely
that it is abstract. An idea must surely be
comprehensible. (Note that “comprehensible” derives from the
Latin verb comprehendere, which means “to grasp, catch, seize,
arrest”.) Now, in order that an idea be comprehensible, minds must
be able to conceive and retain the idea as a whole. Mathematical formulae and
equations meet this requirement. Similarly a simple mathematical algorithm of
the sort that might fairly be described as a “procedure for solving a
given type of mathematical problem” (Diehr) is likely to be
comprehensible. If schoolchildren, university students, accountants etc. can
learn a mathematical algorithm and apply it to carry out calculations (without
the need to refer continually to instruction manuals etc.), then such an
algorithm is surely comprehensible and should most likely be capable of
being categorized as an abstract idea.
Moreover, it should be
noted that Benson states that
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
Now an abstract intellectual concept must surely
be capable of being conceived. The Latin verb concipere means
“to absorb, perceive, conceive, imagine, understand, become
pregnant”. It surely follows that abstract intellectual concepts
must be comprehensible.
Therefore I would suggest that
Benson, Flook and Diehr only affirm that those mathematical
algorithms that can be conceived (i.e., understood and internalized by the human
mind) are not patent-eligible subject matter. This conclusion is surely
consistent with the proposition that algorithms and processes whose steps can be
carried out in the human mind (with or without the assistance of pencil and
paper) are not patent-eligible subject matter.
But now suppose that data
is stored in the "memory" of a computing device, and that the internal
state of the computing device evolves in accordance with a process completely
determined by the stored data in accordance with logical principles, and that,
in principle, in principle, the outcome of the process could be represented by a
formula in some flavour of formal logic (that might be capable of being
represented electronically and stored on an electronic storage device, though
being in itself incapable of being grasped as a whole by a human mind). Do the
holdings and dicta in Benson, Flook and Diehr suffice to
establish that such a process is, per se not patent-eligible subject
According to the Supreme Court in
The Court has recognized, however, that too broad
an interpretation of this exclusionary principle could eviscerate patent law.
For all inventions at some level embody, use, reflect, rest upon, or apply laws
of nature, natural phenomena, or abstract ideas.
caution against extrapolating from Benson, Flook, Diehr the
principle that an algorithm whose evolution in time is determined in terms of
rules expressible through formal logic must necessarily be patent-ineligible
subject-matter. Accordingly these cases provide little if any ground for
asserting that a process implemented in software that implements a
‘mathematical’ algorithm must therefore also be in itself
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