It
has long been a distinguishing mark that ideas and concepts generated by the
queen of quantitative and formal sciences are incapable of patent protection.
If we are charitable, one might say this is because the queen does not touch
money. But, as it goes so often in matters legal, this is a case of “not so
fast” because there are, of course, exceptions. And questionable logic.

First,
let’s take a look at the topology of mathematics in the USPTO’s value system: while it requires mathematics coursework as a
prerequisite of its employees working as patent examiners in the computer arts,
it does not
recognize mathematics courses as qualifying for patent practitioners. Quite
the contrary: while bachelor’s degrees in 32 subjects will constitute adequate
proof of requisite scientific and technical training, not to mention a full
two-and-one-half pages of acceptable alternatives, the

*General Requirements Bulletin for Admission to the Examination for Registration to Practice in Patent Cases Before the United States Patent and Trademark Office*lists Typical Non-Acceptable Course Work that is not accepted to demonstrate scientific and technical training, notably “… machine operation (wiring, soldering, etc.), courses taken on a pass/fail basis, correspondence courses, home or personal independent study courses, high school level courses, mathematics courses, one day conferences, …” Consequently, it cannot come as a surprise that there are precious few patent attorneys with significant mathematical training as required to understand the mathematics underlying contemporary, much less future, science and technology.
Now,
as almost everybody knows, software
is just a mathematical algorithm. But as also everybody knows, software
patents do exist (see

*State Street Bank and Trust Company v. Signature Financial Group, Inc.*, 149 F.3d 1368 (Fed. Cir. 1998), even though the USPTO does not require the disclosure of source code. The U.S. Supreme Court had in*Diamond v. Diehr*, 450 U.S. 175, 101 S. Ct. 1048, 67 L. Ed. 2d 155; held three categories of subject matters to be not patentable under 35 U.S.C. 101: laws of nature, natural phenomena, and abstract ideas. But it also said that the control of a physical process through a computer program did not preclude patentability of the invention as a whole. A physical machine or process employing a mathematical algorithm is different from an invention claiming the algorithm itself in the abstract. Without citing any supporting authority, the court held that, under § 101, the invention needs to be considered as a whole. And if, taken as a whole, it meets patentability requirements by "transforming or reducing an article to a different state or thing,” it is eligible for patent protection even if it does include a software component. Thus, while the holding in*Gottschalk v. Benson*, 409 U.S. 63 (1972), “the patent would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself" and "[d]irect attempts to patent programs have been rejected [and] indirect attempts to obtain patents and avoid the rejection ... have confused the issue further and should not be permitted,” the U.S. Court of Appeals for the Federal Circuit has since deviated from this interpretation in a series of rulings by broadening the scope of the exception created by State Street with regard to considering the invention as a value-creating process overall. The U.S. Supreme Court appears to be preparing a similar value-creation-oriented approach as in*State Street*with regard to business processes starting in*Bilski v. Kappos*, 545 F. 3d 943, 120 S.Ct. 3218. It would appear that the trend for patent eligibility is to include anything so long as it is not a purely mathematical algorithm and produces a concrete and tangible result, raising concern about Pandora’s box once*State Street*removed the business method exception.
The
real question is not so much whether mathematics is discovered or
invented – “two
too-brittle words.”

The real question was
framed by David A.
Edwards:

“Since the end of World War II, our society has been moving onto an information stage, and it is becoming more and more important to have property rights appropriate to this stage. We believe that this would best be accomplished by Congress amending the patent laws to allow anything not previously known to man to be patented.More specifically, the distinction between discovery and invention should be eliminated.This would allow the patent incentive to motivate exploration for previously unknown useful forms of bacteria, plants, animals, materials, molecules, atoms, particles, etc.Previously unknown mathematical formulas, laws of nature should also be patentable. Since patents only give control over the commercial applications of his or her discovery or invention to the patentee, granting patents on mathematical formulas, laws of nature, and natural phenomena would have no negative side effects on pure science. The economic stimulation of pure science that would be provided by such patents is particularly important today as the traditional economic support of pure science, namely university faculty positions and government grants, are in decline. For the society as a whole, the positive economic effects of such extended intellectual property rights would be quite substantial.Today’s technology depends upon yesterday’s science.” (Emphasis added).

While
the Supreme Court has held since

*Gottschalk*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,” the Federal Circuit has since taken an ever-more pragmatic view by distinguishing the facts in a sometimes far-fetched manner: for example, it held in*Research Corp. Technologies v. Microsoft Corp.,*Fed. Cir. 2010-1037 (December 8, 2010) that an algorithm was patentable because it “required the manipulation of computer data structures.” Well, “manipulating data structures” is a very common mathematical task – yet, it is probably fair to assume that the Federal Circuit will not (or not yet, anyway) concede patents for new results in linear algebra because “manipulation of data structures” is involved. Since, however, the Supreme Court has not granted certiorari on an issue covered by Gottschalk since 32 years, the confusion about the applicable rationale and test endures.
While the Electronic Frontier Foundation is
concerned with the current patent system’s chilling effect on innovation and
periodically declares victory about relatively insignificant courts’ rulings (“Texas
court confirms you can’t patent math”) the trend – and social need – is
really pointing somewhat in the opposite direction. Of course it should be uncontested
that ideas that are otherwise abstract cannot be patented simply because they
are executed on the Internet or in a computer system. But practical exigencies
of complex data technology are chipping away at the mathematical algorithm
exception provided that it “produces a concrete and tangible result.” All else
would specifically exclude intellectual property because it has a mathematical
component, which would inevitably result in a chilling effect on the incentive
to engage in mathematical and logical research.

Role and tolerability of patent trolls and how
they might be penalized are not questions germane to mathematics. Not only is
too much money at stake, there is also too much applied mathematics at stake
that might otherwise not get funded. Yes, “software is mathematics.”
Mathematics and logic have, at this juncture, become indistinguishable in
important ways. It is more than a metaphysical query about whether pre-existing
truth underlies our existence, and the answer may be of logico-philosophical
but not of legal, much less of economic importance, because there may not be a
mathematical question with higher stakes today: software algorithms contribute
in excess of $300
billion a year to the global economy. It seems to be a very safe bet that
effective intellectual property rights in mathematical applications of
significant practical value will have to be recognized – by the courts or by
congressional action (or both) – before long.

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