I was subbing at Durant Branch in late 2014. A patron who spoke Russian (but very little English) approached the reference desk together with a staff member who translated for him. The patron was a mathematician who wanted to know how to patent some original work he had done in mathematics.

I was inclined to tell him that mathematical discoveries were, just that, **discoveries** – not **inventions** (which can be patented). Credit for a discovery in nature is claimed by writing a scholarly paper describing it. The US Patent Office states the following:

“The laws of nature, physical phenomena, and abstract ideas have been held not patentable.” . . . “Thus, 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.”.

A patent law page at www.legalmatch.com states the following:

“Even if you make a new and useful scientific discovery that no one else has ever thought of, you cannot get a patent on it because you did not actually create the fact you discovered. That fact was always in existence, you were just the first to notice it. However, if you can come up with an invention that makes use of that fact, you can patent the invention. . . .

. . . . . . . . . . . . .

Abstract ideas are concepts like pure mathematics and algorithms. You cannot patent a formula. However, you can patent an application of that formula. Thus, while you cannot patent a mathematical formula that produces nonrepeating patterns, you can patent paper products that use that formula to prevent rolls of paper from sticking together. . . .

. . . . . . . . . .

Although software functions by using algorithms and mathematics, it may be patentable if it produces some concrete and useful result. However, what cannot be patented is software whose only purpose is to perform mathematical operations. Thus, software that converts one set of numbers to another will not be patentable; but software that converts one set of numbers to another to make rubber will be patentable.”.

On the other hand, a discussion by scientists at ResearchGate.net tends to show movement in this direction:

“Mathematical equations have become the raw material of the software industry. Business developers are now moving towards patenting mathematical equations arguing that math is an “invention” that is worth protection. They believe patenting math will help mathematicians form their own companies and start a whole new industry. . . .”.

A controversy rages in the area of software patents. Consider the following excerpts from a letter to the US Patent Office:

“At its core, software is mathematics. The rendition of a mathematical function or algorithm in software is, in reality, a version of that function or algorithm itself, which

cannot be patented. . . . As to the application of mathematics to business, software development is a rapidly paced and ever-changing field with many participants. What appeared new and innovative even six months ago may be obvious and well-known territory today. Often seemingly new developments are, in reality, merely rediscoveries of something already proven and in wide use, hearkening back to the mathematical reality of software. It is my belief that if the current body of software patents were to be uniformly enforced by the holders, no software could be written that was not in violation of some patent. . . . To continue to issue software patents will have a chilling effect on the ability of the United States to continue to innovate and lead the world in software production.”.

Another letter to the US Patent Office clearly states the case against software patents.

In any case, after I provided our mathematical patron some books about patents, my patron decided to consult a fellow Russian-speaking mathematician about what to do (e.g., jointly publish a scholarly paper).

Sometime later, I turned up yet another dimension to this question. Whether mathematical work is discovery or invention is also a pure philosophical question.

“Perhaps the most important constant in Wittgenstein’s Philosophy of Mathematics, middle and late, is that he consistently maintains that mathematics is our, human invention, and that, indeed, everything in mathematics is invented. Just as the middle Wittgenstein says that “[w]e make mathematics,” the later Wittgenstein says that we ‘invent’ mathematics (RFM I, §168; II, §38; V, §§5, 9 and 11; PG 469–70) and that “the mathematician is not a discoverer: he is an inventor” (RFM, Appendix II, §2; (LFM 22, 82). Nothing exists mathematically unless and until we have invented it.”