State of Innovation

Patents and Innovation Economics

Limits of Patentable Subject Matter (35 USC 101)

I was posed the following interesting question, if the constitutional purpose of patent law is to promote science and the useful arts why shouldn’t mathematics be patentable?  Clearly, mathematics is useful and writings about mathematics are covered by copyrights.  However, “mathematical algorithms” have generally not been considered patentable subject matter.

A possible reasons why mathematics has not been considered to be patentable subject matter is that laws of nature and mathematics describe what is, they are not creations of man.  Laws of nature are per se prior art, they clearly existed before man discovered how they worked.  While this is a good explanation for why laws of nature are not patentable, is it a good explanation for why mathematics is not patentable?  Is Euclidean geometry a product nature or is it a human construct?  Euclidean geometry is very helpful in understanding physics, chemistry, and other natural phenomena.  However, Relativity shows us that our universe is not Euclidean, but curved.  Alternatively, if a Fourier transform is a description of nature, are the different methods of calculating a Fourier transform descriptions of nature?  I cannot see how the different methods of calculating Fourier transforms can be considered a description of nature.  In my opinion the “per se prior art” reasoning for why natural laws are not patentable does not cover all areas of mathematics.

In my opinion there should not be a per se rule on whether mathematics is patentable.  The “use” requirement for patentable subject matter should be the filter for whether new mathematical discoveries are patentable.  If the inventor cannot describe a practical use for their new area of mathematics, beyond just expanding our knowledge, then it fails the “use” requirement of 35 USC 101 and is not patentable.  If they can describe a practical use then a patent for the math in combination with the practical use is not just a description of nature, it is a human creation.  Obtaining a patent in this case should not be predicated on whether or not the mathematics and practical use is implemented on a computer or other machine.

How does the theory proposed in this post apply to software, business method, and financial product patents?  As explained in other posts software when executed is just an electronic circuit.  Electronic circuits are physical, they take up space, they consume energy, give off heat, and move electrons.  Software should clearly be considered patentable subject matter.  The problem with business method patents is that no one has come up with a consistent definition of a business method patent.  As explained in an early post all patents are directed to business methods in that they relate to how a company intends to operate their business.  Business methods are not natural laws and they clearly are useful.  What about patents on financial products?  To the extent that the financial products are implemented using software, then they clearly should be patentable.  From a practical point of view it is unlikely that any new financial products will be not be implemented using a computer.  However, it is still interesting to ask if they should be patentable when implemented separate from a computer.  For instance, if double entry accounting was invented today or if an update to double entry accounting was invented, should this be patentable.  Based on the thesis presented herein, double entry accounting is not a law of nature, and it has a practical use, therefore the process of double entry accounting should be patentable subject matter.

This is a complex subject with many nuances.  The Supreme Court’s opinions have not been the model of clarity and therefore provide only minimal guidance.  Attorneys tend to answer these questions, by giving examples rather than explaining the differences based on first principles.  I have attempted to create a framework from first principles.  I would greatly appreciate any thoughts the reader has on this subject.


October 12, 2009 - Posted by | -Law, -Philosophy, Patents, Uncategorized


  1. DB,

    While one part of me would like to throw my 2cents at this question, the better answer is to point you to a book called “Road to Reality” by Penrose.

    In one of the early chapters, Penrose has a Venn diagram with 3 constructs: (a) All math devised so far by mankind, (b) All math not yet devised by mankind and some that may never be so devised, and (c) The way the Universe is. The question that Penrose poses is whether a and c fully intersect if at all? He points out that it may very well be that at least part of b intersects with c, and the intersection may include math that mankind will never devise. The answer is unclear.

    But what is clear is that Mother Nature is a deaf mute. She does proclaim any laws as being hers (Laws of Nature) and she does not listen to the nonsense spouted from the mouths of men (even if those men happen to be, cough, cough, Supreme Court Justices).

    Comment by step back | October 13, 2009 | Reply

  2. step back thanks for your feedback.

    Comment by dbhalling | October 14, 2009 | Reply

  3. Interesting to view the practical implications of differing philosophies of mathematics as well.

    Comment by Jacques Knight | November 3, 2009 | Reply

  4. There is obviously a lot to learn. There are some good points here.

    Robert Shumake Fifth Third

    Comment by Robert Shumake | February 2, 2010 | Reply

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