May 15, 2012

Can you patent a mathematical algorithm?

by MARK HAIMAN, UC Berkeley


Historically, U.S. courts held that \laws of nature, natural phenomena, and abstract ideas" could
not be patented. Mathematical algorithms were considered to be abstract ideas and therefore
unpatentable. A computer program is a form of mathematical algorithm, and so, although the
code for an individual program could be protected by copyright, the underlying algorithm could
not be patented.

In the 1980's and 90's, patent attorneys for software companies began to le for patents on
inventions consisting in part or entirely of algorithms, in a gradual e ort to get the patent of-
ce and the courts to expand the de nition of patentable inventions until it would include pure
algorithms. In one famous case, ATT in 1988 patented an algorithm for linear programming de-
veloped by N. Karmarkar, a researcher at its Bell laboratories. Karmarkar's algorithm was an
important mathematical development and the e ort to patent it created much controversy, partic-
ularly because before the patent was applied for, Karmarkar and ATT boasted about how well the
algorithm worked while refusing to reveal any details. The earlier Berlekamp-Welch patent seems
to have attracted less attention.
When these patents were granted in the 80's, their validity was doubtful, as courts then still
held mathematical algorithms per se to be unpatentable. However, the broadening of the de nition
has continued to the point that under U.S. law today, there are e ectively no barriers to patenting

software and algorithms. If an algorithm has \some type of practical application," the courts no
longer consider it an unpatentable abstract idea.

In my opinion and that of many other mathematicians, and also software developers, the present
state of a airs is a bad one. In mathematics, claims of ownership over ideas serve no useful purpose
and only impede progress. In commerce and industry, patents are supposed to serve the public
interest by providing a reward for innovation. However, many observers have made the case that
software patents have the opposite overall e ect, sti
ing innovation by threatening in e ect to make
much non-commercial software development illegal.

Patents and copyrights are often spoken of today as intellectual property. This rather loaded
term carries with it the suggestion that it is natural or desirable for individuals or corporations to
own ideas and control their dissemination and use, prohibiting their sharing in the public domain.
Historically, however, the basis of patent law is not the concept of natural property but that of
a social contract, in which society grants to inventors a temporary monopoly on the use of their
inventions in return for publicizing those inventions and as an incentive to invent. It's interesting to
note that the basis for the authority of Congress to establish patents and copyrights is the following
clause in Article I, Section 8 of the U.S. Constitution, which explicitly speci es the temporary nature
of such rights and the social interest that they should serve:
The Congress shall have the power. . .

To promote the Progress of Science and useful
Arts, by securing for limited Times to Authors and Inventors the exclusive Right to
their respective Writings and Discoveries;
When patents on algorithms, software, genes, and life forms begin to obstruct more than to promote
the \Progress of Science and useful Arts," perhaps the rules governing them need reconsideration.
Here are some sources of additional information and opinions on this subject
http://lpf.ai.mit.edu
(League for Programming Freedom web site)
www.softwarepatents.co.uk
(UK Resource on Software Patents: web site about UK and European software patents
also discusses the U.S. experience)
http://swpat.ffii.org/index.en.html
(Foundation for a Free Information Infrastructure: German web site about European
software patents)