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{{law proposals}}
'''Mathematical formulas''' are generally recognised as non-patentable because math is not [[patentable subject matter]].

Since the logic (idea) of software can be reduced to a mathematical formula (idea) with Church-Turing Thesis, and because mathematical formulas (idea) are not patentable, patent applications for software ideas should be rejected.

Respected computer scientist [[Donald Knuth]] makes the argument:
<blockquote>
''To a computer scientist, this makes no sense, because every algorithm is as mathematical as anything could be. An algorithm is an abstract concept unrelated to physical laws of the universe.''<ref>http://progfree.org/Patents/knuth-to-pto.txt</ref>
</blockquote>

==Math is not patentable==

===Case law in the USA===

In the USA, math is unpatentable because it is a "law of nature", that is to say a "scientific truth", and as such it can never be "invented", only "discovered", and patents are not granted for discoveries.

The non-patentability of math was confirmed in the case [[Parker v. Flook (1978, USA)]]:

<blockquote>
''Respondent's method for updating alarm limits during catalytic conversion processes, in which the only novel feature is a mathematical formula, held not patentable under 101 of the Patent Act.''
</blockquote>

Also, in the 1948 case ''Funk Bros. v. Kalo Inoculant'':

<blockquote>
''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.''<ref>http://caselaw.lp.findlaw.com/cgi-bin/getcase.pl?navby=case&court=us&vol=333&invol=127#130</ref>
</blockquote>

Ideas which ''use'' math can be patentable, but this is not controversial:

<blockquote>
''While a scientific truth, or the mathematical expression of it, is not patentable invention, a novel and useful structure created with the aid of knowledge of scientific truth may be.''<ref>http://caselaw.lp.findlaw.com/cgi-bin/getcase.pl?navby=case&court=us&vol=306&invol=86#94</ref>
</blockquote>

==Some judges say math is patentable==
In the 2011 UK High Court [[The Halliburton rulings by UK High Court - 2005-2011|decision on the Halliburton case]], the judge said that math can be patentable because:

<blockquote>
the data on which the mathematics is performed ... represent’s something concrete (a drill bit design). 
</blockquote>

Also in 2011, the [[US CAFC Cybersource v. Retail 16 Aug 2011]] case, an algorithm was held patentable because:

<blockquote>
as a practical matter, the use of a computer is required.
</blockquote>

==Church-Turing Thesis or Curry-Howard isomorphism?==
There are two mathematical bases that can be used to make this argument.{{help|This page was written by a non-specialist.  Any help would be appreciated.}}

The Church-Turing Thesis is the more commonly used based.  It is discussed by some documents linked in the [[#External links]] section.

Another approach would be the Curry-Howard isomorphism, which demonstrates that computer programs are equivalent to mathematical proofs.  If proofs are unpatentable, then computer programs must be too.

==EPO says software is math==
According to the EPO, as written in [[EPO EBoA referral G3-08]] (''page 12 of 18''):

<blockquote>
computer programs were to be understood as a 'mathematical application of a logical series of steps in a process which was no different from a mathematical method
</blockquote>

==Related pages==
* [[Anti-lock braking example]] - if the physical car invention is patentable, should an in-computer game-simulation be?
* [[Books]]:
** [[Math You Can't Use]]
** [[The Karmarkar Patent and Software - Is Math Patentable?]]
* [[Software does not make a computer a new machine]]
* [[Australia#Case law]] - patents on math might be valid in Australia
* [[Pen and paper patents]] - what if math is ''so'' complicated, a pen and paper are required?

==External links==
{{process}}
* [http://www.bu.edu/law/central/jd/organizations/journals/scitech/volume141/documents/Klemens.pdf The Rise Of The Information Processing Patent], by '''[[Ben Klemens]]''' (''Church-Turing'' is discussed on page 8)
* [http://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis Church-Turing thesis], '''Wikipedia'''
* [http://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence Curry–Howard isomorphism], '''Wikipedia'''
* [http://www.qulix.com/ Offshore Software Development]
* [http://arstechnica.com/tech-policy/news/2011/08/appeals-court-says-only-complicated-math-is-patentable.ars Does not compute: <nowiki>[US]</nowiki> court says only hard math is patentable], Aug 2011, '''[[Timothy B. Lee]]'''
* {{lang de}} http://www.users.sbg.ac.at/~jack/legal/swp/tech-turing-lambda.pdf

===PolR's articles on Groklaw===
(Oldest first)

* [http://www.groklaw.net/article.php?story=20091111151305785 An Explanation of Computation Theory for Lawyers], 11 Nov 2009
* [http://www.groklaw.net/article.php?story=2010092621054289 Physical Aspects of Mathematics (An Open Response to the USPTO)], 27 Sep 2010, (submission to [[USPTO 2010 consultation]])
* [http://www.groklaw.net/article.php?story=20110908075658894 A Simpler Explanation of Why Software is Mathematics], 8 Sep 2011
* [http://www.groklaw.net/article.php?story=20110426051819346 1 + 1 (pat. pending) — Mathematics, Software and Free Speech], 26 Apr 2011
* [http://www.groklaw.net/article.php?story=20121013192858600 What Does "Software Is Mathematics" Mean? Part 1 - Software Is Manipulation of Symbols], 13 Oct 2012

===Counter arguments===
* [http://www.ipwatchdog.com/2008/12/15/computer-software-is-not-math/ Computer Software is Not Math], 15 Dec 2008, '''[[IP Watchdog]]'''
* [http://andrewchin.com/chin/scholarship/abstraction-equivalence.pdf On Abstraction and Equivalence in Software Patent Doctrine: A Response to Bessen, Meurer, and Klemens] (challenging, inter alia, Klemens's "''repeated mischaracterizations of the Church-Turing Thesis''")

==References==
{{reflist}}


{{footer}}
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