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# Talk:Software is math

## [edit] Subject matter or novelty

Why does this argument apply to whether software as subject matter is patentable? I believe that application of the Church-Turing Thesis is perfectly valid under a 35 U.S.C. 102/103 analysis, but not under section 101. That is, if the assertion is "piece of software X is not patentable because mathematical formula Y is already known, and software X is just an implementation of mathematical formula Y," then reject the patent under sections 102 and/or 103. Why then do we need a blanket prohibition of software patents under section 101?

- Hi. My understanding (but I'm not an expert) is that the math exclusion is broader than what you describe. It's not just that "formule Y is already known", but that
*all*formula exist already in nature, so they can't be "invented". I'm pretty sure I read this in a US Supreme Court ruling, but I might have misinterpreted something. I'll look for that ruling... Ciaran 12:21, 8 May 2010 (UTC)

## [edit] Use Curry-Howard isomorphism

Actually, I would argue not based on the Church-Turing thesis - which is not a mathematical theory but just a "thesis" - but would use the Curry-Howard isomorphism http://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence. My understanding of it is that a software program is actually a proof in a given theory, i.e. that writing software is nothing but proving that a solution exists for a problem. So, as such, because a program is a mathematical proof then it cannot be patented.

- Hi,
- I wrote this article based on documents and info I found around the Internet, but I have no specialist training in math, so I'm sure I made terminology mistakes. I also had to leave some points vague because I wasn't sure of the details.
- If you could fix any sentences, or add more info, that would be appreciated. Ciaran 05:06, 4 January 2012 (EST)

- Hi,
- I am not an expert but have a maths background and I am happy to help. Let me explain what I have found digging further.
- Upon reading the wikipedia article I found the proof-to-program direction is easier than the program-to-proof.
- The former has been "used" in DeCSS (see http://www.cs.cmu.edu/~dst/DeCSS/Gallery/, "Mathematical description") by Ralph Loader.
- The other way, from programs to proofs would be the big one, as would render any software program as pure maths. Unfortunately this direction requires someone how is able to write the program using a rich programming language (actually using dependent types).
- There is good news, such languages exists (see http://www.ats-lang.org/ for one), so what I see as possible is to ask a programmer in that language to write an implementation of a claimed software patent and then, invoking the isomorphism, translate that into a proof. I bet this would be a recipe to invalidate all software patents one by one.
- There is a recent twist though. "Maths is non-patentable ... unless is complicated" (http://arstechnica.com/tech-policy/news/2011/08/appeals-court-says-only-complicated-math-is-patentable.ars) Carlos

## [edit] Parallels with the DRM schemes?

Isn't this theme somewhat analogous to the "secret numbers" of DRM? I.e. how can a number be somebody's secret, private property? For example http://en.wikipedia.org/wiki/AACS_encryption_key_controversy 85.76.189.136 17:08, 18 January 2011 (EST)

- Yes, it's quite similar.

- But we need more review of this. For example, if I fill a 200-page book with nothing but a single long number, can I have copyright on my book? What if I use letters instead of numbers?

- That copyright debate is outside the scope of swpat.org, but we have similar issues regarding patents. The "software is math" argument is sometimes seen as a discussion finisher, but it's really only the start of a discussion.

- Every program can be seen as a number, but you don't patent programs, you patent ideas. Further, math my not be patentable, but when is the
*application*of math to a class of problems patentable?

- This argument isn't one of my specialities, so help with developing it would be very welcome. (My relevant speciality is foreseeing the counter-arguments which could spoil such arguments.) Ciaran 23:55, 18 January 2011 (EST)