EDIT: It occurs to me upon reflecting on my reply that you're making a statement unqualified by present legal precedent. In that case, I respectfully disagree. Patenting fundamental mathematical truths seems like a very bad idea to me, and I'm glad that nominally such things are not allowed (though of course practically it goes on all the time).
Perhaps another way to say this: the problem most people have with software patents is that it's more or less patenting little pieces of math. I think it's more or less well known how most "practitioners of the art" feel about this.
Sorry. By "patentable" I meant when embodied by a clearly-defined machine.
And anyway, why not patent algorithms in the abstract? There are an infinity of "fundamental mathematical truths", but only a few are spectacularly useful. If a given algorithm truly is obvious and trivial, then you can evade the patent by spending 30 seconds to find another obvious and trivial algorithm. (I note that most of the people complaining about the trivial obviousness of all software patents are not cranking out 50 algorithms a day like RSA or the fast Fourier transform. When they talk about software being obvious, they're talking about other people's software.)
> And anyway, why not patent algorithms in the abstract?
Because the costs outweigh the benefits, unless you're a patent lawyer.
Software patents already create huge legal risks to businesses that did nothing wrong except come up with a simple idea that someone patented first, they're ridiculously expensive to enforce, and most of the money ends up driving more lawsuits rather than more research.
http://en.wikipedia.org/wiki/Gottschalk_v._Benson
EDIT: It occurs to me upon reflecting on my reply that you're making a statement unqualified by present legal precedent. In that case, I respectfully disagree. Patenting fundamental mathematical truths seems like a very bad idea to me, and I'm glad that nominally such things are not allowed (though of course practically it goes on all the time).
Perhaps another way to say this: the problem most people have with software patents is that it's more or less patenting little pieces of math. I think it's more or less well known how most "practitioners of the art" feel about this.