According to Donald Knuth[1]:

"[To a computer scientist] every algorithm is as mathematical as anything could be... An algorithm is an abstract concept unrelated to physical laws of the universe."

[1]http://www.pluto.it/files/meeting1999/atti/no-patents/brevet...

And this proves what? I can find quotes to support an arbitrary position too. :P

It proves nothing of course. I just think that Knuth makes a compelling argument and I tend to agree with him. Mathematics by definition has no relationship to the physical world. When we create these relationships they fall outside of mathematics and become things like physics or chemistry. Patenting mathematical formulas is kind of meaningless, but more importantly, very harmful. If we were to patent them, we couldn't afford to teach them for example.

Next, the question is whether algorithms fall under mathematic. Knuth argues that they do and I agree.

Ok, this isn't an answer to your points, but have you read Tegmark's Mathematical Universe Hypothesis?http://arxiv.org/abs/0704.0646

"I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems."

I have not. From a quick look this stuff feels like String theory, which we conveniently cannot prove. Once again, only a mathematical concept with no connection to the real world that we need to concern ourselves with. It's also a "theory of everything" which I have learned not to trust (these theories tend to overlook some big issues, like the fact that quantum effects only show themselves at roughly atomic scales and just assume that the cumulative effect at large scales does not cancel out).

I realize that combinations of algorithms are still algorithms, but where do you stop?

The main problem with software patents for me are that

1) They stifle innovation by killing small projects or forcing innovators to not care about infringing (for which they can be sued later).

2) A lot of them are BS. There may be not prior art in the patent database, but for a specialist in the field, they're obvious.

3) It costs too much to patent, which puts too much power in large companies' hands. They can spam the USPTO with brain farts, with some non-zero probability of having them approved. If I save for a year, I can make one patent application per year.

In other words, there's no problem with software (or other) patents in theory, but currently the pragmatics are out of whack. Software patents are no different than other forms of patents except that many of the coefficients involved are very different from other industries, which significantly changes the calculus. Complete elimination of software patents would be preferable to what we have now, but IMO wouldn't necessarily be the optimal solution.