If you'll pardon the self-reference, I wrote up a description of how patent claims work at http://www.ontechnologylaw.com/how-patent-claims-work-a-vari....
In a nutshell:
1. Each claim of a patent is an AND statement, or if you like, an infringement checklist: If even one element in a given claim is missing from the accused product or process---and is not present by a "substantial equivalent" either---then that claim is not infringed.
2. In determining infringement, the different independent claims of a patent are OR'd together---only one of them need be infringed for the defendant to be liable.
3. A patent claim is invalid it if returns TRUE on the prior art, or on something that would have been "obvious" in view of the prior art at the time of the invention. How to determine obviousness in hindsight is perhaps the big question of patent law.
4. The claims of a patent are like a salvo of cruise missiles. The patent owner will launch as many claims as it can against a purported infringer. Some claims will miss, that is, they simply aren't infringed. Some claims will be knocked down by defensive fire, that is, by proof of invalidity. If even one claim gets through to the target, the patent owner is entitled to damages and (quite possibly) an injunction against further infringement.
what
The US legal system is baffling.
I can see why you'd think that. Could you try referencing which case you think involved a lower court overruling the Supreme court (like find a news story that mentions it or something)? That way someone might be able to clear up the misconception for you. I agree that civil procedure and matters of precedent can be very confusing, but I promise you the lower courts aren't going about overruling the Supreme Court, much as they might like to.
Umm, no. Lower courts can not overrrule the US Supreme Court. (The Supreme Court can overrule on some issue and remand. The lower court may then rule as it did before based on different issues, but that's not the same as the lower court overruling the supremes.)
> Then those lower court precedents were invalidated, yet software patents are still not abolished.
Invalidated by whom? (And then there's the question of exactly what was done.)
> The US legal system is baffling.
It's a lot less confusing if you don't rely on the media to figure out what's going on.
As to the "conclusion", In re. Bilski wouldn't invalidate Bezos One Click patent.
Also, one shouldn't assume that all software is a "mathematical algorithm".
And then there's the RSA patent - while one can't patent algorithms, one can patent using a specific algorithm for a specific purpose. (That's been done since before computers were invented.)
All you're saying about the conclusion is that you disagree with it.
One can't make statements about all software that will ever run on new technologies that we haven't seen yet. However, general purpose digital computers as we know them today are equivalent to Turing machines, so it is safe to assume that all software for them is mathematical algorithms. If you have some reason to question the consensus of theoretical computer scientists, please be specific about it.
My assertion is that what happens all the way from the Patent Office to the Federal Circuit is inconsistent with what the Supreme Court said. The RSA patent does not refute this assertion; it's an example of it. The RSA patent preempted all uses of a mathematical algorithm within a general-purpose digital computer. By the legal reasoning in Gottschalk v. Benson it should have been considered invalid.
Anyone who writes that title is demonstrating significant ignorance about how the US legal system works. Any "legal analysis" by such an individual would have a broken clock's chance of being accurate.
And, the conclusion shows that you didn't get lucky.
> However, general purpose digital computers as we know them today are equivalent to Turing machines,
Yes.
>so it is safe to assume that all software for them is mathematical algorithms.
No.
I can describe any sequence of steps using mathematics. However, that doesn't make all such steps a mathematical algorithm.
If it did, then no sequence of steps would be patentable under the "no patenting of mathematical algorithms" rule.
Do you really want to argue that no sequence of steps is patentable? Or, do you think that some sequences can't be described mathematically?
> The RSA patent preempted all uses of a mathematical algorithm within a general-purpose digital computer.
No, it didn't. The RSA patent explicitly says that it's for a specific use of a given (class of) algorithms, not all uses of those algorithms.
Patent language is pure, uncut crystal nerdbait. If you don't know how patent claims language works (and why would you?), most patents will appear ludicrous --- and that's assuming your programmer patent reviewers even know the difference between claims and background material.
Incidentally, reviewing patents prior to their issue isn't necessarily a win for defenders. I remember reading an analysis showing that defenders stand a better chance invalidating a patent in court than during the patent process. The crowdsourced review process could just end up helping patentholders by providing a first wave of claims strengthening.
It would be far more feasible to fight and win the battle to abolish software and business method patents.