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.
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.