And yet, we've had plenty of software patents which have held up in court and caused significant damage to companies which were found to be infringing, and many more which have backed off due to fear of the same.
Mathematical facts aren't patentable. That much has been established. Perhaps a "pure" algorithm isn't patentable; but all software patents start out with something like "a general purpose computer which...", tying it to hardware and making it patentable. Good luck implementing that algorithm without a general purpose computer.
For instance, the i4i patent is a patent purely on an algorithm, and Microsoft lost that case and had to remove the feature from its software: http://en.swpat.org/wiki/I4i_v._Microsoft . I'm not sure how you can square that with algorithms not being patentable.
No problem, just find a way to implement the algorithm which doesn't violate at least one of at least 121 "fast fourier transform" pattents and you're all set (http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sec...). Just repeat that process for every algorithm you might want to implement and you'll have no problem writing software.
That's why they patent the idea of having a general purpose computer do the math. And no, they don't care if the novel part isn't patentable subject matter and the patentable subject matter has already been invented. That's a pretty well-established dodge, except insofar as the recent Supreme Court decisions impact it.
The "Marching Cubes"[1] algorithm got patented ages ago and the patent was enforced. Some clever people had to come up with a similar solution called "Marching Tetrahedrons" to work around the patent.
The key phrase is "supposed to be"; "are not supposed to be patentable" does not imply "are not patented" in a system where patent examiners usually have very little idea what they're actually warding patents for and legal fees for challenging invalid patents are prohibitively high.
As a famous American statesman once put it: "Justice Marshall has made his decision - now let him enforce it."
It's commonly supposed that the Supreme Court could void these illegal patents - could dissolve this entire illegal industry - with a swish of their shiny polyester robes. Actually they already tried that, in Flook. Jedi mind tricks, which in the end is all the Court really has, worked about as well on Andrew Jackson.
I think this explains the disappointing result of Bilski. If you are supposed to have a magic power which in reality doesn't exist, make every excuse to avoid using it. You may still be suspected of impotence, but at least the suspicion is not confirmed.
Unfortunately there isn't really a solution to the patent problem that's compatible with the rule of law, mostly because the rule of law was so long ago abandoned for the rule of lawyers. Perhaps Andrew Jackson could round them all up and march them to Oklahoma - or at least, Marshall, Texas.
A large fraction of the native population that was rounded up and marched in that incident died. Accurate records were not kept, but according to estimates about a quarter of those evicted died as a direct result. Including some of my relatives.
Almost all my relatives are dead. Including all who remember the Jackson administration.
Some of them died justly, others not. I'm not an Albanian and have no interest in investing emotional energy in multi-generational blood feuds. Eg, some of my relatives were killed by the Germans, who make a really fine motorcycle.
Also, life was pretty cheap before the 20th century. It's easy to appall kids these days with the death rate among chained slaves crossing the Atlantic. In fact the death rate among Europeans voluntarily crossing the Atlantic was quite similar. It also wasn't easy or safe to walk across half of North America, whether voluntarily or not. Basically, to anyone who lived in this era - regardless of race, color or creed - we're all a bunch of whining pussies.
Really the main difference between the expulsion of the Cherokees and my proposed ethnic cleansing of the Palo Alto patent lawyers is that the Cherokees didn't deserve it, whereas the patent lawyers do. Lawless force can work good as well as evil. And when we've already left law behind, what's the alternative?