Remember what happens when drug companies re-discover a useful molecule that turns out to have “prior art” as a molecule that people have been consuming in some every-day herb or some-such. They can’t patent that molecule (because they didn’t invent it), and there’s no profit motive to go through FDA compliance for a non-patented drug.
But, there’s nothing stopping them from finding the “theorem” behind the “algorithm”—figuring out what it is about the molecule’s structure that makes it have the effect it has—and then discovering another molecule in the same class (another “algorithm” constructively proving the same “theorem”), and then patenting that.
Same is true for actual algorithms: if PageRank is patented, I can just look at the theorem behind it—efficient eigenvalue derivation—and then come up with a different constructive proof of it. It’s easy once you know it’s possible. And, because there are so many known isomorphisms between algorithms (e.g. between algorithms on pointer machines vs. RAM word machines) there are often “obvious” transformations of the algorithm that aren’t considered the same algorithm from the patent office’s POV. (And, I mean, technically they aren’t; they might have a very slightly higher time-complexity, by a factor of the inverse Ackermann function or something. But these are things that don’t matter in practice, just like the random extra bits that the drug companies tack onto their molecules don’t matter in practice.)
See: Johnson & Johnson/Janssen Pharmaceutica esketamine patent. [0]
The FDA just approved the use of the drug, [1] which is basically a ketamine molecule cut in half (ketamine is a racemic molecule), [2] and J&J is selling it for HUNDREDS of dollars per treatment, while regular Ketalar brand ketamine is damn-near as cheap as saline.
Whether or not an invention is really covered by a current patent is not the issue; the issue is that patent holders can keep anyone who tries to exploit an invention in perpetual legal jeopardy, by continually filing patents on _related_ inventions.
Remember what happens when drug companies re-discover a useful molecule that turns out to have “prior art” as a molecule that people have been consuming in some every-day herb or some-such. They can’t patent that molecule (because they didn’t invent it), and there’s no profit motive to go through FDA compliance for a non-patented drug.
But, there’s nothing stopping them from finding the “theorem” behind the “algorithm”—figuring out what it is about the molecule’s structure that makes it have the effect it has—and then discovering another molecule in the same class (another “algorithm” constructively proving the same “theorem”), and then patenting that.
Same is true for actual algorithms: if PageRank is patented, I can just look at the theorem behind it—efficient eigenvalue derivation—and then come up with a different constructive proof of it. It’s easy once you know it’s possible. And, because there are so many known isomorphisms between algorithms (e.g. between algorithms on pointer machines vs. RAM word machines) there are often “obvious” transformations of the algorithm that aren’t considered the same algorithm from the patent office’s POV. (And, I mean, technically they aren’t; they might have a very slightly higher time-complexity, by a factor of the inverse Ackermann function or something. But these are things that don’t matter in practice, just like the random extra bits that the drug companies tack onto their molecules don’t matter in practice.)