TFA boils down to the following points, and a lot of people are (rightfully) questioning it:
> The courts have repeatedly said that mathematical algorithms can't be patented. But many judges also seem to believe that some software is worthy of patent protection. The problem is that "software" and "mathematical algorithm" are two terms for the same thing.
This is false on multiple levels:
1) Laws of physics and laws of nature and cannot be patented. Elements of the periodic table are naturally occurring materials and cannot be patented. Yet machines applying these very same laws of physics and made out of these very same materials can be patented. As can compounds that are new arrangements of atoms of various elements.
This is because machines and compounds are specific applications of patent-ineligible physical laws using configurations of patent-ineligible individual materials. Similarly, software is an application of patent-ineligible mathematical algorithms (along with a healthy dose of I/O that translates wholly non-mathematical things into mathematical representations). Just as machines are patent-eligible, software is too.
Laws of Physics : Machines :: Elements : Compounds :: Algorithms : Software
2) As evidence of the above, note that most claims for software don't even claim specific algorithms, but rather just high-level descriptions that could be implemented in a thousand ways using a thousand different algorithms. A claim will almost never say, as one of its steps, "looking up a value using a key in a hashtable" -- it will almost always say something like "determining a value corresponding to a key", which covers all O(1), O(logN) or O(N) algorithms. (If they even get to that level of detail at all... most claims are at an even higher level, e.g. "receiving a compressed image and detecting faces in it", where each element would involve a multitude of disparate algorithms) Such language could cover any number of ways of doing something.
Some take this as a sign of abstractness. But when you look at patents on physical machines, their claims also rarely ever mention the precise measurements of the various components and the actual materials used. The number of materials and relative sizes that could be used in making a mechanical invention is as numerous as the number of languages, data representations and storage technologies that could be used in making a software invention. As such, machine patents also cover all ways in which to implement it. This is not abstractness, but rather the eliding of details that are irrelevant to the essence of the invention.
3) When the court says algorithms are un-patentable, they mean abstract formulae like E = MC^2. By itself, that formula does nothing, and hence is not useful. On the other hand, software for a web browser can cause your computer to fetch data from another machine a thousand miles away and display it on your screen. Regardless of level of technical competence, everyone can agree that this is non-abstract and useful. That's the primary reason that software is worthy of patent protection: it meets the statutory requirements, i.e. "any thing under the sun that is made by man".