This is further to my questions on the patentability of complex mathematical algorithms used thereafter in a simple manner to effect something useful. Sorry for its length. My previous question was (please refer), "a question on patent eligibility of a methodology of computation". I was given the impressions (in the answer) that they are in essence out rightly not patentable unless there is a physically tangible step coming in between. If not, it is an abstract idea and such cannot be patented. However, I see that ...
You can't patent an 'algorithm'":
Not true. An algorithm, even a mathematical algorithm, is patentable unless (1) it is not sufficiently disclosed to overcome the "abstract idea" exception, or (2) it is executed with no useful application in mind.26 This description of just what an "algorithm" is may be helpful: "Although one may devise a computer algorithm for the Pythagorean theorem, it is the step-by-step process which instructs the computer to solve the theorem which is the algorithm, rather than the theorem itself."27 Under Alappat, the algorithm might be patentable. The theorem itself, being an abstract idea, certainly would not.
"You can't patent a process unless it involves a 'physical' element.'":
False. The Diehr court lists "transforming or reducing an article to a different state or thing"31 as "an example, not an exclusive requirement" of patentability.32 The Court of Custom and Patent Appeals (CCPA)'s Freeman-Walter-Abele test, which required a mathematical algorithm to be "applied to or limited by physical elements," has been seriously called into question by Alappat, State St., and AT&T. "Whatever may be left of the earlier test, if anything, this type of physical limitations analysis seems of little value."33 As discussed above, patents are being issued and upheld on inventions that amount to no more than calculating a number, as long as that number is useful information.
Also, here is an issued patent which seems a mathematical algorithm/methodology at heart, "Computational method and apparatus for finite field multiplication" US 4745568 A. The computational method too is patented in this.
Would appreciate help and clarification, as I am a little confused in this area. Thank you.