1854 O'Reilly v. Morse 15 How. 62. Electrical Signal itself (morse code) not patentable but repeaters to allow morse code to be transmitted long distances is patentable. Wikipedia.
Gottschalk v. Benson 409 U.S. 63 (1972). process claim directed to a numerical algorithjm , as such, was not patentable because "the patent would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself." BCD (binary coded decimal) to digital converter unpatentable as algorithm. Wikipedia.
Parker v. Flook 437 U.S. 584 (1978). Claims directed to "alarm limits," algorithm values that indicated catalytic converter malfunctioning.
Even though a phenomenon of nature or mathematical formula may be well known, an inventive application of the principle may be patented. Conversely, the discovery of such a phenomenon cannot support a patent unless there is some other inventive concept in its application. Wikipedia
Diamond v. Diehr, 450 U.S. 175 (1981), was a 1981 U.S. Supreme Court decision which held that the execution of a physical process, controlled by running a computer program was patentable. Wikipedia
State Street Bank & Trust Co. v. Signature Financial Group, Inc., 149 F.3d 1368 (Fed. Cir. 1998), Claim eligible for patentability if "it produces a useful, concrete and tangible result." Opened door to business method patents.
In re Bilski, 545 F.3d 943, 88 U.S.P.Q.2d 1385(Fed. Cir. 2008), “A claimed process is surely patent-eligible under § 101 if: (1) it is tied to a particular machine or apparatus, or (2) it transforms a particular article into a different state or thing.” Wikipedia