The US courts do place weight on the "it's patenting a mathematical formula" argument. There's some nuance and murk, but an application will probably have to pass the "Machine or Transformation Test" to be patentable:
http://en.wikipedia.org/wiki/Machine-or-transformation_test
Essentially, software implementations of algorithms cannot generally be patented either because they are simply an expression of the algorithm in a particular language. The fact that this language can be interpreted by a particular hardware device does not change the situation. The hardware is a pre-existing piece of general-purpose commodity hardware that is easily interchangeable with any number of other pre-existing pieces of general-purpose commodity hardware, up to and including a human being equipped with a pen and paper, and therefore cannot really be claimed as part of the patent.
A physical device which implements the algorithm can, of course, be patented. And a hardware/software combination where the computer is an integral part of the mechanism (e.g., it cannot in principle be replicated by a human with a pen and paper) can also be patented, so Amazon's 'One-Click' patent is safe. However, simply tacking on the phrase, "Written in a programming language," does not take an unpatentable idea and make it patentable.
Essentially, software implementations of algorithms cannot generally be patented either because they are simply an expression of the algorithm in a particular language. The fact that this language can be interpreted by a particular hardware device does not change the situation. The hardware is a pre-existing piece of general-purpose commodity hardware that is easily interchangeable with any number of other pre-existing pieces of general-purpose commodity hardware, up to and including a human being equipped with a pen and paper, and therefore cannot really be claimed as part of the patent.
A physical device which implements the algorithm can, of course, be patented. And a hardware/software combination where the computer is an integral part of the mechanism (e.g., it cannot in principle be replicated by a human with a pen and paper) can also be patented, so Amazon's 'One-Click' patent is safe. However, simply tacking on the phrase, "Written in a programming language," does not take an unpatentable idea and make it patentable.