Algorithms are mathematical equations. They cannot be patented.
I know the mantra. I just don't buy it. Math provides the building blocks used to produce creative (and sometimes very innovative) solutions to problems in the form of software. Material properties and laws of physics similarly provide the building blocks used to produce creative solutions to problems in the form of physical devices or mechanisms.
Just because the basic building blocks used to formulate an innovation aren't patentable, it doesn't necessarily follow that the innovation itself shouldn't be patentable if it's truly innovative and worth protecting (which most software patents certainly aren't, but some undoubtedly are).
That leaves the patentability of math. Man I wish I had a time machine so I could go back in time and convince Pythagorous to patent his little triangle formula in the context of architecture. I could make a killing.