"The US patent office no longer grants patents on perpetual motion machines, but has recently granted at least two patents on a mathematically impossible process: compression of truly random data" (from Gailly.net)
Also you might be interested in the topic, there's a second patent that seems also to be fatally flawed -- It is analyzed here.
I am not opposed to software patents as a matter of principle. And of course a patent that describes something that is mathematically impossible is harmless inasmuch no one is forced to use it. But it does shine a light on the problems with Patents in general. Is it mathematically impossible though?
I wonder how the inventors of these patents would respond to the allegations above. Well it turns out that he has devoted a whole web site to the topic: "Michael Cole, Inventor of Recursive Data Compression Patent 5,488,364 created andy utilized a recursive data compression structure." The site has lots of details and mathematical symbols. I have not taken the time to try to understand either his arguments or the counter arguments.
I mainly got fascinated by the conflict.