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There has been a lot of discussion about software patents and how evil they are over the past months. Even without the insanities concerning RIM and those concerning "business methods," there has been a lot to really dislike.
But nothing has gotten my back up the way patents (in the US) have been distributed on mathematics.
No, I'm not kidding.
If you studied advanced algebra or calculus, you know that Fourier analysis is an important and often-employed method. It is based on the notion that complex wave forms can be approximated by a sum of sinusoids, each of a different frequency. There are a number of techniques that have been developed to perform analyses employing computers.
Jean-Baptiste-Joseph Fourier (1768-1830) was a brilliant mathematician, successor of Lagrange at the Ecole Polytechnique, and member of the Academie des Sciences. He was born poor and never became wealthy.
In Math You Can't Use Ben Klemens * points out (p. 63) that there at least 10 patents on Fourier transformations, e.g.:
And there are many more.
The US Patent and Trademark Office has made it possible for a practicing statistician, physicist or mathematician to be sued for infringing on a patent on a method of analysis that's over 200 years old. (But, of course, the "innovation" claimed is executing the analysis on a computer. Bah!)
These are not the result of examiner oversights. Gale and Shapley (1962 [!]) pointed out that there is no difference between an application of an algorithm and the algorithm itself; and the Church-Turing thesis  states "the algorithm and pure math are entirely equivalent."
So here we are. The US Court of Appeals for the Federal Circuit has moved the line of patentability in such a way that someone can now "own" a part of pure mathematics. C60 would have started Canada along the well-greased slide to the patent and copyright hell south of us.
Read Klemens. Read Michael Geist. And don't let the steamroller crimp your style.
* Math You Can't Use By Ben Klemens (Brookings Institution Press, 2006; 181 pages)
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