Well, between holiday lethargy (thanks Shawn Standefer), the beginning of the winter semester here at Northeastern, the CSF deadline a couple of weeks back and the upcoming UAI deadline, I have found precious little time to post since the beginning of the year. But I'm back, and ready to tackle the backlog.
I just received the March issue of the Notices of the AMS in the mail yesterday, and two articles caught my eye.
B. Poonen talks about "Undecidability in Number Theory", surveying the solution to Hilbert's Tenth problem by Davis, Putnam, Robinson, and Matiyasevich - coming up with the main theorem that a set is recursively enumerable if and only if it is diophantine (very roughly, it can be obtained as the solution to a diophantine equation). This amount, interestingly enough, to programming using diophantine equations. Applications of the result beyond Hilbert's Tenth's are discussed.
Also in the issue, J. Ewing talks about "Where Are Journals Headed? Why We Should Worry About Author-Pay", yet another article discussing the journal subscription prices crisis. The author makes the interesting point, which I had never thought of before, that mathematics (and CS) are hardly in any position to dictate policy, given that we have such a tiny proportion of the published journals. Biomedical sciences, with half the journals, drive the show. And the reason why this is important is that the publication model for biomedical sciences is quite different than that for the core sciences.
I will let you explore those articles in your copious free time. The issue is freely available: