The mathematical content may be a bit elementary for some readers here, but this is an entertaining article from American Scientist nonetheless. It’s not every day that there’s an article about group theory in the newsstands, and it’s about a real world problem that I believe many people have pondered over.

There is a great wealth of mathematical fiction. There are obviously works of science fiction with a high mathematical content such as the writings of Greg Egan and Stephen Baxter. But there are popular mainstream works that have a high mathematical content too. For example the excellent The Curious incident of the Dog in the Night-Time has, among other things, some discussion of the Conway’s Soldiers problem and the plays of Tom Stoppard often have non-trivial mathematial content. But if you’d like to have a list of it all, I recently found a fairly comprehensive list of mathematical fiction: MATHFICTION.

Metamath is a project to construct mathematics as proofs in ZFC. This what what we’re all supposed to be doing but in practice proofs tend to be informal arguments that we can convince people could be converted into derivations in ZFC. It looks like a long haul. There are now over 5000 theorems proved but they’ve only just proved a<=b => a<=b+1 in the reals. On the other hand they seem to have several hundred proofs about Hilbert spaces and quantum logic. Meanwhile, Wim Hesselink is hoping to verify a proof of Fermat’s Last Theorem by machine.

There’s a nice little trove of lecture notes on discrete mathematics here. The emphasis is on design theory but other topics are covered too. Design theory isn’t the biggest area in mathematics but the design S(5,8,24) has many interesting properties which have echoes through many branches of mathematics via its connections with certain sporadic simple groups , the Leech lattice and hence subjects like modular forms.

Vis – a – vis the comments in sigfpe’s last post, Krzystof Burdzy has a booklet online: Probability is Symmetry. On Foundations of the Science of Probability which introduces, discusses and critiques the Frequentist and Subjectivist foundational positions of Probability Theory. For any of our readers unfamiliar with either the terms or the arguments behind these philosophies of Probablility, this book forms an excellent primer on the subject, in addition to arguing for Burdzy’s own interpretation.