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Tim Gowers just announced that the Tricki – a wikipedia of tricks and tips for proving mathematical results – is up and running (it has been visible but un-editable for a few days). It features articles from various prominent people, including Terry Tao. After a quick glance it looks pretty awesome and has the potential to become even awesome-er.

Over at Ars Mathematics Walt points out two articles that blaim mathematicians and physicists for the fall of Wall Street. His conclusion is that mathematics is dangerous when it falls into the wrong hands. I think the problems is more that mathematics is dangerous when it falls into stupid and greedy hands!

I’m reading the book Prime Obsession, by John Derbyshire, which tries to explain the Riemann Hypothesis to non-mathematicians. I got the book early in my undergraduate but never got around to reading it and then came across it in my book shelf the other day. I’m about half-way through and it has been a delightful read. Derbyshire manages to explain a lot of difficult mathematics without getting too technical and I would recommend the book to anyone starting an undergraduate in mathematics.

When I turned page 268 I was a bit surprised to see Derbyshire’s notation for the quotient rings $\mathbb{Z}/n \mathbb{Z}$; he uses $\mathbb{CLOCK}_n$. The reason for his choice is that arithmetic modulo $n$ is just like adding numbers (or positions) on a (analog) clock. Let’s work this out for $n = 12$. We begin by replacing the $12$ on our clock by ${0}$. Then we can start adding things. Say it’s $11$ and we’re starting to drive home from work which will take $2$ hours (damn commute). What will the time be when we arrive at our doorstep (late for dinner)? Well it’s $1$ of course, $11 + 2 = 1$ on the clock face. This is exactly the same as addition modulo $12$.

The paper Nonisomorphic Verdier Octahedra on the same Base, by Matthias Künzer, popped up on the Arxiv today. It answers the following question: Given a morphism $f : A \to B$ in a triangulated category the cone on $f$ is determined up to a (non-unique) isomorphism; is the same true for a Verdier octahedron constructed from a commutative triangle? The answer is: No, there exist non-isomorphic Verdier octahedra constructed from the same base! The non-uniqueness mentioned above has been a thorn in the side of the standard axioms for triangulated categories and this result doesn’t exactly make their life easier!

To prove this result Künzer uses something called Heller triangulated categories which he describes in detail in the paper Heller Triangulated Categories. These two papers are definitely being added to my list of things that I want to understand!

On a related note, J.P. May has proved that the standard axioms for triangulated categories are over-determined in the sense that one of the axioms can be proved using the other three. This is explained in his paper The Axioms for Triangulated Categories.

I have uploaded a new design to my capitalist shop at CaféPress. It features the slogan: Category theorists go Hom for the holidays. You can check it out at www.cafepress.com/cctops.

I ran across this awesome video on Zero Divides. I think it must be the best math-inspired song I’ve ever heard! The song is written and performed by a group of graduate students at Northwestern University, calling themselves the Klein Four. They run a web site at www.kleinfour.com.

I stumbled upon this self referential aptitude test at The Unapologetic Mathematician. It reminded my of the first problem set I was given in my first year linear algebra course as an undergrad. I think the problems there where from a book by Lewis Carroll, the author of Alice in Wonderland. Anyway, the aptitude test looks like a lot of fun, I can’t wait to sit down and try to figure it out!

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