So what is it good for?

You know you’ve been asked “what’s math research good for?”  I’m talking about at that party that wasn’t full of other math grad students.  You know, right after, “you do new mathematics?  I thought it was all finished!”

I’ve made a stab at writing an answer to this for the general public, and I’d love input from other mathematicians.  Do you think I’m right?  So what is it good for?

Teaching without Permission!

Many of the math blogs that I read (and you can find in the blogroll) are writing about the plight of Ali Nesin and his Summer School. Apparently, Prof. Nesin was arrested for running his yearly Summer School in Turkey since he was “teaching without permission”! You can even see pictures of black boards behind police tape on Mathematics under the Microscope. A petition was set up to protest and I urge you to sign it!

New Paper on Arxiv: Nonisomorphic Verdier Octahedra on the same Base

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 in a triangulated category the cone on 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.

Arguing with Other Mathematicians

I use an RSS thread to follow what is new on the arXiv and recently I came across a paper that claims that the theory of mathematics isn’t consistent. That sounded intriguing so I downloaded the paper and read it. I discovered, what I think is, a serious error and notified the authors. Every night since then I have been in email contact with the authors. We are in complete disagreement about whether there is an error or not but our discussions are (still) very polite and it doesn’t look like either one of us will convince the other(s).

I would appreciate any comments or advice from anyone reading this post that has similar experiences of conversing/arguing with the author(s) of a paper about errors and how such conversations/arguments have turned out.

I don’t want to post a link to the paper, since I feel like that would be like trying to make fun of other people’s work. I can email a link to anyone who is interested in taking a look at the paper, just drop a comment.

New shirt!

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.

The Klein Four

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.

Self Referential Aptitude Test

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!

New links in blogroll

I added my favorite math blogs to the blog roll. Some of them updated almost daily while others seem to hibernate for long periods of time. All of them, however, feature great posts on math and related subjects. Check them out!

Capitalism takes hold

I have succumbed to capitalism and opened a store at CafePress.com. The direct link is www.cafepress.com/cctops and if you are wondering the “cc” in “cctops” stands for crazy cool, (I know that’s really lame, by the way). So far I’ve only uploaded one design featuring your favorite math mistresses, . I hope to upload some more elaborate designs soon.

experimenting with exams

I experimented with a new format for the midterm of my single variable calculus class (which is running during the summer session here at Brown). The midterm consisted of 10 problems and at the beginning of the class the students were allowed to work on all the problems but at the end they each had to choose 5 problems to turn in. The remaining problems then turned into a take-home midterm which was due the next day.

The students liked this format but found the midterm itself a bit hard. I’m in the midst of grading it right now and it seems to have come out just fine.

Here is why I like this format:

• Students don’t need to know and worry about every single type of problem that I might put on the midterm.
• It takes most of the time pressure away.
• It is less likely that students collaborate on the take-home part since they might not even have the same problems chosen.

I think that next time I give a midterm I’ll experiment with different ratios, only allowing students to take 3-4 problems to work on at home.