Ars Mathematica

Just under the wire…

The February Notices of the AMS features an article on the Four Vertex Theorem. The Four Vertex Theorem states that any simple closed curve in the plane (other than the circle) must have four extrema in its curvature.

Alexander Yong does the honors in this month’s entry in the What is… series, What is… a Young tableau. Young tableau arise in many contexts in combinatorics, most dramatically in parametrizing the irreducible representations of the symmetric group.

There are two articles about Mikio Sato, one a summary of his research contributions, and the other an interview. Sato is the inventor hyperfunctions,

We live in a golden age for popular accounts of advanced mathematical research. Robert Griess reviews Symmetry and the Monster, One of the Greatest Quests of Mathematics, by Mark Ronan. The book documents the history of the classification of finite simple groups. (In his review, Griess sounds like a skeptic on the question of whether the classification can truly be said to be done.)

Alain Connes has joined the web as a member of the group weblog, Noncommutative Geometry. From a quick scan of the posts, it looks as if the other members are Arup, Masoud Khalkhali, and David Goss. (David Corfield mentioned the new site last week. The comment thread there features an interesting discussion of how mathematicians would rather be torn apart by wild dogs than be identified as members of someone else’s “school”.)

Terry Tao has started a solo weblog, What’s new. I welcome everyone concerned to the world of weblogs, and congratulate them for making the wise choice of getting no real work done ever again.

The second Carnival of Mathematics is out.

I have a fever, so posting from me will be light. Before I go back to my sick-bed, though, I wanted to draw your attention to this web site that documents bias in Wikipedia. Most of the examples listed are not math-related, but item number 16 is:

Wikipedia has many entries on mathematical concepts, but lacks any entry on the basic concept of an elementary proof. Elementary proofs require a rigor lacking in many mathematical claims promoted on Wikipedia.

Further perusing of the site reveals that they mean elementary proofs in number theory, i.e. proofs don’t use complex analysis. Apparently belief in the complex numbers is a form of bias.

Via Good Math, Bad Math.

New York Magazine has an interesting article on the best way to use praise in education. Experiments show that praise can be an effective teaching technique, but interestingly, only praise for someone’s work ethic. Praise of someone’s intelligence can actually hurt performance.

The inaugural edition of the Carnival of Mathematics is up.

Using fMRI, scientists can now distinguish (with 70 percent accuracy) whether you are thinking about addition or subtraction.

I have a question about projective determinancy that I was hoping someone could answer. Is projective determinancy provably consistent with ZFC , or does its consistency require large cardinals to prove?