The US does not produce enough mathematical stars

The New York Times has an article today, “Math Skills Suffer in U.S., Study Finds“, which announces an upcoming article in the Notices of the AMS by Janet Mertz, Jonathan Kane, Joseph Gallian, and Titu Andreescu. The Times writes: The United States is failing to develop the math skills of both girls and boys, especially…

Create your own word clouds

This post is not really math-related.  I discovered a cool website called Wordle, which you can use to generate custom word clouds. Here’s how Wordle describes itself. Wordle is a toy for generating “word clouds” from text that you provide. The clouds give greater prominence to words that appear more frequently in the source text….

Flatland and other videos about dimension

Not long ago I watched the DVD of Flatland staring Martin Sheen as the voice of Arthur Square. The movie is based on Edwin Abbott Abbott’s 1884 book of the same title. Flatland is a story of polygons living in a two dimensional world and A. Square’s discovery of the third dimension. It is also…

Cutting and folding paper

Inspired by Chaim Goodman-Strauss’s recent video about symmetries, paper snowflakes, and paper dolls, I decided to post a few other paper-related videos. First is a video showing some cutting tricks for a Möbius strip. I show this to my topology class, then have them play around with Möbius strips—twisting them various numbers of times and…

Flash cards are a good idea

I recently came across an article by the mathematician Ethan Akin, whose work in topology and dynamical systems I admire greatly, called “In Defense of ‘Mindless Rote’“.  In the article he defends the traditional education model of having students memorize mathematical facts and techniques. He begins with the following quote from Alfred North Whitehead’s Introduction to Mathematics….

DARPA’s 23 mathematical questions

DARPA (The Defense Advanced Research Projects Agency) recently released the DARPA Mathematical Challenges (Word document)—23 challenging mathematical problems “with the goal of dramatically revolutionizing mathematics and thereby strengthening DoD’s scientific and technological capabilities.” The titles of the challenges are: The Mathematics of the Brain The Dynamics of Networks Capture and Harness Stochasticity in Nature 21st Century Fluids…

Math quotes on Freakonomics blog

There’s a mathematical topic today on the New York Times’ Freakonomics blog.  Their daily bleg (definition: using a blog to beg for information): What’s been said about math? Readers are invited to leave their favorite quotes about mathematics (or quotes by mathematicians) in the comments.

Kuratowski’s closure-complement theorem (solution)

Stop!  This post contains spoilers.  This page has the solution to the problem posed in yesterday’s post. We challenged you to find a set from which we can make as many new sets as possible using only the closure and complement operations. In 1922 Kuratowski proved the following theorem. Theorem. At most 14 sets can…

Kuratowski’s closure-complement theorem

One of my favorite theorems in elementary topology is Kuratowski’s closure-complement theorem. First some notation.  For any set let denote the complement of and  denote the closure of .  (Recall that and  is the union of and all the limit points of ). Here’s the problem.  Find a set so that we can construct as many…