In my opinion, compactness is the most important concept in mathematics. Here’s an article, recently published in Pro Mathematica, that tracks compactness from the one-dimensional real line in calculus to infinite dimensional spaces of functions and surfaces. Continue reading »

Crocodilia, Sex Ratios, and Fisher’s Theorem

Crocodilia, the biological order that includes alligators and crocodiles, have the interesting property that the gender of offspring is not determined by random genetics but by the environment of the nesting site. Prime nesting sights, in wet marshes near water sources, produce nearly 80% female hatchlings. The… Continue reading »

Cildo Meireles and the Poisson-Clock transition

Cildo Meireles is a well-known Brazilian artist, associated with the art movement “Neo-concrete art”. He was recently given a full retrospective by the Tate Modern Museum in London, which I had the opportunity to see in December 2008. Meireles’ intriguing and aesthetically seductive installations… Continue reading »

Tasty Math to keep you Warm

NPR's Here and Now from November 24th, 2008 featured a discussion of some mathematical recipes for the holidays. The first recipe from Instructibles is for a "pie-cosahedron". The name (and shape) come from the icosahedron, a 20-sided platonic solid. The pie-cosahedron is a 20-sided pie. Check out the recipe here. (This pie would also make a great snack for anyone playing Dungeons and Dragons.) Continue reading »

Art – Sol LeWitt – Math

This past week marks the rising of the Sol LeWitt sun in my part of the world.  At the Williams College Museum of Art (WCMA), a beautiful new exhibition on The ABCDs of Sol LeWitt has just opened, exploring the underlying grammar of his art and ideas. … Continue reading »

Elections – can we do better?

It is highly unlikely that the Electoral College will be abolished anytime soon. A constitutional amendment requires ratification by three-fourths of all states, over half of which have single-digit numbers of electoral votes. Given that most people believe the Electoral College favors small states, these small states will… Continue reading »

Random thoughts on primes

Recently, we saw in the headlines that a new world record has been set for the largest prime (not surprisingly, it’s a Mersenne prime, which means it’s of the form for some n); see here, or for more details, see here. Also, StewJo started a blog… Continue reading »

Dada Math

Math departments are full of smart people.  But with the demands (and joys) of research and teaching (and of our personal lives), most people in math departments do not talk to each other about math nearly enough.  Certainly that is true at Williams.  We do have a fairly… Continue reading »

Guesstimation and Benford’s Law

Nice senior colloquium presentation today (9/22/08) by Richard McDowell ’09 on Benford’s Law. This law explains why, when looking at numbers that come to us from newspapers, stock quotes, and various data sources, the digit 1 appears most often as the leading digit. Benford’s Law derives from… Continue reading »