I found this fantastic quote by the artist Chuck Close. It was his advice for young artists. However, I think that if you replace artist by researcher,* the same advice applies. I would certainly pass this advice along to young mathematicians: just start working, the ideas will come. Conversely, if you don’t put in the…
Category: Math
Music is math: ten songs about mathematics
Just for fun, here are ten songs about mathematics. Am I missing any good ones? Post them in the comments. 1. Finite Simple Group (of Order 2) by the Klein Four Group (lyrics). This excellent song was written and performed by graduate students at Northwestern University, where I did my graduate work. I think it…
Irving Kaplansky’s “A Song about Pi”
Perhaps I should wait until mid-March to post this, but oh, well. Irving “Kap” Kaplansky (1917–2006), the mathematician and former head of MSRI, was also a pianist and songwriter. In 1973 he brought all of these interests together to pen a song called “A Song about Pi.” The tune is was inspired by the digits of…
Beautiful theorems about dynamical systems on the plane
I was reading through some papers written by my Ph.D. advisor (John Franks) from the early 1990’s and was reminded of a few beautiful results about the dynamics of planar homeomorphisms. So I thought I’d share them here. For those of you who are not familiar with the terminology, a planar homeomorphism is a bijective…
Three geometric theorems
Just for fun I thought I’d share a few interesting geometric theorems that I came across recently. Morley’s miracle In 1899 Frank Morley, a professor at Haverford, discovered the following remarkable theorem. The three points of intersection of the adjacent trisectors of the angles of any triangle form an equilateral triangle. I’ve made a Geogebra…
Google Translate now knows Latin
Yesterday Bruce Petrie (a graduate student studying the history of mathematics) and I were discussing Google Translate. While it is no substitute for a human translator, it is pretty good and getting better. In particular, it is perfect if you need a quick, approximate translation of a language that you do no know or don’t…
An amazing paragraph from Euler’s Introductio
Today I’d like to share an amazing paragraph from Euler’s 1748 textbook Introductio in analysin infinitorum (Introduction to analysis of the infinite). This two–volume book is what Carl Boyer calls “The foremost textbook of modern times,” edging out, for example, Descartes’s Géométrie, Gauss’ Disquisitiones, and Newton’s Principia. Boyer writes that “Euler accomplished for analysis what Euclid…
Odds and ends: the genius of Euler, Bulgarian solitaire, and mathematical surprises
Yesterday I attended the first-ever (as far as we know) joint meeting of the EPaDel (Eastern Pennsylvania and Delaware) and New Jersey sections of the MAA. It was held at LaSalle University. I was very happy to see so many familiar faces and to make some new friends. I thought I’d share a few fun…
Top ten transcendental numbers
Everyone loves a top ten list, and what’s better than a top ten list about numbers? (I’m reminded of David Letterman’s top ten numbers between one and ten from September 22, 1989.) So, on the heels of my previous posts about algebraic and transcendental numbers (here and here), here’s my list of the… Top Ten…
Trigonometric functions and rational multiples of pi
Recall that a real number is algebraic if it is the root of a polynomial with integer coefficients and that it is transcendental otherwise. For example is algebraic because it is a root of the polynomial , but is transcendental because it is not the root of any such equation. (On a recent blog post…
David Richeson: Division by Zero 