A Classic Math Joke
For those of you starting to enjoy my short videos, I thought I would squander all that good will by recording a classic math joke. (link)
Let A be a Pedant and Let B be a Pedant
One of my favorite mathematical anecdotes is the following story that Gian-Carlo Rota told about Solomon Lefschetz: He [Solomon Lefschetz] liked to repeat, as an example of mathematical pedantry, the story of one of E. H. Moore’s visits to Princeton, when Moore started a lecture by saying, “Let a be […]
Imputing Out of Mixtures, or Un-Stirring Spicy Soup
Here is a fun combinatorial puzzle. I’ve probably seen this used to teach before, but let’s try to define or work this one from memory. I would love to hear more solutions/analyses of this problem. Suppose you have n kettles of soup labeled 0 through n-1. For our problem we […]
A Beautiful 2 by 2 Matrix Identity
While working on a variation of the RcppDynProg algorithm we derived the following beautiful identity of 2 by 2 real matrices: The superscript “top” denoting the transpose operation, the ||.||^2_2 denoting sum of squares norm, and the single |.| denoting determinant. This is derived from one of the check equations […]
Proof style in the Erdős-Ko-Rado theorem
I recently wrote a tiny bit about the style of the original published proof of the Erdős-Ko-Rado theorem. In this note I’ll write a bit about the theorem and a bit more about the style of some later proofs. In particular I want to write about two different readings of […]
Erdős writing like a programmer
Here is a neat example of famous mathematician Pál Erdős (often rendered in English as Paul Erdős) writing like a programmer in 1961. He goes to some trouble to introduce notation that allows him to index everything from zero.
The Mathematician’s Dilemma
A recent run of too many articles on the same topic (exhibits: A, B and C) puts me in a position where I feel the need to explain my motivation. Which itself becomes yet another article related to the original topic. The explanation I offer is: this is the way […]