Last Thursday, a pair of mathematicians launched a new podcast.
On "My Favorite Theorem," hosts Kevin Knudson and Evelyn Lamb talk to a guest about a personally compelling result. In the course of less than 25 minutes' conversation, they often touch upon that theorem's historical context, related work, the guest's own career path, and other personal connections and anecdotes.
At the end of every segment, guests take their favorite theorems and pair them with something -- which Lamb has suggested might take the form of "the perfect wine, or ice cream, or work of 19th century German romanticism."
The first few podcasts have paired--
- the Ham Sandwich Theorem with a pale ale; - the Uniformization Theorem with Neapolitan ice cream; - the Fundamental Theorem of Calculus with "something like a mango"; and - the Circle Area Theorem with pizza.
For transcripts, follow the parenthetical "click to expand" prompts below a given episode from Knudson's archive:
Robin Whitty has added over 150 theorems, lemmas, laws, formulas, and identities to his gallery since it last appeared in these pages.
Referring to them as math's "crowning achievements," Whitty has distilled each result so as to "be appreciated by as wide an audience as possible." All of his one-page PDFs feature a diagram or some other instructional illustration; nearly 50 accommodate sketches of proofs, as indicated by the green "QED"s in the main theorem listing.
In addition to complete alphabetical and chronological listings, theoremoftheday.org organizes theorems by subject and mathematician (or statistician, physicist, economist, composer, or computer program). See, in particular, the list of theorems proven by women:
What do you get when you unleash teenagers on a programming language packed with knowledge -- about algorithms and about the world?
The software company behind Wolfram|Alpha wrapped up its sixth residential program for high schoolers a month ago. Students came to Wolfram Summer Camp from a wide range of schools. They arrived with diverse programming backgrounds, as well; founder Stephen Wolfram blogged on Wednesday that "quite a few had never really done anything computational before -- even though they were often quite advanced in various STEM areas such as math."
Sparked by twelve days of math lectures and programming classes, teens went on to code such projects as--
- Teaching Algebra by Generating Hints from Wrong Answers; - Finding Spikes in Electrophysiological Data from Neurons; - Using Voronoi Diagrams to Optimize Offensive Schemes; and - Fully Functional ParametricPlot4D: Curves, Surfaces, and Volumes.
Beyond sharing their thinking and Mathematica notebook files with the Wolfram community, some campers took to the Wolfram Cloud, where they posted simple interactive microsites, including--