This fall I woke up to a surprise comprehensive exam, with my toddler as the examiner, starting with the demand for a nonconvex regular [simple] polygon. It was 4:30 am. I had not yet had coffee. Everything I Need to Know About Polygons I Learned from My Pre-Kindergartner Courtney GibbonsRead More →
The negative hypergeometric distribution isn’t labeled negative because it uses negative numbers. It’s negative because we’re thinking about failure… The Hypergeometric Flower Pot Ursula Whitcher Mathematical Reviews (AMS) I spent the hottest days of summer engrossed by Balatro, a video game cross between poker and solitaire that’s catnip for probabilityRead More →
Inevitably, I think back to my favorite result in mathematics: when Diaconis used the representation theory of the symmetric group to show us that psychologists just don’t get along… What I Think About When I Think About Voting Sarah Wolff Denison University It’s November. Here in Ohio, that means cozyRead More →
Who might have realized that when the mathematics community studied the properties of cubes, they might be used in error correction technology? Correcting Errors Joe Malkevitch York College (CUNY) Introduction Humans sometimes make errors. Perhaps you have been sloppy with a calculation on a mathematics examination. You made an error.Read More →
Up until recently, all known aperiodic tilings used a minimum of two shapes, and it has long been a major problem to find a tiling that uses just one. Quite recently this problem has been solved, although only with a qualification… Hat Tricks Bill Casselman University of British Columbia “ButRead More →
Decoding, Gerrymanders, and Markov Chains David Austin Grand Valley State University In 2009, crypto miner James Howells of southern Wales mistakenly threw away a hard drive containing 8,000 bitcoins. That’s over $100 million even in today’s sinking crypto landscape. Thirteen years later, Howells has a plan, backed by venture capital,Read More →
What is the $E_8$ lattice that appears in Viazovska's proof? What makes it special? How do you use it to pack spheres? Eight-dimensional spheres and the exceptional $E_8$ Ursula Whitcher Mathematical Reviews (AMS) In Helsinki this summer, Ukrainian mathematician Maryna Viazovska was awarded a Fields Medal "for the proof thatRead More →
Studying supersymmetry in physically realistic situations requires a tremendous amount of physical and mathematical sophistication. We’re going to simplify as much as possible: all the way down to zero spatial dimensions! Designing supersymmetry Ursula Whitcher Mathematical Reviews (AMS) Mathematicians and physicists both love symmetry, but depending on who you’re talkingRead More →
A remarkable theorem involving decompositions is that if one has two plane simple polygons of the same area, it is possible to decompose either of the polygons into polygonal pieces that can be reassembled to form the other polygon… Geometric Decompositions Joe Malkevitch York College (CUNY) Introduction When looking atRead More →
Rook Polynomials: A Straight-Forward Problem For an integer $k$, is it possible to place $k$ rooks on a chess board so that no piece sits on the same row or column as any others? We wouldn’t want them stepping on each others’ toes. Tamsyn Morrill Trine University In the gameRead More →