Alan Turing and the Countability of Computable Numbers Turing’s methodology was unique: he imagined hypothetical machines that could perform complicated mathematical tasks in a deterministic manner, in the way computers do today. In this way, he inadvertently kickstarted the entire field of modern computer science… Adam A. Smith University ofRead More →

Decomposition Mathematics too has profited from the idea that sometimes things of interest might have a structure which allowed them to be decomposed into simpler parts… Joe Malkevitch York College (CUNY) Introduction One way to get insights into something one is trying to understand better is to break the thingRead More →

Meet me up in space! Rather than closing the distance, however, the target seemed to move down and away in defiance of everyday intuition… David Austin Grand Valley State University Complex space missions rely on the ability to bring two spacecraft together, a procedure called orbital rendezvous. A spacecraft dockingRead More →

Principal Component Analysis: Three Examples and some Theory Very often, especially in applications to the life sciences, useful low-dimensional projections exist and allow humans to grasp a data set that would otherwise be inscrutable. Tony Phillips Stony Brook University Introduction Principal component analysis (PCA), an algorithm for helping us understandRead More →

The Battle of Numbers Our topic is the game called rithmomachia or rithmomachy—literally, the battle of numbers… Ursula Whitcher AMS | Mathematical Reviews, Ann Arbor, Michigan This month, we’re going to explore a very old—indeed, medieval—educational game and correct a mathematical error in a sixteenth-century game manual. But before weRead More →

The Once and Future Feature Column We’re going to look back at the Column’s history, revisit some of our favorite columns, and talk about what comes next. Spoiler alert: We’re recruiting new columnists! Ursula Whitcher AMS | Mathematical Reviews, Ann Arbor, Michigan The number 24 has many charming properties. ForRead More →

An epidemic is a sequence of random events If a contact is made, then whether or not infection is transferred is much like tossing a (loaded) coin. How can a simulation take all this uncertainty into account? Bill Casselman University of British Columbia Just recently, I started thinking about makingRead More →

In Praise of Collaboration Take a look at an extraordinary collaboration in discrete geometry and related geometrical mathematics, the collaboration of Branko Grünbaum and Geoffrey Colin Shephard. Joe Malkevitch York College (CUNY) Introduction Point and line do many activities together—their collaborations create a rich texture for many mathematicians and geometers,Read More →

Lost (and found) in space There are standard references, such as the Sloan Digital Sky Survey, that provide an atlas for the stars. What’s needed is a way to search through this enormous atlas to find the view presented by a given image. David Austin Grand Valley State University MyRead More →