Volume: 12; 2022; 126 pp; Softcover
Print ISBN: 978-1-4704-6498-1
Product Code: HAPPENING/12
List Price: $25.00
AMS Member Price: $20.00
MAA Member Price: $22.50
What’s Happening in the Mathematical Sciences, Volume 12
Share this pageDana Mackenzie
As always, What's Happening in the Mathematical Sciences
presents a selection of topics in mathematics that have attracted
particular attention in recent years. This volume is dominated by an
event that shook the world in 2020 and 2021, the coronavirus (or
COVID-19) pandemic. While the world turned to politicians and
physicians for guidance, mathematicians played a key role in the
background, forecasting the epidemic and providing rational frameworks
for making decisions. The first three chapters of this book highlight
several of their contributions, ranging from advising governors and
city councils to predicting the effect of vaccines to identifying
possibly dangerous “escape variants” that could re-infect
people who already had the disease.
In recent years, scientists have sounded louder and louder alarms
about another global threat: climate change. Climatologists predict
that the frequency of hurricanes and waves of extreme heat will
change. But to even define an “extreme” or a
“change,” let alone to predict the direction of change, is
not a climate problem: it's a math problem. Mathematicians have been
developing new techniques, and reviving old ones, to help climate
modelers make such assessments.
In a more light-hearted vein, “Descartes' Homework”
describes how a famous mathematician's blunder led to the discovery of
new properties of foam-like structures called Apollonian
packings. “Square Pegs and Squiggly Holes” shows that
square pegs fit virtually any kind of hole, not just circular
ones. “Much Ado About Zero” explains how difficult
problems about eigenvalues of matrices can sometimes be answered by
playing a simple game that involves coloring dots on a grid or a
graph.
Finally, “Dancing on the Edge of the Impossible”
provides a progress report on one of the oldest and still most
important challenges in number theory: to devise an effective
algorithm for finding all of the rational-number points on an
algebraic curve. In the great majority of cases, number theorists know
that the number of solutions is finite, yet they cannot tell when they
have found the last one. However, two recently proposed methods show
potential for breaking the impasse.
Readership
Undergraduate and graduate students interested in expository accounts of recent developments in mathematics.