What’s Happening in the Mathematical Sciences

Dana Mackenzie

In What’s Happening in the Mathematical Sciences, some of the most significant recent advances in mathematics are highlighted. These contain the mathematics underlying newsworthy incidents as well as intriguing mathematical tales that were never published in print media. The world’s first flu pandemic in more than 40 years occurred in 2009, and it served as a test case for a new generation of mathematical models that remove some of the uncertainty from public health choices. Mathematicians worked just as quickly to find solutions to issues like the following: health officials raced to contain the H1N1 flu outbreak: Was the pandemic severe enough to warrant quarantines or school closures? Who should get their shots first, the young or the old? Their findings significantly impacted how the World Health Organization, national governments, and municipal governments responded. Other natural and man-made disasters can also be anticipated with the use of mathematics. Similar to the one that occurred in the Indian Ocean seven years prior, a massive tsunami struck Japan in 2011, bringing to light shortcomings in our knowledge of these catastrophic catastrophes and weaknesses in our early warning systems. Geoscientists and mathematicians are collaborating to increase our capacity for short-term forecasting and estimate the long-term risks of tsunamis. Another team of mathematicians in California, meanwhile, was successful in converting earthquake prediction algorithms to predict criminal activities. Their “predictive policing” program was trialed in Los Angeles and is now being used by other American cities. Thankfully, not all mathematics involves emergencies. In order to make room for new problems, pure mathematicians have started clearing out their problem closets. Two conjectures—the Willmore Conjecture (minimizing energy) and the Lawson Conjecture—about various types of minimizing surfaces were resolved in 2012. (minimizing area). Also, in 2012, topologists demonstrated a number of hypotheses that guarantee that three-dimensional spaces can be built in a uniform manner, building on the remarkable demonstrations of the Poincaré Conjecture and Thurston’s Geometrization Conjecture. In the meantime, over the past ten years, a new approach to comprehending algebraic surfaces and curves has emerged, giving rise to the field of tropical geometry. Several challenging algebraic geometry issues become surprisingly simple with the new concepts, and some string theory “mathematical riddles” make sense. In physics, the nine billion dollar hunt for the elusive Higgs boson was successful in 2012, capturing its prey. This finding offers experimental support for the “Higgs mechanism,” a nearly 50-year-old mathematical theory that explains how some subatomic particles acquire mass. It is one of the most extensively reported science stories of the year. Chapters on topic modeling, a novel statistical method bridging the gap between mathematics and the humanities, and fresh insights into the Rubik’s Cube, a beloved toy of mathematicians (and many other people), round out this volume.