Short works

Books : reviews

Barry A. Cipra.
What's Happenining in the Mathematical Sciences 5.
AMS. 2002

Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What’s Happening series contradicts that view by showing that mathematics is indeed found everywhere—in science, art, history, and our everyday lives.

Here is some of what you’ll find in this volume:

Mathematical biology: Mathematics was key to cracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code.

Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology’s most fundamental questions: What is the size and shape of the universe?

Traffic jams: New models are helping researchers understand where traffic jams come from—and maybe what to do about them!

Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks.

Beyond Fermat’s Last Theorem: Number theorists are reaching higher ground after Wiles’ astounding 1994 proof: new developments in the elegant world of elliptic curves and modular functions.

The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems.

These are just some of the topics of current interest that are covered in this latest volume of What’s Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.

Dana Mackenzie, Barry A. Cipra.
What's Happenining in the Mathematical Sciences 10.
AMS. 2015

What’s Happening in the Mathematical Sciences is a collection of articles highlighting some of the most recent developments in mathematics. These include important achievements in pure mathematics, as well as its fascinating applications.

On the pure mathematics side, “Prime Clusters and Gaps: Out-Experting the Experts” talks about new insights into the distribution of prime numbers, the perpetual source of new problems, and new results. Recently, several mathematicians (including Yitang Zhang and James Maynard) significantly improved our knowledge of the distribution of prime numbers. Advances in the so-called Kadison-Singer problem and its applications in signal processing algorithms used to analyze and synthesize signals are described in “The Kadison-Singer Problem: A Fine Balance”. “Quod Erat Demonstrandum” presents two examples of perseverance in mathematicians’ pursuit of truth using, in particular, computers to verify their arguments. And “Following in Sherlock Holmes’ Bike Tracks” shows how an episode in one of Sir Arthur Conan Doyle’s stories about Sherlock Holmes naturally led to very interesting problems and results in the theory of completely integrable systems.

On the applied side, “Climate Past, Present, and Future” shows the importance of mathematics in the study of climate change and global warming phenomena. Mathematical models help researchers to understand the past, present, and future changes of climate, and to analyze their consequences. “The Truth Shall Set Your Fee” talks about algorithms of information exchange in cyberspace. Economists have known for a long time that trust is a cornerstone of commerce, and this becomes even more important nowadays when a lot of transactions, big and small, are done over the Internet. Recent efforts of theoretical computer scientists led to the development of so-called “rational protocols” for information exchange, where the parties in the information exchange process find that lies do not pay off.

Over the last 100 years many professional mathematicians and devoted amateurs contributed to the problem of finding polygons that can tile the plane, e.g., used as floor tiles in large rooms and walls. Despite all of these efforts, the search is not yet complete, as the very recent discovery of a new plane-tiling pentagon shows in “A Pentagonal Search Pays Off”. Mathematics can benefit coaches and players in some of the most popular team sports as shown in “The Brave New World of Sports Analytics”. The increased ability to collect and process statistics, big data, or “analytics” has completely changed the world of sports analytics. The use of modern methods of statistical modeling allows coaches and players to create much more detailed game plans as well as create many new ways of measuring a player’s value. Finally, “Origami: Unfolding the Future” talks about the ancient Japanese paper-folding art and origami’s unexpected connections to a variety of areas including mathematics, technology, and education.