# What's Happening in the Mathematical Sciences

What's Happening in the Mathematical Sciences is a series of publications that report on the latest mathematical research in a way that both mathematicians and non-mathematicians can appreciate.

Order What's Happening in the Mathematical Sciences, Volume 11 on the AMS Bookstore

### Needles in an Infinite Haystackby Dana Mackenzie

Order What's Happening in the Mathematical Sciences, Volume 10 on the AMS Bookstore

### Origami: Unfolding the Futureby Dana Mackenzie

The ancient Japanese art of paper-folding is going high-tech, as engineers invent new devices that deploy or undeply folding. These inventions lead in turn to challenging mathematical problems about assembly pathways, defects, and curved folds in flat materials.

### Prime Clusters and Gaps: Out-Experting the Expertsby Dana Mackenzie

Mathematics got its real-life Walter Mitty story in 2013, when Yitang Zhang shocked number theorists with the first finite upper bound on the minimum size of prime gaps. One of the oldest problems in number theory, the Twin Prime Conjecture, may now be within reach.

### The Truth Shall Set Your Feeby Barry Cipra

When you pay a stranger, especially online, for help, how can you be sure you're getting honest answers? A new theory in computer science shows how rational self-interest dovetails with the pressing need for trustworthy computation.

### Climate Past, Present, and Futureby Dana Mackenzie

Change is everywhere you look in Earth’s climate, and always has been. Throughout climate science, mathematical models help sort out what did happen (mass extinctions), what is happening (melting ice sheets), and what might happen (tipping points).

### Following in Sherlock Holmes' Bike Tracksby Dana Mackenzie

In a story published in 1905, Sherlock Holmes incorrectly deduced which way a bicycle went, on the basis of its tracks. The subtle relationship between a bike’s front and rear tracks recently helped mathematicians solve another Victorian-era problem on the operation of planimeters.

### Quod Erat Demonstrandumby Barry Cipra

A proof is a kind of mathematical poem—and sometimes an epic one, at that. Two recent proofs, each years in the making, show the lengths to which mathematicians will go in the dogged pursuit of truth, including, these days, enlisting computers to double check their logic.

### The Kadison-Singer Problem: A Fine Balanceby Dana Mackenzie

Great problems come in many disguises. The Kadison-Singer problem, first posed as a problem in theoretical physics, popped up in many other mathematical contexts over more than half a century until it was finally solved in 2013 graph theorists.

### A Pentagonal Search Pays Offby Barry Cipra

Finding shapes that tile the plane isn’t hard to do. Finding all of them is trickier. Mathematicians still don't know how many different convex pentagons are capable of tiling the plane. But the list, long stalled at 14, just inched up, thanks to a new algorithm and a computer search.

### The Brave New World of Sports Analyticsby Dana Mackenzie

In the last few years, professional sports have been swept a new wave of statistical methods, or “analytics.” These methods, coupled with new data sources like video capture, quantify elusive skills and challenge cherished assumptions about in-game strategy.

### Ising on the Cake

A new theorem helps explain why statistical physics has had such a hard time with one of its central problems.

Order What's Happening in the Mathematical Sciences, Volume 4 on the AMS Bookstore

### A Blue-Letter Day for Computer Chess

Deep Blue's victory over Garry Kasparov is the end of a long road in computer chess, but the mathematical study of "perfect" play in combinatorial games has an even longer ways to go.

### Proof by Example: A Mathematician's Mathematician

Paul Erdős, the "Johnny Appleseed" of mathematics, inspired hundreds of colleagues and left a rich legacy of mathematical problems--and solutions.

### Computers Take Algebraic Geometry Back to Its Roots

Computer power has brought algorithmic questions in algebraic geometry back to the fore.

### As Easy as EQP

An automated theorem prover succeeeds in settling a decades-old conjecture in symbolic logic. What's left for human minds to do?

### Beetlemania: Chaos in Ecology

A collaboration between mathematicians and biologists has led to the first experimental evidence for chaotic dynamics in a population.

### From Wired to Weird

Mathematical discoveries are shaping research in a potentially revolutionary kind of computing, based on principles of quantum mechanics.

### Tales from the Cryptosystem

A breakthrough in the theory of computational complexity has implications for cryptographic systems with "guaranteed" security.

### But Is It Math?

Mathematics and art have more in commmon than is commonly supposed. Two twentieth-century artists, M. C. Escher and Marcel Duchamp, used mathematics as an inspiration for works of art.

### Mathematical Discovery (by Henri Poincaré)

Henri Poincaré's thoughts on thinking, written near the beginning of the twentieth century, are well worth repeating at century's end.

Order What's Happening in the Mathematical Sciences, Volume 3 on the AMS Bookstore

### Fermat's Theorem--At Last!

Andrew Wiles has completed the astonishing tour de force that resolves the most famous problem in mathematics. His proof is the realization of a boyhood dream.

### A Tale of Two Theories

A breakthrough in theoretical physics has simplified a notoriously difficult theory in 4-dimensional geometry, and given mathematicians a lot to think about.

### Computer Science Discovers DNA

Will computers of the future be bio-engineered? It's a possibility.

### The Gentle Art of Control

Modern technology relies on mathematical control theory to keep things on an even keel. How do the equations know what to do?

### Computational Fluid Dynamics--Verging on Turbulence

Mathematical techniques, faster computers, and better algorithms are gaining ground in the study of complex fluid flows. For some researchers, computtational turbulence is literally a pipe dream.

### Cellular Automata Offer New Look on Life, the Universe, and Everything

The continuously increasing power of computers has enabled researchers to take a discrete look at the world. Theorists seek to explain the complex patterns that are often seen.

### Are Group Theorists Simple-Minded?

Researchers are working hard to simplify one of the most complicated proofs in mathematical history--the classification of simple groups.

### The Secret Life of Large Numbers

A computational challenge in number theory has been met, considerably sooner than the 20,000 years it was expected to take.

### In Math We Trust

A theorem about multivariate integration may find a home on Wall Street. You could call it a get-rich-quick scheme.

### "A Truly Remarkable Proof"

The announcement last year of a proof of Fermat's Last Theorem stunned the mathematical world. Andrew Wiles's proof, though currently incomplete, has nonetheless drawn rave reviews.

### From Knot to Unknot

What's the quickest way to untie a knot? Researchers have untangled a good part of the answer.

### New Wave Mathematics

Will compact waves cruise the information superhighways of the future? In theory, it's possible.

### Mathematical Insights for Medical Imaging

A team of mathematicians, computer scientists, and engineers has designed a new medical imaging technology based on the safe application of electric current

### Parlez-vous Wavelets?

Mathematicians and scientists are rapidly learning to speak a new language. The results are making a big splash.

### Random Algorithms Leave Little to Chance

Computer scientists will do anything to avoid bottlenecks and speed up computations. But gamble on the results? You bet!

### Soap Solution

Undergraduate students at a summer mathematics research program have found some slick answers to some old problems about the geometry of soap bubbles.

### Straightening Out Nonlinear Codes

A complicated class of error-correcting codes has suddenly gotten much easier to use.

### Quite easily Done

A combinatorial problem, long thought to be difficult, has finally been solved--with surprising ease.

### (Vector) Field of Dreams

A clever construction "pulls the plug" on a 40-year old conjecture about the topology of vector fields.

Unfortunately, Volume 2 is no longer available.

### Equations Come to Life in Mathematical Biology

Mathematicians are working with biologists to delve into some of the most challenging problems in biology today, from understanding the human immune system to "computing" the human heart.

### New Computer Insights from "Transparent" Proofs

Can a computer be trusted when it produces a proof so long and complicated that no human can check the details? Theorists have cooked up a new way to tell whether or not a computer proof is right.

### You Can't Always Hear the Shape of a Drum

Can you hear the shape of a drum? is a famous problem that asks if two drums that look different can make the same sound. After decades of head-scratching, mathematicians have come up with the answer.

### Environmentally Sound Mathematics

Mathematicians have been teaming up with scientists to work on solving environmental problems, from ocean modeling to dealing with hazardous waste.

### Disproving the Obvious in Higher Dimensions

Intuition about our three-dimensional world can be surprisingly misleading when it comes to higher dimensions, as two recent results in geometry show.

### Collaboration Closes in on Closed Geodesics

An unusual blend of differential geometry and dynamical systems has led to an important theoretical result about the number of closed "geodesic" curves on distorted spheres.

### Crystal Clear Computations

Growing crystals--on a computer? Mathematicians are helping materials scientists to better understand the nature of crystals, while picking up some challenging mathematical problems along the way.

### Camp Geometry

A group of talented and inquisitive undergraduates "camped out" last summer at the Geometry Center. Using sophisticated computer graphics and their own imaginations, they came up with some fascinating mathematics.

### Number Theorists Uncover a Slew of Prime Imposters

Strange as it may sound, there are composite numbers that "masquerade" as primes. A group of mathematicians trying to hunt down these prime imposters ended up proving there are infinitely many of them.

### Map-Coloring Theorists Look at New Worlds

How many colors are needed to distinguish neighboring colors on a map? The famous Four Color Theorem notwithstanding, this is a challenging problem in graph theory--especially when your maps aren't flat.

Unfortunately, Volume 1 is no longer available.