Mathematical Moments from the American Mathematical Society

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea i...

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea i...

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea i...

The spools of wire below contain the only known live recording of the legendary folk singer Woody Guthrie. A mathematician, Kevin Short, was part of a team that used signal processing techniques associated with chaotic music compression to recapture the live performance, which was often completely unintelligible. The modern techniques employed, instead of resulting in a cold, digital output, actua...

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea i...

The colored "strings" you see represent air flow around the soccer ball, with the dark blue streams behind the ball signifying a low-pressure wake. Computational fluid dynamics and wind tunnel experiments have shown that there is a transition point between smooth and turbulent flow at around 30 mph, which can dramatically change the path of a kick approaching the net as its speed decreases through...

Invisibility is no longer confined to fiction. In a recent experiment, microwaves were bent around a cylinder and returned to their original trajectories, rendering the cylinder almost invisible at those wavelengths. This doesn't mean that we're ready for invisible humans (or spaceships), but by using Maxwell's equations, which are partial differential equations fundamental to electromagnetics, ma...

Votes are cast by the full membership in each house of Congress, but much of the important maneuvering occurs in committees. Graph theory and linear algebra are two mathematics subjects that have revealed a level of organization in Congress groups of committees above the known levels of subcommittees and committees. The result is based on strong connections between certain committees that can be d...

Origami paper-folding may not seem like a subject for mathematical investigation or one with sophisticated applications, yet anyone who has tried to fold a road map or wrap a present knows that origami is no trivial matter. Mathematicians, computer scientists, and engineers have recently discovered that this centuries-old subject can be used to solve many modern problems. The methods of origami ar...

The outcome of elections that offer more than two alternatives but with no preference by a majority, is determined more by the voting procedure used than by the votes themselves. Mathematicians have shown that in such elections, illogical results are more likely than not. For example, the majority of this group want to go to a warm place, but the South Pole is the group.s plurality winner. So if t...

Mathematics is not just numbers and brute force calculation there is considerable art and elegance to the subject. So it is natural that mathematics is now being used to analyze artists. styles and to help determine the identities of the creators of disputed works. Attempts at measuring style began with literature based on statistics of word use and have successfully identified disputed works such...

Storm surge is often the most devastating part of a hurricane. Mathematical models used to predict surge must incorporate the effects of winds, atmospheric pressure, tides, waves and river flows, as well as the geometry and topography of the coastal ocean and the adjacent floodplain. Equations from fluid dynamics describe the movement of water, but most often such huge systems of equations need to...

Mathematics and music have long been closely associated. Now a recent mathematical breakthrough uses topology (a generalization of geometry) to represent musical chords as points in a space called an orbifold, which twists and folds back on itself much like a Mobius strip does. This representation makes sense musically in that sounds that are far apart in one sense yet similar in another, such as...

Actually, they weren.t caught together at all their images were put together with software. The shadows cast by the stars. faces give it away: The sun is coming from two different directions on the same beach! More elaborate digital doctoring is detected with mathematics. Calculus, linear algebra, and statistics are especially useful in determining when a portion of one image has been copied to an...

Detection and treatment of cancer have progressed, but neither is as precise as doctors would like. For example, tumors can change shape or location between pre-operative diagnosis and treatment so that radiation is aimed at a target which may have moved. Geometry, partial differential equations, and integer linear programming are three areas of mathematics used to process data in real-time, which...

Many movie animation techniques are based on mathematics. Characters, background, and motion are all created using software that combines pixels into geometric shapes which are stored and manipulated using the mathematics of computer graphics. Software encodes features that are important to the eye, like position, motion, color, and texture, into each pixel. The software uses vectors, matrices, an...