Mathematical Moments promote an appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. Hear experts talk about how they use mathematics in various applications from improving film animation to analyzing voting strategies.
Explaining Wildfires Through Curvature
Dr. Valentina Wheeler of University of Wollongong, Australia, shares how her work influences efforts to understand wildfires and red blood cells.
In Australia, where bushfires are a concern year-round, researchers have long tried to model these wildfires, hoping to learn information that can help with firefighting policy. Mathematician Valentina Wheeler and colleagues began studying a particularly dangerous phenomenon: When two wildfires meet, they create a new, V-shaped fire whose pointed tip races along to catch up with the two branches of the V, moving faster than either of the fires alone. This is exactly what happens in a mathematical process known as mean curvature flow. Mean curvature flow is a process in which a shape smooths out its boundaries over time. Just as with wildfires, pointed corners and sharp bumps will change the fastest.
Bridges and Wheels, Tricycles and Squares
Dr. Stan Wagon of Macalester College discusses the mathematics behind rolling a square smoothly.
In 1997, inspired by a square wheel exhibit at The Exploratorium museum in San Francsico, Dr. Stan Wagon enlisted his neighbor Loren Kellen in building a square-wheeled tricycle and accompanying catenary track. For years, you could ride the tricycle at Macalester College in St. Paul, Minnesota. The National Museum of Mathematics in New York now also has square-wheeled tricycles that can be ridden around a circular track. And more recently, the impressive Cody Dock Rolling Bridge was built using rolling square mathematics by Thomas Randall-Page in London.
Bringing Photographs to Life
Dr. Rekha Thomas from the University of Washington discusses three-dimensional image reconstructions from two-dimensional photos.
The mathematics of image reconstruction is both simpler and more abstract than it seems. To reconstruct a 3D model based on photographic data, researchers and algorithms must solve a set of polynomial equations. Some solutions to these equations work mathematically, but correspond to an unrealistic scenario — for instance, a camera that took a photo backwards. Additional constraints help ensure this doesn't happen. Researchers are now investigating the mathematical structures underlying image reconstruction, and stumbling over unexpected links with geometry and algebra.
Giving Health Care Policy a Dose of Mathematics
Imelda Flores Vazquez from Econometrica, Inc. explains how economists use mathematics to evaluate the efficacy of health care policies.
When a hospital or government wants to adjust their health policies — for instance, by encouraging more frequent screenings for certain diseases — how do they know whether their program will work or not? If the service has already been implemented elsewhere, researchers can use that data to estimate its effects. But if the idea is brand-new, or has only been used in very different settings, then it's harder to predict how well the new program will work. Luckily, a tool called a microsimulation can help researchers make an educated guess.
Using Math to Support Cancer Research
Stacey Finley from University of Southern California discusses how mathematical models support the research of cancer biology.
Cancer research is a crucial job, but a difficult one. Tumors growing inside the human body are affected by all kinds of factors. These conditions are difficult (if not impossible) to recreate in the lab, and using real patients as subjects can be painful and invasive. Mathematical models give cancer researchers the ability to run experiments virtually, testing the effects of any number of factors on tumor growth and other processes — all with far less money and time than an experiment on human subjects or in the lab would use.
Keeping the Lights On
Rodney Kizito from U.S. Department of Energy discusses solar energy, mathematics, and microgrids.
When you flip a switch to turn on a light, where does that energy come from? In a traditional power grid, electricity is generated at large power plants and then transmitted long distances. But now, individual homes and businesses with solar panels can generate some or all of their own power and even send energy into the rest of the grid. Modifying the grid so that power can flow in both directions depends on mathematics. With linear programming and operations research, engineers design efficient and reliable systems that account for constraints like the electricity demand at each location, the costs of solar installation and distribution, and the energy produced under different weather conditions. Similar mathematics helps create "microgrids" — small, local systems that can operate independent of the main grid.
Great info but poor sound quality
Loved getting info on all sorts of careers in math; however, the sound levels are uneven and often too low. It is hard to hear some parts of it, especially the people being interviewed. It’s frustrating but the information I’m getting is worth it. Looking forward to incorporating this knowledge with my students.
Whenever my students ask why they should pursue a degree in mathematics, I show them this podcast. They quickly learn and enjoy the vast plethora of careers in math.