Mathmoments
The American Mathematical Society's Mathematical Moments program promotes appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. Listen to researchers talk about how they use math, from creating realistic animation to beating cancer.

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. 
Driving Up Air Pollution
Karen Rios Soto explains how mathematics illuminates the link between air pollution from motor vehicle emissions and asthma. Air pollution causes the premature deaths of an estimated seven million people each year, and it makes life worse for all of us. People with asthma can experience chest tightness, coughing or wheezing, and difficulty breathing when triggered by air pollution. One major source is gas and dieselpowered cars and trucks, which emit "ultrafine" particles less than 0.1 micrometers across. That's about the width of the virus that causes COVID19, so tiny that these particles are not currently regulated by the US Environmental Protection Agency. Yet ultrafine particles can easily enter your lungs and be absorbed into your bloodstream, causing health issues such as an asthma attack or even neurodegenerative diseases. Mathematics can help us understand the extent of the problem and how to solve it. 
Deblurring Images
Malena Espanol explains how she and others use linear algebra to correct blurry images. Imagine snapping a quick picture of a flying bird. The image is likely to come out blurry. But thanks to mathematics, you might be able to use software to improve the photo. Scientists often deal with blurry pictures, too. Linear algebra and clever numerical methods allow researchers to fix imperfect photos in medical imaging, astronomy, and more. In a computer, the pixels that make up an image can be represented as a column of numbers called a vector. Blurring happens when the light meant for each pixel spills into the adjacent pixels, changing the numbers in a way that can be mathematically represented as an enormous matrix. But knowing that matrix is not enough if you want to reconstruct the original (nonblurry) image. 
Exploring Thermodynamics with Billiards
Tim Chumley explains the connections between random billiards and the science of heat and energy transfer. If you've ever played billiards or pool, you've used your intuition and some mental geometry to plan your shots. Mathematicians have gone a step further, using these games as inspiration for new mathematical problems. Starting from the simple theoretical setup of a single ball bouncing around in an enclosed region, the possibilities are endless. For instance, if the region is shaped like a stadium (a rectangle with semicircles on opposite sides), and several balls start moving with nearly the same velocity and position, their paths in the region soon differ wildly: chaos. Mathematical billiards even have connections to thermodynamics, the branch of physics dealing with heat, temperature, and energy transfer.