Mathematical Moments from the American Mathematical Society

Mathematical Moments from the American Mathematical Society

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.

Episodes

Using Math to Support Cancer Research

August 25, 2025 • 10 mins
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 cance...
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Tapering AI Limits with Mathematcial Formalization

December 3, 2024 • 15 mins
Dr. Alex Best, of Harmonic discusses AI's struggles with technical and ethical limitations like uninterpretable methods and a lack of diverse datasets make facial recognition and medical software dangerously biased. If algorithms output answers without little explanation, how can one trust those results? Interpretability is a prerequisite to replace the work of human researchers. But using AI for formalizing mathematics offers some...
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Unlocking the Secrets of AI

December 3, 2024 • 12 mins
Dr. Kristen Lauter, director of FAIR (Fundamental AI Research) Labs, Meta, North America, discusses how cryptographers are using AI. Online, private information is secured using difficult-to-solve math problems. Researchers must test those problems thoroughly to be sure they are truly difficult - if hackers can solve the problem, they'll have access to your information.
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Modernizing Math with Artificial Intelligence

October 24, 2024 • 12 mins
Dr. Po-Shen Loh of Carnegie Mellon University, discusses how AI is changing the landscape of mathematics and looks ahead at what might come. As algorithms have matured, mathematicians have embraced computation as means to accelerate math discoveries. Researchers integrate AI with "proof checking" tools, like the software Lean, to avoid errors more quickly. According to Loh, this makes it easier for large teams to collaborate...
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Smashing Particles up Against Mathematics

March 8, 2024 • 9 mins
Dr. Abiy Tasissa of Tufts University, discusses the mathematics he and colleagues used to study particle collider data, including optimal transport and optimization. Collider physics often result in distributions referred to as jets. Dr. Tasissa and his team used "Earth Mover's Distance" and other mathematical tools to study the shape of jets. "It is interesting for me to see how mathematics can be applied to study these f...
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Supporting Wildlife with Statistics

February 16, 2024 • 9 mins
Dr. Outi Tervo of Greenland Institute for Natural Resources, shares how mathematics helps recommend speed limits for marine vessels, which benefits narwhals and Inuit culture. Narwhals "can only be found in the Arctic," said Outi Tervo, a senior scientist at GINR. "These species are going to be threatened by climate change more than other species that can live in a bigger geographical area." The collaboration has already lo...
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Explaining Wildfires Through Curvature

October 17, 2023 • 11 mins
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...
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Bridges and Wheels, Tricycles and Squares

October 13, 2023 • 11 mins
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 Mathematic...
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Bringing Photographs to Life

July 13, 2023 • 11 mins
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 unrealis...
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Giving Health Care Policy a Dose of Mathematics

April 5, 2023 • 11 mins
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...
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Keeping the Lights On

November 15, 2022 • 14 mins
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 o...
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Driving Up Air Pollution

June 28, 2022 • 12 mins
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 diesel-powere...
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Deblurring Images

May 19, 2022 • 10 mins
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,...
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Exploring Thermodynamics with Billiards

February 14, 2022 • 13 mins
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...
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Pinpointing How Genes Interact

October 21, 2021 • 14 mins
Lorin Crawford explains how he uses math to analyze interactions between genes. Your DNA (the biological instruction manual in all of your cells) contains a mind-boggling amount of information represented in roughly 20,000 genes that encode proteins, plus a similar number of genes with other functions. As the cost of analyzing an individual's DNA has plummeted, it has become possible to search the entire human genome for ge...
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Securing Data in the Quantum Era

September 1, 2021 • 13 mins
Angela Robinson explains the math behind the next generation of cryptographic algorithms. Whenever you log in to a website, send an email, or make an online purchase, you're counting on your data being sent securely, without hackers being able to crack the code. Our standard cryptographic systems hinge on mathematical problems that stump present-day computers, like finding the prime factors of a very large number. But in th...
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Taking the "Temperature" of Languages

July 6, 2021 • 17 mins
Ricardo Bermudez-Otero and Tobias Galla discuss the mathematics describing the evolution of human languages. The sounds and structures of the world's approximately 7,000 languages never stop changing. Just compare the English in Romeo and Juliet or the Spanish in Don Quixote to the modern forms. But historical records give an incomplete view of language evolution. Increasingly, linguists draw upon mathematical models to fig...
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Doing the Math

May 24, 2021 • 11 mins
Math may sometimes seem as if it's comprised of countless meaningless unconnected exercises, but in reality, it's much more. It's figuring out how to do something, and, even better, why something works the way it does. The math you're doing now can open doors for you so that you can answer deep questions yourself about a subject or idea that you're interested in. Give those questions a shot and perhaps someday also help others solv...
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Making Room for Patients

April 26, 2021 • 15 mins
We've seen that the availability of hospital beds is important during a pandemic, and it's important during normal times as well. Whether it's for emergency medical help or for a scheduled procedure (for example, chemotherapy), access to hospital space, staff, and equipment can be a matter of life and death. Mathematics helps medical center staff manage their resources more efficiently so that they are available when needed. An opt...
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Fighting Fires

March 22, 2021 • 18 mins
In many places, fire seasons keep getting longer with larger and ever more destructive wildfires. Teams of mathematicians, computer scientists, meteorologists, and firefighters are working to reduce the number of large fires before they happen and to contain those that do occur. Mark Finney talks about the math involved in modeling and fighting wildfires.
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