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.

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.

Bringing Photographs to Life

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.

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.

Giving Health Care Policy a Dose of Mathematics

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.

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.

Using Math to Support Cancer Research

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.

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.

Keeping the Lights On

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-powered cars and trucks, which emit "ultrafine" particles less than 0.1 micrometers across. That's about the width of the virus that causes COVID-19, 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.

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-powered cars and trucks, which emit "ultrafine" particles less than 0.1 micrometers across. That's about the width of the virus that causes COVID-19, 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.

Driving Up Air Pollution

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 (non-blurry) image.

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 (non-blurry) image.

Deblurring Images

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.

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.

Exploring Thermodynamics with Billiards

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 genetic variants that are associated with traits such as height or susceptibility to certain diseases. Sometimes, one gene has a straightforward impact on the trait. But in many cases, the effect of one gene variant depends on which variants of other genes are present, a phenomenon called "epistasis." Studying such interactions involves huge datasets encompassing the DNA of hundreds of thousands of people. Mathematically, that requires time-intensive calculations with massive matrices and a good working knowledge of statistics.

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 genetic variants that are associated with traits such as height or susceptibility to certain diseases. Sometimes, one gene has a straightforward impact on the trait. But in many cases, the effect of one gene variant depends on which variants of other genes are present, a phenomenon called "epistasis." Studying such interactions involves huge datasets encompassing the DNA of hundreds of thousands of people. Mathematically, that requires time-intensive calculations with massive matrices and a good working knowledge of statistics.

Pinpointing How Genes Interact

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 the coming decades, powerful quantum computers are expected to be able to rapidly solve some such problems, threatening the security of our online communications. To develop new methods that can withstand even the most sophisticated quantum computer, cryptographers are using a wide range of mathematical tools, many of which were originally developed without any real-life applications in mind.

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 the coming decades, powerful quantum computers are expected to be able to rapidly solve some such problems, threatening the security of our online communications. To develop new methods that can withstand even the most sophisticated quantum computer, cryptographers are using a wide range of mathematical tools, many of which were originally developed without any real-life applications in mind.

Securing Data in the Quantum Era

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 figure out which features of a language change often and which ones change more rarely over the course of thousands of years. A new model inspired by physics assigns a "temperature" to many sounds and grammatical structures. Features with higher temperatures are less stable, so they change more often as time goes on. The linguistic thermometer will help researchers reconstruct how our languages came to be, and how they might change in future generations.

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 figure out which features of a language change often and which ones change more rarely over the course of thousands of years. A new model inspired by physics assigns a "temperature" to many sounds and grammatical structures. Features with higher temperatures are less stable, so they change more often as time goes on. The linguistic thermometer will help researchers reconstruct how our languages came to be, and how they might change in future generations.

Taking the "Temperature" of Languages

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.

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.

Great info but poor sound quality

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.

Great

Mathematical Moments from the American Mathematical Society

Muthu Alagappan explains how topology and analytics are bringing a new look to basketball.

Thinking Outside the Box Score - Math and basketball: Part 1

Researcher: Cristina Stoica, Wilfrid Laurier University  Description: Cristina Stoica talks about celestial mechanics.

Researcher: Cristina Stoica, Wilfrid Laurier University Description: Cristina Stoica talks about celestial mechanics.

Working With the System: Part 1

Researcher: Daniel Rothman, MIT. Dan Rothman talks about how math helped understand a mass extinction.

Maintaining a Balance Part 2

Tom Patterson and Bojan Savric discuss the Equal Earth projection map that they created with Bernhard Jenny.

Making the Earth Flat

Edward Witten talks about math and physics.

Going Back to the Beginning - The Big Bang

Being Knotty: Part 1

Researcher: Meredith Greer, Bates College. Going Over the Top Description: Meredith Greer talks about math and roller coasters.

Going Over the Top - Designing roller coasters

Researcher: Michael C. Ferris, University of Wisconsin-Madison.  Moment Title: Providing Power Description: Michael C. Ferris talks about power grids

Providing Power

Researcher: Michel C. Molinkovitch, University of GenevaDescription: Michel C. Milinkovitch used math, physics, and biology for an amazing discovery about the patterns on a lizard's skin.

Researcher: Michel C. Molinkovitch, University of Geneva Description: Michel C. Milinkovitch used math, physics, and biology for an amazing discovery about the patterns on a lizard's skin.

Generating Patterns Part 2

Lydia Bourouiba talks about surface tension and the transmission of disease

Exploiting a Little-Known Force: Part 2

Researcher: Jordan Hashemi, Duke UniversityDescription: Jordan Hashemi talks about an easy-to-use app to screen for autism.

Researcher: Jordan Hashemi, Duke University Description: Jordan Hashemi talks about an easy-to-use app to screen for autism.

Screening for Autism

No one can predict who will commit a crime but in some cities math is helping detect areas where crimes have the greatest chance of occurring. Police then increase patrols in these "hot spots" in order to prevent crime. This innovative practice, called predictive policing, is based on large amounts of data collected from previous crimes, but it involves more than just maps and push pins. Predictive policing identifies hot spots by using algorithms similar to those used to predict aftershocks after major earthquakes. Just as aftershocks are more likely near a recent earthquake.s epicenter, so too are crimes, as criminals do indeed return to, or very close to, the scene of a crime.Cities employing this approach have seen crime rates drop and studies are underway to measure predictive policing.s part in that drop. One fact that has been determined concerns the nature of hot spots. Researchers using partial differential equations and bifurcation theory have discovered two types of hot spots, which respond quite differently to increased patrols. One type will shift to another area of the city while the other will disappear entirely. Unfortunately the two appear the same on the surface, so mathematicians and others are working to help police find ways to differentiate between the two so as to best allocate their resources.

No one can predict who will commit a crime but in some cities math is helping detect areas where crimes have the greatest chance of occurring. Police then increase patrols in these "hot spots" in order to prevent crime. This innovative practice, called predictive policing, is based on large amounts of data collected from previous crimes, but it involves more than just maps and push pins. Predictive policing identifies hot spots by using algorithms similar to those used to predict aftershocks after major earthquakes. Just as aftershocks are more likely near a recent earthquake.s epicenter, so too are crimes, as criminals do indeed return to, or very close to, the scene of a crime. Cities employing this approach have seen crime rates drop and studies are underway to measure predictive policing.s part in that drop. One fact that has been determined concerns the nature of hot spots. Researchers using partial differential equations and bifurcation theory have discovered two types of hot spots, which respond quite differently to increased patrols. One type will shift to another area of the city while the other will disappear entirely. Unfortunately the two appear the same on the surface, so mathematicians and others are working to help police find ways to differentiate between the two so as to best allocate their resources.

Forecasting Crime Part 1

Nazareth Bedrossian explains more about math's role in maneuvering spacecraft and why he's a consumer of mathematical results.

Making an Attitude Adjustment: Part 2

Researcher: John A. Adam, Old Dominion University. John A. Adam explains the math and physics behind rainbows.

Explaining Rainbows

Researcher: Andrew Beveridge, Macalester College  Moment Title: Dis-playing the Game of Thrones  Description: Andrew Beveridge uses math to analyze Game of Thrones.

Researcher: Andrew Beveridge, Macalester College Moment Title: Dis-playing the Game of Thrones Description: Andrew Beveridge uses math to analyze Game of Thrones.

Dis-playing the Game of Thrones: Part 1

Forecasting Crime Part 2

Dis-playing the Game of Thrones: Part 2

Researcher: Thomas Snitch, University of Maryland  Description: Thomas Snitch talks about nabbing poachers with math.   Audio files: podcast-mom-poaching-1.mp3 and podcast-mom-poaching-2.mp3

Researcher: Thomas Snitch, University of Maryland Description: Thomas Snitch talks about nabbing poachers with math. Audio files: podcast-mom-poaching-1.mp3 and podcast-mom-poaching-2.mp3

Thwarting Poachers: Part 1

Researcher: Hamsa Balakrishnan, MIT. Hamsa Balakrishnan talks about her work to shorten airport runway queues.

Trimming Taxiing Time

The heart.s function of pumping blood may seem fairly simple but the underlying mechanisms and electrical impulses that maintain a healthy rhythm are extremely complex. Many areas of mathematics, including differential equations, dynamical systems, and topology help model the electrical behavior of cardiac cells, the connections between those cells and the heart.s overall geometry. Researchers aim to gain a better understanding of the normal operation of the heart, as well as learn how to diagnose the onset of abnormalities and correct them.Of the many things that can go wrong with a heart.s rhythm, some measure of unpredictability is (surprisingly) not one of them. A healthy heartbeat is actually quite chaotic not regular at all. Furthermore, beat patterns become less chaotic as people age and heart function diminishes. In fact, one researcher recommends that patients presented with a new medication should ask their doctors, "What is this drug going to do to my fractal dimensionality?"For More Information: Taking Mathematics to Heart: Mathematical Challenges in Cardiac Electrophysiology, John W. Cain, Notices of the AMS, April 2011, pp. 542-549.

The heart.s function of pumping blood may seem fairly simple but the underlying mechanisms and electrical impulses that maintain a healthy rhythm are extremely complex. Many areas of mathematics, including differential equations, dynamical systems, and topology help model the electrical behavior of cardiac cells, the connections between those cells and the heart.s overall geometry. Researchers aim to gain a better understanding of the normal operation of the heart, as well as learn how to diagnose the onset of abnormalities and correct them. Of the many things that can go wrong with a heart.s rhythm, some measure of unpredictability is (surprisingly) not one of them. A healthy heartbeat is actually quite chaotic not regular at all. Furthermore, beat patterns become less chaotic as people age and heart function diminishes. In fact, one researcher recommends that patients presented with a new medication should ask their doctors, "What is this drug going to do to my fractal dimensionality?" For More Information: Taking Mathematics to Heart: Mathematical Challenges in Cardiac Electrophysiology, John W. Cain, Notices of the AMS, April 2011, pp. 542-549.

Keeping the beat - Part 1

The best podcast episodes on non-current politics. Covering topics such as universal basic income, democracy, poverty & justice and more. For anyone interested in learning more about politics that affect that world, not just now, but in the longer term. Add episodes you're interested into your queue below!

Best Non-Current Politics Podcasts

The best podcast episodes of the most interesting stories and things. From skyping someone while they're in space, to tracking down and meeting a telephone scammer in person, to the story of a Galapagos. These episodes will keep you and all your friends entertained and captivated for hours. Learn something new in every episode! Add episodes you're interested into your queue below!