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...

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...

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...

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...

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...

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...

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...

Math is often described as the science of patterns, which makes it a natural subject to help in the study of the underlying causes of patterns found in nature, for example, bands of vegetation that often occur on gently sloped terrains in certain near-desert ecosystems worldwide. We are starting to...

Math's connection with cooking extends beyond the mathematical constant that sounds like a dessert. For example, using differential equations to model fluid flow and heat transfer, research teams have found how spaghetti curls as it's cooked, how to rotate a pan to make the perfect crepe (thin...

Zhihong Chen, Dongsheng Li. Source: Advances in Differential Equations, Volume 26, Number 1/2, 83--106.Abstract: In this paper, we consider a system related to Maxwell's equations, which has different structure with general elliptic systems. The existence of the weak solution is obtained in...