Graph theory began as an obscure subfield of mathematics, but it has since turned into an incredibly useful tool for understanding the modern world. It essentially is a streamlined method for dealing with abstract objects and the links between them. This area of study is usually contained within the broader…

Forecasting the weather is a notoriously difficult job! Our atmosphere is a complex system with a lot of moving parts. Models have to work with limited data and make predictions for multiple days in advance. Thanks to multiple advancements made over the last century, forecasting quality has improved greatly. However…

Set theory is often considered to be the foundational field of mathematics. It relies on a few very basic axioms and deals with structures called “sets” and actions involving them. In fact, nearly every area of math relies on set theory somehow for making definitions. Set theory has gone through…

Humans like regularity. Our brains drive us to seek out that which is predictable. If we could have our way, then everything would fall into neat categories. Unfortunately, the universe does not work this way. Nature is chaotic and scattered. Scientists must constantly work with randomness and try to extract…

You’ve almost certainly heard about it on the news: there is an El Niño developing right now. It is already causing all sorts of havoc around our planet like heat waves, flooding, and likely a worse hurricane season in the Atlantic Ocean. El Niño events are complex phenomena that arise…

Possibly the most famous objects in all of mathematics, the Platonic Solids have been inspiring mathematical thought for thousands of years. Much of early mathematics, which focused on geometry, was centered around these objects. Later philosophers and scientists attempted to explain the universe using these five shapes. While we now…

Most of us have probably heard of the Pythagorean Theorem. This simple equation relates the length of sides in a right triangle, commonly taught in high school math. Unfortunately, most of us have not heard of the fascinating history behind the discovery of this theorem. It likely emerged from an…

Mathematicians are always looking for ways to visualize their work. Having a distinct picture of the object they are working with can help them understand the concepts being used, lead to new insights, and aid in communication. One particularly interesting visual is the Young diagram, with many examples shown above…

Abstract algebra is one of the foundational fields of modern mathematics. It contains a wide variety of subfields and has an immense number of applications. More specifically, abstract algebra is the study of algebraic structures, which are all sorts of things like groups, rings, fields, modules, magmas, and many more…