Latest Articles
Networks Hold the Key to a Decades-Old Problem About Waves
Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous and powerful tools. A new result marks an exciting advance toward that goal.
What Are Lie Groups?
By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most powerful tools.
A Simple Way To Measure Knots Has Come Unraveled
Two mathematicians have proved that a straightforward question — how hard is it to untie a knot? — has a complicated answer.
New Physics-Inspired Proof Probes the Borders of Disorder
For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that model semiconductors. A new method could change that.
Epic Effort to Ground Physics in Math Opens Up the Secrets of Time
By mathematically proving how individual molecules create the complex motion of fluids, three mathematicians have illuminated why time can’t flow in reverse.
Graduate Student Solves Classic Problem About the Limits of Addition
A new proof illuminates the hidden patterns that emerge when addition becomes impossible.
New Proof Settles Decades-Old Bet About Connected Networks
According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong.
After 20 Years, Math Couple Solves Major Group Theory Problem
Britta Späth has dedicated her career to proving a single, central conjecture. She’s finally succeeded, alongside her partner, Marc Cabanes.
‘Groups’ Underpin Modern Math. Here’s How They Work.
What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question.