In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere
High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.
New Proof Shows That ‘Expander’ Graphs Synchronize
The proof establishes new conditions that cause connected oscillators to sway in sync.
Surprise Computer Science Proof Stuns Mathematicians
For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.
Coloring by Numbers Reveals Arithmetic Patterns in Fractions
In a recent paper, two mathematicians showed that a particular pattern is unavoidable when fractions are categorized.
Quantum Field Theory Pries Open Mathematical Puzzle
Mathematicians have struggled to understand the moduli space of graphs. A new paper uses tools from physics to peek inside.