Mathematicians are “reinventing the wheel” by giving it a new shape. Their newly imagined wheel looks like a many-dimensional guitar pick, and it could theoretically roll in ways beyond our ...

One hundred twenty years after it was first discovered, mathematicians have successfully mapped out a 248-dimensional object called E8. The complete description of E8—one of the most complicated ...

It is rare to read about “spectacular progress” or a “once-in-a-century” result in mathematics. That’s for good reason: if a problem has not had a solution for many years, then completely new ...

Normal and spun normal surfaces are key tools for algorithms in 3-dimensional geometry and topology, especially concerning essential surfaces. In a recent paper of Dunfield and Garoufalidis, an ...