Automorphisms such as this are the 'fearless symmetries' of the title of Avner Ash and Robert Gross's book. They can be thought of as symmetries because they are transformations of a mathematical ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...

Imaginary numbers might seem like unicorns and goblins — interesting but irrelevant to reality. But for describing matter at its roots, imaginary numbers turn out to be essential. They seem to be ...